Research ArticleLocation Model for Distribution Centers for Fulfilling ElectronicOrders of Fresh Foods under Uncertain Demand

Hao Zhang1 Ying Xiong1 Mingke He12 and Chongchong Qu1

1Beijing Technology and Business University Beijing 100048 China2Beijing Wuzi University Beijing 101149 China

Correspondence should be addressed to Ying Xiong kytjxy358163com

Received 10 July 2017 Accepted 14 September 2017 Published 19 October 2017

Academic Editor Emiliano Tramontana

Copyright copy 2017 Hao Zhang et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Theproblemof locating distribution centers for delivering fresh food as a part of electronic commerce is a strategic decision problemfor enterprisesThis paper establishes a model for locating distribution centers that considers the uncertainty of customer demandsfor fresh goods in terms of time-sensitiveness and freshness Based on the methodology of robust optimization in dealing withuncertain problems this paper optimizes the location model in discrete demand probabilistic scenarios In this paper an improvedfruit fly optimization algorithm is proposed to solve the distribution center location problem An example is given to show that theproposed model and algorithm are robust and can effectively handle the complications caused by uncertain demand The modelproposed in this paper proves valuable both theoretically and practically in the selection of locations of distribution centers

1 Introduction

In recent years customers have enjoyed the fast delivery offresh goods and foods through the rapid development ofelectronic commerce Currently in China some big compet-itive e-commerce companies such as Amazon Fresh OahuFresh and Motion Optimization are providing e-commerceservices with fast distribution network centers The biggestproblem faced by these companies is the uncertainty ofcustomer demand for fresh goods as the fresh goods areperishable and have a definite shelf life Currently up to 30of all fresh food is lost throughout the supply chain before itreaches the consumers implying huge economic loss issues[1] Having the distribution centers strategically located helpsto keep perishable food fresh by keeping the time of storageand transport between facilities as short as possible [2] Thelocation of distribution centers is of great importance duringthe design of the distribution network center because of theperishable nature of fresh food [3]

The size or the location of distribution centers will affectfreshness delivery speed and distribution cost for each firmCompanies can build or rent distribution centers in a targetedarea by analyzing market demand to improve the locations ofthe distribution network center and to reduce cost Once the

size and location of the distribution center are determined itwill not change for a certain period of time but the customerdemand of fresh goods may change An important issue thatarises while designing a distribution network is coping withthe uncertainty of demand [4] Distribution center locationwill be affected when demand uncertainty is considered asdemand uncertainty forces companies to design a more rea-sonable distribution network and distribution plan to reactquickly to variations and tomeet customersrsquo expectations [5]Therefore it is important to consider the uncertain customerdemand in the selection of commodity distribution centers

The rest of the paper is structured as follows Section 2presents a relevant literature review on models of distribu-tion center locations for perishable products and on robustoptimization models In Section 3 an optimization model isestablished to minimize the total costs of distribution centerlocations for delivering fresh goods themethodology and thesolution algorithm are given to solve the model Section 4addresses experimental results Finally Section 5 is devotedto the conclusions and the clarification of our work

2 Related Literature ReviewMany scholars have conducted in-depth studies on thelocation of distribution centers for perishable products and

HindawiScientific ProgrammingVolume 2017 Article ID 3423562 13 pageshttpsdoiorg10115520173423562

2 Scientific Programming

proposed various models and algorithms for optimizing siteselection

Hiassat et al [6] considered the characteristics of per-ishable products An optimization model was proposed toadd a decision regarding the location of the distributioncenter to the inventory path problem A genetic algorithmand a local search heuristic method were used to solve theproblem Govindan et al [7] established a model of distri-bution center location and path optimization that mainlyconsiders the high quality of perishable food The model wassolved with the multiobjective particle swarm optimizationadaptive multiobjective variable neighborhood search hybridmethod Drezner and Scott [8] considered the location of adistribution center for a single perishable productThemodelwas established based on the inventory and position decisionThe Weiszfeld algorithm was used to solve for the minimumtotal cost Seyedhosseini and Ghoreyshi [9] formulated anew integrated production and distribution planning modelfor perishable products LINGO software was used to solvethe production model and a particle swarm heuristic wasdeveloped to tackle the distribution model de Keizer etal [10] developed a network design model for perishableproducts that integrates decision-making on hub locationswith the positioning of the customer order decoupling pointtaking into account decay in product quality and the het-erogeneity of product quality to allow for a comprehensivedifferentiation of product flows in network design Orjuela-Castro et al [3] present a model for locating facilities ofmountain ranges considering the factors of temperature andrelative humidity on the perishability of fresh food

Yang et al [11] studied the dairy distribution centerlocation model based on two levels of distribution andconsidered the cost of corruption of fresh products Hesolved the model using a genetic algorithm Zhang and Shao-chuan [12] studied amodel of locating fresh food distributioncenters used the addition method to solve the problemand then used field search to replace the improved initialsolution Wu et al [13] proposed a multiperiod locationmodel with transportation economies of scale that distributesa single perishable product and formulated the problem asa mixed integer nonlinear programming model Musavi andBozorgi-Amiri [14] present a novel sustainable hub location-vehicle scheduling model considering responsiveness andenvironmental impacts and propose an adopted nondomi-nated sorting genetic algorithm-II (NSGA-II) metaheuristicapproach to solve problems Rezaei-Malek et al [15] proposeamultiobjectivemodel to design a disaster relief logistics hublocation considering the lifetime of perishable products byadjusting certain time windows and consider the inherentuncertainty of input data Khalili-Damghani et al [16] pro-pose a biobjectivemodel to reduce the total cost of a companyand consider the location of warehouses and the routing ofvehicles for the distribution of perishable products

From the literature review we can see that many scholarsare studying models of fresh perishable product distributionwhile assuming deterministic demand However there existssignificant uncertainty regarding demand as the industrytransitions from the current delivery mode of fresh products

from a mono type and large batch distribution to a multi-type delivery mode and small batch distribution Thereforecompanies should consider the effect of uncertainty in theestablishment of distribution centers

The main method of optimization under uncertainty isrobust optimization Robust optimization assumes that theuncertain parameters belong to a bounded and closed set andobtains a worst-case scenario to help decision makers reducerisk Zhang et al [17] proposed a robust mixed integer linearmodel with multiple objectives (economic environmentaland social objectives) under supply and demand uncertaintyQiu and Wang [18] developed a robust optimization modelfor designing a three-echelon supply chain network thatconsists of manufacturers distribution centers and retailersunder both demand uncertainty and supply disruptions Ben-Tal et al [19 20] developed a robust optimization methodand proposed an optimization framework of comprehensiverobust equivalence The robust optimization method wasapplied to a problem of uncertain and bounded demandGhodratnama et al [21] studied the multiobjective hublocation-distribution problem from a supply chain angleThemodel is optimized by robust and fuzzy target programmingHabibzadeh Boukani et al [22] considered the use of robustoptimization methods to handle problems of locating mul-tiple allocation centers under uncertain parameters It wasfound that ignoring uncertainty in the supply chain networkdesign could result in significant losses and costs

Jakubovskis [23] presents a robust optimizationmodelingapproach to make strategic capacity planning and resourceacquisition decisions The author examines the effects ofeconomies of scale economies of scope and the combinedeffects of scale and scope under uncertain demand realiza-tions Eiselt andMarianov [24] studiedWTE facility locationplanning problems under uncertainty from a governmentperspective in a cost-effective and environmental-friendlyway Bardossy and Raghavan [25] presented a robust opti-mization model for the connected facility location problemwithin the framework and extend the BS robust optimiza-tion approach using heuristics in conjunction with a lowerbounding procedure for the subproblems de Rosa et al [26]presented the robust capacitated facility location problem tocope with uncertainty by dynamically assigning multilevelproduction allocations locations and capacity adjustmentsfor uncertain parameter development over time Ehrgott etal [27] argue that robust optimization can be applied toproblems where a solution is required that hedges againstall possible scenarios with realizations from the uncertaininput data Due to operational environment changes andinformation uncertainty in network designs Xu et al [28]present a general two-stage quantitative framework to helpdecision makers to select the optimal network design schemefor collaborative logistics networks under uncertainty thenadd the robust constraints into the expected value modeland make the model more robustness Majewski et al [29]propose a minndashmax robust multiobjective problem formula-tion to determine a robust sustainable design to cope withuncertainties and the formulation allows the identification ofrobust sustainable designs easily guaranteeing the security ofthe energy supply

Scientific Programming 3

The above literature shows that robust optimization is aneffective way to address uncertain problems These studieshave laid the foundation for the subsequent optimization ofrobust research

In this paper we will consider factors such as uncertaindemand the shelf life of a variety of perishable productsthe timeliness and freshness of those products and theestablishment of a locationmodel for distribution centers thatsatisfies the customer demand for fast delivery of productsRobust optimization can also improve the ability of anti-interference in the model of locating distribution centers toaddress the problem of uncertainty An improved fruit flyalgorithm is used to solve the robust optimization

3 Model Building and Solution Method

31 Problem Description In the practice of fresh goods e-commerce the uncertainty of customer demand for freshproducts and the requirement of customer satisfaction forfresh commodities distribution often exist simultaneouslyBoth factors must be considered at the same time Thedistribution network of an enterprise is often composed ofmultiple distribution centers and this paper will establish alocation model for multiple distribution centers The goalof the location model is to meet the requirements of thecustomers when distributing the goods from the distributioncenter to the customers andmaintain the lowest cost possible

32 Assumptions Many scholars have presented mathemati-cal models and it is crucial to consider all of the assumptionsin this paper In our research it is assumed that fresh goodse-commerce enterprises will set up a number of discretedistribution centers within a certain period of time and acertain area Goods are purchased from a plurality of freshcommodity suppliers and are stored in different distributioncenter locations When an order is received from customersthe nearest distribution center is selected to deliver productsto customers We assume that the quantity and satisfactionrequirements of the fresh commodity consumer (demandpoint) are predetermined but the specific demand for eachorder of the consumer is uncertainThat is each order can beordered withmultiple fresh varietiesThe goal of the distribu-tion center location model is to meet the requirements of thecustomers when distributing the goods from the distributioncenter to the customers andmaintain the lowest cost possibleThe logic diagram is as shown in Figure 1

In addition to the general assumptions described abovethis paper also considers the following specific assumptionsthat the fresh goods e-commerce enterprises operate in aspecific period of time

(1) Fresh goods e-commerce enterprises prefer to rent thedistribution centers from the existing candidate dis-tribution centers and avoid the choice of constructingthem The benefit of selecting from existing distribu-tion centers is that the fixed costs and operating costsare lower than when constructing a new center

Supplier 1

Supplier 2

Supplier q

Distributioncenter 1

Distributioncenter m

Customer 1

Customer 2

Customer n

Figure 1 Logic diagram of locating distribution centers

(2) Customer demand is uncertain and any candidatedistribution center can fully satisfy the demand of aparticular customer

(3) The supply capacity of fresh commodity suppliers canmeet the largest needs of the demand

(4) In the total cost calculation firms do not consider thefresh goods inventory costs loading and unloadinglosses vehicle maintenance costs equipment mainte-nance costs and staff bonus

(5) Unit delivery cost is known and constant(6) The spoilage rate of fresh foods in the distribution

process is constant(7) Fresh goods remain fresh when leaving the distribu-

tion center(8) Freshness of fresh produce can be perceived at all

times during distribution(9) Delivery times may fluctuate but drivers are penal-

ized according to the degree of deviation from theservice standard

(10) This model is appropriate only for a certain periodof time and static location assumptions regardless offuture costs and earnings changes

33 Notation The following notation is used to formulate theproblem considered in this paper Parameters are as follows

119867 Set of suppliers119867 = ℎ | ℎ = 1 2 119902119868 Set of distribution centers 119868 = 119894 | 119894 = 1 2 119898119869 Set of customers 119869 = 119895 | 119895 = 1 2 119899119870 Set of fresh food types119880ℎ Maximum supply capacity of supplier ℎ to theenterprise119873119894 Maximum inventory capacity of distribution cen-ter 119894120579119896 Corruption rate coefficient of fresh food 119896 con-stant119897ℎ119894 Distance between supplier ℎ and distributioncenter 119894

4 Scientific Programming

119897119894119895 Distance between distribution center 119894 and cus-tomer 119895V Average speed of vehicle

119862ℎ119894 Transportation cost per unit from supplier ℎ todistribution center 119894119862119894119895 Transportation cost per unit from distributioncenter 119894 to customer 119895119860 119894 Fixed cost of distribution center 119894119861119894 Operating cost of distribution center 119894119891119894119895 Penalty costs of vehicle arriving late to customer 119895119908 The largest number of new distribution centersavailable to rent

119903119896 The average selling price of the variety 119896 of freshgoods

119905119894119895 Time of vehicle from distribution center 119894 tocustomer 119895119879119895 The serve time that customer 119895 requires from thedelivery center

119879119895maxThe shortest waiting time that customer 119895 is notdissatisfied

119879119895min The longest waiting time that customer 119895 isdissatisfied

120572119895119896 The freshness satisfaction threshold for customer119895 of variety 119896 of fresh goods

120573119895 The time satisfaction threshold for customer 119895Decision Variables

119889ℎ119894 The transport quantity of goods from supplier ℎto distribution center 119894119889119894119895 The transport quantity of goods from distributioncenter 119894 to customer 119895119889119895 The demand of customer 119895119910119894 Binary variable that takes the value 1 if distributioncenter 119894 is selected119911ℎ119894 Binary variable that takes the value 1 if distribu-tion center 119894 is supplied by supplier ℎ119911119894119895 Binary variable that takes the value 1 if customer 119895is supplied by distribution center 119894119911119895119896 Binary variable that takes the value 1 if fresh food119896 is supplied to customer 119895

34 Distribution Center Location Mathematical Model Thispaper constructs the locationmodel of the distribution centerunder the condition of determinate customer demand thenintroduces the demand uncertainty function and optimizesthe model using the robust optimization method

341 Location Mathematical Model under DeterminateDemand The total cost of the distribution center model isthe minimum total cost which is composed of fixed costsoperating expenses transportation costs delayed penaltycosts and fresh goods corruption costs for distribution cen-tersThe consumer satisfactionmodel includes themaximumfreshness of fresh goods and the maximum accuracy of thedistribution center service time

(1) Fixed costs and operating expenses (1205751)1205751 = sum119894isin119868

119860 119894119910119894 +sum119894isin119868

119861119894119910119894 (1)

(2) Transportation costs (1205752)1205752 = sumℎisin119867

sum119894isin119868

119862ℎ119894119897ℎ119894119889ℎ119894 +sum119894isin119868

sum119895isin119869

119862119894119895119897119894119895119889119894119895 (2)

(3) Delayed penalty costs (1205753)

1205753 = 119891119894119895 (119905119894119895 minus 119879119895)0

119905119894119895 ge 119879119895119905119894119895 lt 119879119895 (3)

(4) Fresh goods corruption costs (1205754)Fresh goods corruption costs can be expressed in terms

of freshness Consumers care about the freshness of productsas visual indicators of their quality Product transport timeand mileage have a large impact on the freshness of certainperishable products Therefore this paper which is based onthe freshness model established by Zhang and Shao-chuan[12] takes the transportation time and the transport distanceas the variables into account We form a new freshnessformula

120601119895119896 = (1 minus 120579119896)sumℎisin119867sum119894isin119868 sum119895isin119869[1205821(119897ℎ119894V+119905119894119895)+1205822(119897ℎ119894+119897119894119895)]119911119894119895 (4)

where the transit time weight is 1205821 the transport distanceweight is 1205822 and the weight is determined according to thespecific transportation distance and the transportation timeFor the convenience of follow-up study in this article 1205821 =1205822 = 05

Fresh goods corruption costs

1205754 = sum119896isin119870

119903119896 (1 minus 120601119895119896) (5)

(5) The freshness of fresh goods (120591119895119896)120591119895119896 = sum119895isin119869sum119896isin119870 119911119895119896120601119895119896sum119895isin119869sum119896isin119870 119911119895119896 (6)

(6) The distribution center service time (120583119895)

120583119895 = sum119894isin119868sum119895isin119869 119911119894119895120596 (119905119894119895)sum119894isin119868sum119895isin119869 119911119894119895 (7)

Scientific Programming 5

120596(119905119894119895) is the consumer satisfaction time function Weuse the satisfaction formula introduced to the literature inYunfeng et al [30]

120596 (119905119894119895) =

1 119905119894119895 le 119879119895min

( 119879119895max minus 119905119894119895119879119895max minus 119879119895min

)120574

119879119895min lt 119905119894119895 le 119879119895max

0 119905119894119895 ge 119879119895max(8)

In summary the models of e-commerce distribution centerlocations are as follows

min 120575 = 1205751 + 1205752 + 1205753 + 1205754 (9)

max 120591119895119896 (10)

max 120583119895 (11)

st sum119894isin119868

119889ℎ119894 le 119880ℎforallℎ isin 119867

(12)

sumℎisin119867

119889ℎ119894 le 119873119894119910119894sum119895isin119869

119889119894119895 le 119873119894119910119894forall119894 isin 119868

(13)

sum119894isin119868

119910119894 le 119908 (14)

sum119894isin119868

119911119894119895 = 1forall119895 isin 119869

(15)

sum119894isin119868

119889119894119895 ge 119889119895forall119895 isin 119869

(16)

119911119894119895 le 119910119894119911ℎ119894 le 119910119894forall119894 isin 119868 forall119895 isin 119869

(17)

119889ℎ119894 ge 0119889119894119895 ge 0 (18)

119910119894 119911ℎ119894 119911119894119895 isin 0 1forall119894 isin 119868 forall119895 isin 119869 (19)

The objective function (9) indicates that the total cost isto be minimized The objective function (10) indicates themaximum freshness of fresh goods The objective function(11) indicates the maximum accuracy of the distributioncenter service time

Constraint (12) is the supply constraint of the supplier Itensures that the total amount of products transported from

supplier ℎ does not exceed the maximum supply capacityConstraints (13) are the distribution center 119894 inventory con-straints and they enforce that the storage of the total freshproduct does not exceed the maximum inventory capacityConstraint (14) represents the number of new distributioncenter constraints Constraint (15) ensures that each customerhas only one candidate distribution center to deliver to himor her Constraint (16) indicates that the volume of freshfoods delivered to the customer cannot be less than thecustomer demand due to possible cargo damage Constraint(17) ensures that the selected distribution center can providedelivery Equations (18) and (19) are constrained by decisionvariables

In the calculation the multiobjective function is trans-formed into a single objective function by the main objectivemethod to select themain objective function according to theenterprisersquos strategic plan If the business goal is to minimizethe total cost and the freshness and the distribution centerservice time only need to achieve a consumer satisfactionthreshold then consumer satisfaction does not have to bemaximized but consumer satisfaction is transformed intoa constraint In this paper the main objective function ischosen to be the minimum total cost and the satisfaction ofthe consumer is set as a constraint

120591119895119896 ge 120572119895119896120583119895 ge 120573119895 (20)

Constraint (20) requires that the freshness of the productmust reach the customer satisfaction threshold and thesatisfaction degree of the distribution center service timemust meet the customer satisfaction threshold for time

In the abovementioned distribution center locationmodel it is assumed that the demand 119889119895 is known and thetotal cost of the decision method can be obtained from theobjective function (9) However in real life there is a greatdeal of uncertainty in the demand for fresh goods so we needto use a robust optimizationmethod to optimize the selectionof locations for distribution centers

342 LocationMathematicalModel underUncertainDemandThe abovementioned distribution center location model isconverted into an equivalent auxiliary model by using robustoptimization The uncertainty of demand is at the coreof obtaining the equivalent auxiliary model This paperuses a series of discrete scenarios to describe the possiblerequirements of the customer

The specific demand of each location is unknown and isconsidered to vary in a closed and bounded box This is acommon description of the uncertainty method

Assuming that the demand scenario is 119904 where 119904 =1 2 119878 is the probability that the demand scenario 119904 ofcustomer 119895 satisfies the ellipsoid uncertainty set The generalform of the box can be specified as follows

119901119895119904 isin Ω = 1199010119895119904 + 119876119906 119890119879119876119906 = 01199010119895119904 + 119876119906 ge 0 119906 le 1 (21)

6 Scientific Programming

where 1199010119895119904 is the most probable probability distribution ofdemand points 119876 isin 119877119899119898times119899119898 is the scope of the zoom119906 denotes the Euclidean norm for perturbation 119890119879119876119906 =0 1199010119895119904 + 119876119906 ge 0 is to ensure that the demand scenarioprobability 119901119895119904 is a probability distribution

Assuming that the demand of each customer is indepen-dent of each other and does not interfere with each otherand the total cost of the site under the demand scenario119904 of customer 119895 is 120575119895119904 the cost of a distribution center isdetermined as follows

120575119894119895 = sum119904isin119878

120575119894119895119904119901119895119904 (22)

The total expected cost for all distribution centers isdetermined as follows

119864 (120575119894) = sum119895isin119869

120575119894119895 = sum119895isin119869

sum119904isin119878

120575119894119895119904119901119895119904 = sum119895isin119869

119901119879119895 120575119895

120575119895 = (1205751198951 1205751198952 120575119895119904)119879 119901119895 = (1199011198951 1199011198952 119901119895119904)119879

(23)

The total cost of the distribution center is transformed

min 119864 (120575) = minsum119895isin119869

119901119879119895 120575119895 (24)

The robust correspondence model of (19) is expressed as

min max119901119895119904isinΩ

119864 (120575) = minmax119901119895119904isinΩ

sum119895isin119869

119901119879119895 120575119895 (25)

The above model is equivalent to

min 120603 (26)

st max119901119895119904isinΩ

sum119895isin119869

119901119879119895 120575119895 le 120603 (27)

119901119895119904 satisfies the demand uncertain set (21) then the leftside of formula (27) is

max119901119895119904isinΩ

sum119895isin119869

119901119879119895 120575119895 = max119901119895119904isinΩ

sum119895isin119869

[(1199010119895119904)119879 120575119895 + (119876119906)119879 120575119895]

= sum119895isin119869

(1199010119895119904)119879 120575119895 + max119901119895119904isinΩ

(119876119906)119879 120575119895(28)

Because 119906 le 1max119901119895119904isinΩ

(119876119906)119879 120575119895 = max119901119895119904isinΩ

119876119879120575119895 (29)

Equation (27) is converted to

sum119895isin119869

(1199010119895119904)119879 120575119895 + max119901119895119904isinΩ

119876119879120575119895 le 120603 (30)

In summary the optimization objective of the robustoptimizationmodel ismin120603 and composed of the constraints(30) and (12) to (20)Themodel has good robustness throughthe robust optimization of the model which can meet theuncertain demand of the customer and ensure the economicfeasibility of the location selection scheme

35 Improved Fruit FlyOptimizationAlgorithm (IFOA) Afterthe above two-step modeling this paper establishes a modelof the distribution center of fresh goods e-commerce underuncertain demand The next important problem is the solu-tion of themodelThe location problem in the uncertain situ-ation is anNP-hard problemThe traditional solutionmethodis complicated and the required amount of is prohibitive forfinding a solution Therefore a heuristic algorithm is used tosolve the problem

FOA is suitable for solving the optimization problemwith complex constraints and strong correlation betweenthe constituent elements of the solution [31] It is widelyused in many classical optimization fields such as efficienttruss optimization [32] gasification process operation opti-mization [33] and analysis of service satisfaction [34] TheFOA algorithm is easy to combine with other methods hasstrong robustness and is suitable for robustly optimizing thelocation of distribution centers Therefore FOA is used tosolve the problem in this paper

351 Fruit Fly Optimization Algorithm (FOA) FOA is out-lined as follows

Step 1 Initialize parameters including the maximumnumber of evaluations (maxgen) and the size of fruitflies (sizepop) and initialize the position of the flies(119883 axis 119884 axis)

Step 2 Randomly initialize the flight direction and distanceof the individual flies where Random Value is the distance inthe search

119883119894 = 119883 axis + Random Value119884119894 = 119884 axis + Random Value (31)

Step 3 The distance of each fly from the origin point and thesmell concentration judgment value is defined as follows

Dist119894 = radic1199091198942 + 1199101198942119878119894 = 1

Dist119894 (32)

Step 4 Based on 119878119894 the smell concentration of flies denotedby Smell119894 is calculated as follows

Smell119894 = function (119878119894) (33)

Step 5 Find the fruit flies with the best smell concentrationand allow the flies to fly to the optimal position

[bestSmell bestindex] = min (Smell119894)Smellbest = bestSmell

119909 axis = 119883 (bestindex)119910 axis = 119884 (bestindex)

(34)

Step 6 Stop the search if the maximum evaluation number isreached otherwise repeat Steps 2ndash5

Scientific Programming 7

Table 1 Test function

Test function Range Optimal Peak

min 1198911 = minusexp(minus05 sdot119899sum119894=1

1199091198942) [minus1 1] minus1 Single

min 1198912 =sin2 (radicsum119899119894=1 1199091198942) minus 05(1 + 0001 (sum119899119894=1 1199091198942))2 + 05 [minus100 100] 0 Multiple

Table 2 Mean and standard deviation of function test

Function Result FOA IFOA

1198911(119909) Mean 30546 times 10minus6 minus1Std 75382 times 10minus6 0

1198912(119909) Mean 31266 times 10minus6 467 times 10minus4Std 86307 times 10minus8 2328 times 10minus3

FOA has great ability to achieve global optimization andhigh convergence accuracy and has great research value in thefield of engineering However the original FOA uses a fixedsearch step and cannot take both global search capabilitiesand local search capabilities into account thus affecting theconvergence rate and search ability Additionally it is easyfor FOA to focus on a local optimum leading to prematureconvergence This paper focuses on the shortcomings of thealgorithm and improves FOAThe purpose of improving theFOA is to make it solve the location model better

352 Improved Fruit Fly Optimization Algorithm (IFOA)In this paper an improved fruit fly optimization algorithm(IFOA) is proposed The search step size is dynamicallyadjusted by introducing the weighting functionThe purposeof dynamic adjustment is to divide the search into two partsThe first part contains a large search step in a large area for aglobal search to ensure that the algorithmconsiders the globaloptimum The second part contains a smaller step search toensure local search capabilities

The fruit fly individual random search expression is asfollows

119883119894 = 119883 axis + 120595 sdot rand ( ) 119884119894 = 119884 axis + 120595 sdot rand ( ) (35)

where 120595 represents the weighted function

120595 = exp(minus 10038161003816100381610038161003816100381610038161003816Smell119894 minus Smell119894minus1

Smell119894

10038161003816100381610038161003816100381610038161003816120577) (36)

where Smell119894 is the 119894th optimal fitness value When the ratiochange is large it indicates that the fly group is searching fora new space and that the weighting function is conducive toa global search When the ratio change is small the fruit flygroup has shifted to a local search and the weight functionis reduced 120577 gt 0 and as 120577 increases fruit fly search abilityincreases which prevents the algorithms from concentratingon a local optimum It can be adjusted according to the actualproblem In addition to the random search expression theother IFOA algorithm step expression is consistent with FOA

353 Test Function To test and analyze the performanceof the improved algorithm the following two classic testfunctions were used to test FOA and IFOA respectivelyFunction form range theoretical extremes and peak areshown in Table 1

The specific initialization parameter is set to sizepop =20 maxgen = 100 We randomly initialize the fliesrsquo popula-tion position The results of the functional tests are shown inTable 2 and the optimization process is shown in Figure 2

From the test results in Table 2 and optimization processIFOA has stronger capabilities of global search local searchand higher convergence accuracy than FOA Under the sameconditions IFOA results are superior to FOA in termsof both mean and standard deviation Under the sameconvergence accuracy the number of valid iterations of IFOAis less than that of FOA which indicates that IFOA convergesfaster Therefore IFOA effectively improves the convergenceprecision and convergence speed of FOA

36 The Calculation Process of Model

(1) Collect the relevant data needed to establish thedistribution center model (as shown in Section 33)

(2) Convert the distribution center model under uncer-tain demand to a tractable equivalent model by usingrobust optimization

(3) IFOA is used to solve the mathematical model

(1) Set the initial parameters including the maxi-mum number of evaluations (maxgen) and thesize of the fruit flies (sizepop) and the initialposition of the flies (119883 axis 119884 axis)

(2) Randomly setting the flight direction and dis-tance of the individual flies the fruit fly individ-ual random search expression is as follows

119883119894 = 119883 axis + 120595 sdot rand () 119884119894 = 119884 axis + 120595 sdot rand () (37)

(3) According to the fitness function formula theindividual fruit fly is calculated to find the

8 Scientific Programming

Table 3 Distance between supplier ℎ and distribution center 119894 (km)

1198681 1198682 1198683 1198684 1198685 1198686 1198687 11986881198671 1431 2912 19945 12093 7738 8814 3214 79831198672 7382 9424 11886 4712 4500 1204 6527 109651198673 13223 11025 10594 3544 9126 6395 7580 6324

0 10 20 30 40 50 60 70 80 90 100minus1

minus0998

minus0996

minus0994

minus0992

minus099

minus0988

minus0986

minus0984

Iteration number

Smel

l

IFOAFOA

0

0002

0004

0006

0008

001

0012

0014

Smel

l

f1(x)

0 10 20 30 40 50 60 70 80 90 100Iteration number

IFOAFOA

f2(x)

Figure 2 Optimization process of FOA and IFOA

position and optimal value of the individual andthe global optimal individual

(4) Find the fruit flies with the best smell concen-tration and allow the flies to fly to the optimalposition

(5) Stop the search if the maximum evaluationnumber is reached otherwise repeat

(6) According to the IFOA optimal location resultsthen find the corresponding best location of thedistribution center and the optimal distributionpath

4 Computational Results

Experiments are proposed in this part to prove the effective-ness and feasibility of the location model Both deterministicand uncertain demand scenarios are considered and then acomparison and analysis of the results of the two situationsis providedThe numerical calculation problem is consideredto occur in a developed city where a fresh goods e-commercefirm chooses to rent a certain number of distribution centerswithin an appropriate area The area of suppliers is 3 and thearea of customers is 10 The firm chooses to rent 3 locationsfrom a set of 8 candidate distribution centers

The distance between the supplier and the candidatedistribution center and the distance between the candidatedistribution center and the demand point are obtained by

using the Euclidean theorem The details are shown inTables 3 and 4 The tables consider the different qualitiesof each candidate distribution center such as the locationtransportation economy and other conditions Fixed costsoperating costs and the largest inventory are also different asshown in Table 5 The maximum supply capacity of supplierℎ is shown in Table 6

The average traveling speed is 45 kmh for the distributionvehicles in the region the average unit freight from thesupplier to the distribution center is 15 yuan(tsdotkm) and thefreight rate from the distribution center to the demand pointis 18 yuan(tsdotkm) To simplify the follow-up calculation thenumerical calculations only consider the distribution of twofresh goods using the corruption coefficients of 015 and008 and the unit prices of 4 yuankg and 6 yuankg Theaverage satisfaction threshold for customer satisfaction is075 and the average satisfaction threshold for freshness is07 If the delivery vehicle arrives late the compensation feeis 50 yuan(hsdott) The demand point time window is shown inTable 7

We consider cases where demand is both deterministicand uncertain The calculation and comparative analysisof two cases can be conducted more directly to verifywhether the model can help the fresh goods e-commerceto suppress the uncertainty interference by demand Themethod used to predict the consumer demand is the multi-variate autoregressive integrated moving average (AMIMA)model in this paper Fresh e-commerce is characterized

Scientific Programming 9

Table 4 Distance between distribution center 119894 and customer 119895 (km)

1198681 1198682 1198683 1198684 1198685 1198686 1198687 11986881198691 14200 4134 24550 16717 8919 11733 7560 144361198692 5420 9642 20535 14220 5903 8628 10072 180711198693 11610 1170 19564 11682 5178 7156 2469 102011198694 6525 18398 13761 12419 12180 11123 16497 214241198695 4827 7716 17279 10536 2282 4850 7000 145791198696 9904 15932 6296 4810 10720 7694 12857 146731198697 22649 13509 20341 14670 16589 15631 12035 48871198698 10718 3383 17310 9420 4161 5215 721 89051198699 12879 19474 3981 7506 14322 11287 16319 1711411986910 15277 14586 7910 3984 12248 9166 11140 8238

Table 5 Fixed costs operating costs and maximum inventory

Candidate distribution centers 1198681 1198682 1198683 1198684 1198685 1198686 1198687 1198688Fixed costs (million) 145 138 123 148 129 123 138 136Operating costs (million) 007 006 006 009 005 006 007 006Maximum inventoryt 1000 900 700 1100 1000 900 1200 800

Table 6 The maximum supply capacity of supplier

Supplier 1198671 1198672 1198673Themaximum supply capacityt 8800 7900 6300

Table 7 Time window and determined demand of customer

Customer (119879119895min 119879119895 119879119895max) Demand (t)1198691 (2 25 3) 2001198692 (3 4 5) 4001198693 (1 15 2) 3501198694 (1 2 25) 2501198695 (2 3 4) 1501198696 (3 35 4) 3501198697 (15 25 3) 3001198698 (2 3 45) 1801198699 (15 25 3) 35011986910 (3 4 5) 300

by consumers ordering through the Internet so fresh e-commerce companies can collect customer information andorder information (eg customersrsquo purchasing frequencypurchasing preferences and position distribution) Thenthe fresh e-commerce company can use this informationto classify consumers and predict consumer demand Theautoregressive part of the multiple ARIMAmodel representsa linear combination of past values while themoving averagepart of the multiple ARIMAmodel is a linear combination ofpast forecasting errorsThe advantage of themultiple ARIMAmodel is that it improves prediction accuracy facilitatesstatistics and reduces the cost of prediction Moreover it cancombine product cost changes with demand uncertainty topredict consumer demand [35] In view of this the multi-variate ARIMA model is suitable to predict the consumerdemand for fresh e-commerce Although the AMIMAmodel

can more accurately predict the uncertainty of demand thesize of fresh e-commercersquos consumers is small and widelydistributed so there is still uncertainty in demand To learnmore about the multivariate ARIMA model studies [35 36]are suggested The deterministic demand for each customeris shown in Table 7

The affected factors of uncertain supply involve envi-ronmental factors (eg the natural environment economicenvironment and political environment) and the abilities ofsuppliers (eg production capacity equipment capacity) [37]First the planting period for fresh foods is the quarter or yearas a unit the period is longer than for other products Fresh e-commerce can be investigated in advance through the Inter-net and then the product cultivation of the fresh food and thefield investigation can be planned accordingly Second thesuppliers of fresh electricity providers are typically farmersand fresh food bases around the region These suppliersare less affected by global economic changes and politicalchanges The selection diversity of suppliers also allows freshe-commerce companies to evaluate and select suppliers inadvance In addition the equipment failure problem has lessof an effect on fresh e-commerce because fresh productscan be delivered to the distribution center though simplepretreatment packaging In summary the supply of fresh e-commerce is uncertain but fresh e-commerce companies areless affected by these uncertain factors due to the specialnature of fresh foods The current delivery mode of freshproducts is from a mono type and large batch distributionto a multitype delivery mode and small batch distributionEach time an order is made the consumer evaluates thefresh electricity service (eg Amazon Fresh and MotionOptimization) For the majority of instances the perishablenature of a product results in the supply process having alower variability than the demand process [38] Thereforethis paper focuses on the location model for distributioncenters under uncertain demand

10 Scientific Programming

0 009 014027033

071093

119

165 175191

0

0005

001

0015

002

0025

0 01 02 03 04 05 06 07 08 09 1

The i

ncre

ase r

atio

The value of a

Figure 3 The increase ratio of the total cost of uncertain demand

For the case of uncertainty we assume that the demandfor each demand point is 119904 = 5 The number of scenariosfor each demand point can be different from each other Thevalue of the demand scenario is determined by the surveyand then the five cases are generated randomly by Matlab 83as the demand scenario of the demand point 119895 The demandscenario of the 10 demandpoints can be obtained by repeatingthe process ten times

The discrete demand probability distribution is 1199010119895119904 119869 =119895 | 119895 = 1 2 119899For 1199010119895119904 in the range (0 1) the simulations are randomly

generated between the 10 numbers normalized and repeatedten times in order to get all the demand points in theuncertain demand scenarioTheprobability demand scenarioof customer 119895 (119901119895119904) meets the uncertainty set Let thedecentralized matrix be 119876 = 119886119868 where 119886 is a nonnegativeparameter and 119868 is an identity matrix

In the experiment let 119886 = 05 and 119886 = 08 respectivelyCalculate 119901119895119904

The specific initialization parameter is set to maxgen =100 sizepop = 20 The program is implemented in Matlab83 and run on a computer with 26GHz Intel i5-4210MCPU 4GB of RAM andWindows 10The distribution centerdecision-making program and the total cost are shown inTable 8

For the deterministic demand situation the optimal deci-sion is to choose distribution center 119868211986851198686 from the candidatelist The total cost is 7208 million For the uncertain demandsituation when 119886 = 01 to 119886 = 04 the optimal decision isto choose distribution centers 119868211986851198686 The distribution rangeis constant but the cost increases When 119886 = 05 to 119886 = 07the optimal decision is to choose distribution centers 119868211986851198686but the distribution range is different from the deterministicdemand situation When 119886 = 08 to 119886 = 1 the optimaldecision is to choose distribution centers 119868511986861198687 The increaseratio of the total cost in the case of uncertainty is comparedto the total cost in the demand determination as shownin Figure 3 Enterprises in the decision-making before theconsumer demand should be the historical data for statisticaland analysis determine the variation range of parameter119886 and make decisions based on cost and self-conditions(Figure 3)

Then using FOA to solve themodel and initial parametersand operating environment equally with IFOA the results are

Table 8 The decision-making program and the total cost ofdistribution center

The value of 119886 Decision-makingprogram and

distribution rangeCost (RMB)

119886 = 0 1198682 1198691 1198693 11986977208563141198685 1198692 1198695 11986981198686 1198694 1198696 1198699 11986910

119886 = 01 1198682 1198691 1198693 11986977215050851198685 1198692 1198695 11986981198686 1198694 1198696 1198699 11986910

119886 = 02 1198682 1198691 1198693 11986977218655131198685 1198692 1198695 11986981198686 1198694 1198696 1198699 11986910

119886 = 03 1198682 1198691 1198693 11986977228026261198685 1198692 1198695 11986981198686 1198694 1198696 1198699 11986910

119886 = 04 1198682 1198691 1198693 11986977232351401198685 1198692 1198695 11986981198686 1198694 1198696 1198699 11986910

119886 = 05 1198682 1198691 1198693 11986977259452741198685 1198692 1198694 1198695 11986981198686 1198696 1198699 11986910

119886 = 06 1198682 1198691 1198693 11986977275602781198685 1198692 1198694 1198695 11986981198686 1198696 1198699 11986910

119886 = 07 1198682 1198691 1198693 11986977294345041198685 1198692 1198694 1198695 11986981198686 1198696 1198699 11986910

119886 = 08 1198685 1198692 11986957327583631198686 1198694 1198696 1198699 119869101198687 1198691 1198693 1198697 1198698

119886 = 09 1198685 1198692 11986957334712991198686 1198694 1198696 1198699 119869101198687 1198691 1198693 1198697 1198698

119886 = 1 1198685 1198692 11986957346246701198686 1198694 1198696 1198699 119869101198687 1198691 1198693 1198697 1198698

shown in Table 9 the difference value of IFOA and FOA isshown in Figure 4 and the optimization process of FOA andIFOA is shown in Figure 5 (select 119886 = 05)

From the test results in Table 9 and Figures 4 and 5under the same conditions IFOA results are superior to FOAthe convergence accuracy is more accurate and the optimalresults are better Under the same convergence accuracythe number of valid iterations of IFOA is less than that ofFOA which indicates that IFOA converges faster ThereforeIFOA effectively improves the convergence precision andconvergence speed of FOAThe applicability of IFOA is moreextensive

Scientific Programming 11

Table 9 The results of FOA and IFOA

The value of 119886 IFOA optimal FOA optimal119886 = 0 720856314 720874332119886 = 01 721505085 721515326119886 = 02 721865513 721881176119886 = 03 722802626 72285562119886 = 04 723235140 723309877119886 = 05 725945274 726005691119886 = 06 727560278 727613354119886 = 07 729434504 729495412119886 = 08 732758363 732827122119886 = 09 733471299 733549837119886 = 1 734624670 734714368

18018 10241 15663

52994

7473760417

5307660908

6875978538

89698

000100002000030000400005000060000700008000090000

100000

0 01 02 03 04 05 06 07 08 09 1

The d

iffer

ent v

alue

The value of a

Figure 4 The difference value of IFOA and FOA

0 10 20 30 40 50 60 70 80 90 1007

75

8

85

9

95

Iteration number

Cos

t

IFOAFOA

times106

Figure 5 Optimization process of FOA and IFOA (119886 = 05)

5 Conclusions

The location of distribution centers is a complex optimizationproblem To solve the problem of unreasonable networklayout and poor interpretation of customer demand and highcost of distribution this paper optimizes the location ofdistribution centers minimizes the total cost of distributionand establishes a fast and secure distribution center networksystem The conclusions of this paper are summarized asfollows

In this paper a distribution center model is established toreduce the total cost of the enterpriseThemodel is combinedwith the inherent characteristics of fresh goods e-commercetaking into account the principles of distribution centerselection service levels and freshness constraints Due to theincrease in the number of fresh goods e-commerce enter-prises with more intense competition consumer demand ismore and more uncertain Robust optimization is used tooptimize the distribution center model which makes themodel more robust

An improved fruit fly optimization algorithm (IFOA) isproposed in this paper The search step size is dynamicallyadjusted by introducing a weighting function IFOA willserve to solve the established model However the applica-bility of IFOA is more general In this paper we validatethe uncertain demand model by using an example and weprove that the model of distribution centers is valid and caneffectively handle the uncertainty of demand

This paper considers the influence of uncertain demandon the location of distribution centers for fresh goods Itenriches the fresh goods e-commerce distribution centermodel and provides a theoretical basis for a scientific methodof selecting the locations of fresh e-commerce distributioncenters The applicability of the proposed model is mean-ingful and useful for the selection of fresh e-commercedistribution center locations The shortcomings of this paperis that it only considers the uncertainty of customer demandand does not take into account other factors of uncertaintysuch as uncertain delivery weather conditions and uncertaincorruption rate

It is worth noting that some aspects of the model needto be improved For example we will pay more attentionto a variety of uncertain factors so that the model is moresuitable formore complex situations Because the distributioncenter will be related to the distribution of fresh productscoupled with the international awareness of environmentalprotection strengthened gradually the future will take intoaccount the impacts of low-carbon environmental aspects ofthe distribution center location model

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

This research was sponsored by Project of National SocialScience Foundation of China (15BGL202) project of theplanning subject of ldquothe 12th Five-Year Planrdquo in NationalScience and Technology for the Rural Development inChina Demonstration of Key Technology and Equipment forSafe Distribution of Agricultural Logistics (2015BAD18B01)Project of Beijing Philosophy and Social Science (17GBL013)Project of Beijing Municipal Commission of Education(SM201410011002) Project of Innovation Ability Promotion(PXM2016 014213 000033) 2017 Beijing Technology andBusiness University postgraduate student research abilityenhancing project

12 Scientific Programming

References

[1] RAccorsi AGallo andRManzini ldquoA climate driven decision-support model for the distribution of perishable productsrdquoJournal of Cleaner Production vol 165 pp 917ndash929 2017

[2] E Morganti and J Gonzalez-Feliu ldquoCity logistics for perishableproducts The case of the Parmarsquos Food Hubrdquo Case Studies onTransport Policy vol 3 no 2 pp 120ndash128 2015

[3] J A Orjuela-Castro L A Sanabria-Coronado and Peralta-Lozano A M ldquoCoupling facility location models in the supplychain of perishable fruitsrdquo Research in Transportation Businessamp Management 2017

[4] M Merakli and H Yaman ldquoRobust intermodal hub loca-tion under polyhedral demand uncertaintyrdquo TransportationResearch Part B Methodological vol 86 pp 66ndash85 2016

[5] M a Schuster Puga and J-S Tancrez ldquoA heuristic algorithmfor solving large location-inventory problems with demanduncertaintyrdquo European Journal of Operational Research vol 259no 2 pp 413ndash423 2017

[6] A Hiassat A Diabat and I Rahwan ldquoA genetic algorithmapproach for location-inventory-routing problem with perish-able productsrdquo Journal of Manufacturing Systems vol 42 pp93ndash103 2017

[7] K Govindan A Jafarian R Khodaverdi and K DevikaldquoTwo-echelon multiple-vehicle location-routing problem withtime windows for optimization of sustainable supply chainnetwork of perishable foodrdquo International Journal of ProductionEconomics vol 152 pp 9ndash28 2014

[8] Z Drezner and C H Scott ldquoLocation of a distribution centerfor a perishable productrdquo Mathematical Methods of OperationsResearch vol 78 no 3 pp 301ndash314 2013

[9] S M Seyedhosseini and S M Ghoreyshi ldquoAn integrated modelfor production and distribution planning of perishable prod-ucts with inventory and routing considerationsrdquo MathematicalProblems in Engineering vol 2014 Article ID 475606 10 pages2014

[10] M de Keizer R Akkerman M Grunow J M Bloemhof RHaijema and J G van der Vorst ldquoLogistics network designfor perishable products with heterogeneous quality decayrdquoEuropean Journal of Operational Research vol 262 no 2 pp535ndash549 2017

[11] H Yang L I Hong DUWei et al ldquoResearch on location selec-tion of perishable dairy products distribution center based ontwo-stage distributionrdquoComputer Engineering andApplicationsvol 23 pp 239ndash245 2015

[12] J Zhang and F U Shao-chuan ldquoStudy on location of fresh fooddistribution center with demand influenced by the freshnessrdquoChinese Journal of Management Science vol 19 no 10 pp 473ndash476 2011

[13] T Wu H Shen and C Zhu ldquoA multi-period location modelwith transportation economies-of-scale and perishable inven-toryrdquo International Journal of Production Economics vol 169 pp343ndash349 2015

[14] M Musavi and A Bozorgi-Amiri ldquoA multi-objective sus-tainable hub location-scheduling problem for perishable foodsupply chainrdquo Computers amp Industrial Engineering 2017

[15] M Rezaei-Malek R Tavakkoli-Moghaddam B Zahiri and ABozorgi-Amiri ldquoAn interactive approach for designing a robustdisaster relief logistics network with perishable commoditiesrdquoComputers amp Industrial Engineering vol 94 pp 201ndash215 2016

[16] K Khalili-Damghani A-R Abtahi andA Ghasemi ldquoA new bi-objective location-routing problem for distribution of perish-able products evolutionary computation approachrdquo Journal ofMathematical Modelling and Algorithms in Operations Researchvol 14 no 3 pp 287ndash312 2015

[17] Y Zhang Y Jiang M Zhong N Geng and D Chen ldquoRobustOptimization on Regional WCO-for-Biodiesel Supply Chainunder Supply and Demand Uncertaintiesrdquo Scientific Program-ming vol 2016 Article ID 1087845 15 pages 2016

[18] R Qiu and Y Wang ldquoSupply chain network design underdemand uncertainty and supply disruptions a distributionallyrobust optimization approachrdquo Scientific Programming vol2016 Article ID 3848520 15 pages 2016

[19] A Ben-Tal E Hazan T Koren and S Mannor ldquoOracle-basedrobust optimization via online learningrdquo Operations Researchvol 63 no 3 pp 628ndash638 2015

[20] M Melamed A Ben-Tal and B Golany ldquoOn the averageperformance of the adjustable RO and its use as an offlinetool for multi-period production planning under uncertaintyrdquoComputational Management Science vol 13 no 2 pp 293ndash3152016

[21] A Ghodratnama R Tavakkoli-Moghaddam and A AzaronldquoRobust and fuzzy goal programming optimization approachesfor a novel multi-objective hub location-allocation problem Asupply chain overviewrdquoApplied SoftComputing vol 37 pp 255ndash276 2015

[22] F Habibzadeh Boukani B Farhang Moghaddam and M SPishvaee ldquoRobust optimization approach to capacitated singleand multiple allocation hub location problemsrdquo Computationalamp Applied Mathematics vol 35 no 1 pp 45ndash60 2016

[23] A Jakubovskis ldquoStrategic facility location capacity acquisitionand technology choice decisions under demand uncertaintyrobust vs non-robust optimization approachesrdquo European Jour-nal of Operational Research vol 260 no 3 pp 1095ndash1104 2017

[24] H A Eiselt and V Marianov ldquoA bi-objective model for thelocation of landfills formunicipal solidwasterdquoEuropean Journalof Operational Research vol 235 no 1 pp 187ndash194 2014

[25] M G Bardossy and S Raghavan ldquoRobust Optimization forthe Connected Facility Location Problemrdquo Electronic Notes inDiscrete Mathematics vol 44 pp 149ndash154 2013

[26] V de Rosa E Hartmann M Gebhard and J WollenweberldquoRobust capacitated facility location model for acquisitionsunder uncertaintyrdquoComputers amp Industrial Engineering vol 72pp 206ndash216 2014

[27] M Ehrgott J Ide and A Schoobel ldquoMinmax robustness formulti-objective optimization problemsrdquo European Journal ofOperational Research vol 239 no 1 pp 17ndash31 2014

[28] X-F Xu J Hao Y-R Deng and YWang ldquoDesign optimizationof resource combination for collaborative logistics networkunder uncertaintyrdquo Applied Soft Computing vol 56 pp 684ndash691 2017

[29] E D Majewski M Wirtz M Lampe and etal ldquoRobust multi-objective optimization for sustainable design of distributedenergy supply systemsrdquoComputersampChemical Engineering vol102 pp 26ndash39 2016

[30] M Yunfeng Y Chao M Zhang and H Chunyan ldquoTime-satisfaction-based maximal covering location problemrdquo Chi-nese Journal of Management Science vol 2 pp 45ndash51 2006

[31] W-T Pan ldquoA new fruit fly optimization algorithm takingthe financial distress model as an examplerdquo Knowledge-BasedSystems vol 26 pp 69ndash74 2012

Scientific Programming 13

[32] S Kanarachos J Griffin and M E Fitzpatrick ldquoEfficient trussoptimization using the contrast-based fruit fly optimizationalgorithmrdquo Computers amp Structures vol 182 pp 137ndash148 2017

[33] J Niu W Zhong Y Liang N Luo and F Qian ldquoFruit flyoptimization algorithm based on differential evolution andits application on gasification process operation optimizationrdquoKnowledge-Based Systems vol 88 pp 253ndash263 2015

[34] S-M Lin ldquoAnalysis of service satisfaction in web auctionlogistics service using a combination of Fruit fly optimizationalgorithm and general regression neural networkrdquoNeural Com-puting and Applications vol 22 no 3-4 pp 783ndash791 2013

[35] J Huber A Gossmann andH Stuckenschmidt ldquoCluster-basedhierarchical demand forecasting for perishable goodsrdquo ExpertSystems with Applications vol 76 pp 140ndash151 2017

[36] M Shukla and S Jharkharia ldquoApplicability of ARIMA modelsin wholesale vegetable market An investigationrdquo InternationalJournal of Information Systems and Supply Chain Managementvol 6 no 3 pp 105ndash119 2013

[37] C Sun and X Luo ldquoThe influencing factors and countermea-sures of supply uncertainty in supply chainrdquo Economic ResearchGuide vol 11 pp 146-147 2013

[38] S Minner and S Transchel ldquoOrder variability in perish-able product supply chainsrdquo European Journal of OperationalResearch vol 260 no 1 pp 93ndash107 2017

Submit your manuscripts athttpswwwhindawicom

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Distributed Sensor Networks

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Hindawi Publishing Corporationhttpwwwhindawicom

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International Journal of

ReconfigurableComputing

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 201

Applied Computational Intelligence and Soft Computing

thinspAdvancesthinspinthinsp

Artificial Intelligence

HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014

Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Electrical and Computer Engineering

Journal of

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httpwwwhindawicom Volume 2014

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Multimedia

International Journal of

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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RoboticsJournal of

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Computational Intelligence and Neuroscience

Industrial EngineeringJournal of

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Scientific Programming 3

The above literature shows that robust optimization is aneffective way to address uncertain problems These studieshave laid the foundation for the subsequent optimization ofrobust research

In this paper we will consider factors such as uncertaindemand the shelf life of a variety of perishable productsthe timeliness and freshness of those products and theestablishment of a locationmodel for distribution centers thatsatisfies the customer demand for fast delivery of productsRobust optimization can also improve the ability of anti-interference in the model of locating distribution centers toaddress the problem of uncertainty An improved fruit flyalgorithm is used to solve the robust optimization

3 Model Building and Solution Method

31 Problem Description In the practice of fresh goods e-commerce the uncertainty of customer demand for freshproducts and the requirement of customer satisfaction forfresh commodities distribution often exist simultaneouslyBoth factors must be considered at the same time Thedistribution network of an enterprise is often composed ofmultiple distribution centers and this paper will establish alocation model for multiple distribution centers The goalof the location model is to meet the requirements of thecustomers when distributing the goods from the distributioncenter to the customers andmaintain the lowest cost possible

32 Assumptions Many scholars have presented mathemati-cal models and it is crucial to consider all of the assumptionsin this paper In our research it is assumed that fresh goodse-commerce enterprises will set up a number of discretedistribution centers within a certain period of time and acertain area Goods are purchased from a plurality of freshcommodity suppliers and are stored in different distributioncenter locations When an order is received from customersthe nearest distribution center is selected to deliver productsto customers We assume that the quantity and satisfactionrequirements of the fresh commodity consumer (demandpoint) are predetermined but the specific demand for eachorder of the consumer is uncertainThat is each order can beordered withmultiple fresh varietiesThe goal of the distribu-tion center location model is to meet the requirements of thecustomers when distributing the goods from the distributioncenter to the customers andmaintain the lowest cost possibleThe logic diagram is as shown in Figure 1

In addition to the general assumptions described abovethis paper also considers the following specific assumptionsthat the fresh goods e-commerce enterprises operate in aspecific period of time

(1) Fresh goods e-commerce enterprises prefer to rent thedistribution centers from the existing candidate dis-tribution centers and avoid the choice of constructingthem The benefit of selecting from existing distribu-tion centers is that the fixed costs and operating costsare lower than when constructing a new center

Supplier 1

Supplier 2

Supplier q

Distributioncenter 1

Distributioncenter m

Customer 1

Customer 2

Customer n

Figure 1 Logic diagram of locating distribution centers

(2) Customer demand is uncertain and any candidatedistribution center can fully satisfy the demand of aparticular customer

(3) The supply capacity of fresh commodity suppliers canmeet the largest needs of the demand

(4) In the total cost calculation firms do not consider thefresh goods inventory costs loading and unloadinglosses vehicle maintenance costs equipment mainte-nance costs and staff bonus

(5) Unit delivery cost is known and constant(6) The spoilage rate of fresh foods in the distribution

process is constant(7) Fresh goods remain fresh when leaving the distribu-

tion center(8) Freshness of fresh produce can be perceived at all

times during distribution(9) Delivery times may fluctuate but drivers are penal-

ized according to the degree of deviation from theservice standard

(10) This model is appropriate only for a certain periodof time and static location assumptions regardless offuture costs and earnings changes

33 Notation The following notation is used to formulate theproblem considered in this paper Parameters are as follows

119867 Set of suppliers119867 = ℎ | ℎ = 1 2 119902119868 Set of distribution centers 119868 = 119894 | 119894 = 1 2 119898119869 Set of customers 119869 = 119895 | 119895 = 1 2 119899119870 Set of fresh food types119880ℎ Maximum supply capacity of supplier ℎ to theenterprise119873119894 Maximum inventory capacity of distribution cen-ter 119894120579119896 Corruption rate coefficient of fresh food 119896 con-stant119897ℎ119894 Distance between supplier ℎ and distributioncenter 119894

4 Scientific Programming

119897119894119895 Distance between distribution center 119894 and cus-tomer 119895V Average speed of vehicle

119862ℎ119894 Transportation cost per unit from supplier ℎ todistribution center 119894119862119894119895 Transportation cost per unit from distributioncenter 119894 to customer 119895119860 119894 Fixed cost of distribution center 119894119861119894 Operating cost of distribution center 119894119891119894119895 Penalty costs of vehicle arriving late to customer 119895119908 The largest number of new distribution centersavailable to rent

119903119896 The average selling price of the variety 119896 of freshgoods

119905119894119895 Time of vehicle from distribution center 119894 tocustomer 119895119879119895 The serve time that customer 119895 requires from thedelivery center

119879119895maxThe shortest waiting time that customer 119895 is notdissatisfied

119879119895min The longest waiting time that customer 119895 isdissatisfied

120572119895119896 The freshness satisfaction threshold for customer119895 of variety 119896 of fresh goods

120573119895 The time satisfaction threshold for customer 119895Decision Variables

119889ℎ119894 The transport quantity of goods from supplier ℎto distribution center 119894119889119894119895 The transport quantity of goods from distributioncenter 119894 to customer 119895119889119895 The demand of customer 119895119910119894 Binary variable that takes the value 1 if distributioncenter 119894 is selected119911ℎ119894 Binary variable that takes the value 1 if distribu-tion center 119894 is supplied by supplier ℎ119911119894119895 Binary variable that takes the value 1 if customer 119895is supplied by distribution center 119894119911119895119896 Binary variable that takes the value 1 if fresh food119896 is supplied to customer 119895

34 Distribution Center Location Mathematical Model Thispaper constructs the locationmodel of the distribution centerunder the condition of determinate customer demand thenintroduces the demand uncertainty function and optimizesthe model using the robust optimization method

341 Location Mathematical Model under DeterminateDemand The total cost of the distribution center model isthe minimum total cost which is composed of fixed costsoperating expenses transportation costs delayed penaltycosts and fresh goods corruption costs for distribution cen-tersThe consumer satisfactionmodel includes themaximumfreshness of fresh goods and the maximum accuracy of thedistribution center service time

(1) Fixed costs and operating expenses (1205751)1205751 = sum119894isin119868

119860 119894119910119894 +sum119894isin119868

119861119894119910119894 (1)

(2) Transportation costs (1205752)1205752 = sumℎisin119867

sum119894isin119868

119862ℎ119894119897ℎ119894119889ℎ119894 +sum119894isin119868

sum119895isin119869

119862119894119895119897119894119895119889119894119895 (2)

(3) Delayed penalty costs (1205753)

1205753 = 119891119894119895 (119905119894119895 minus 119879119895)0

119905119894119895 ge 119879119895119905119894119895 lt 119879119895 (3)

(4) Fresh goods corruption costs (1205754)Fresh goods corruption costs can be expressed in terms

of freshness Consumers care about the freshness of productsas visual indicators of their quality Product transport timeand mileage have a large impact on the freshness of certainperishable products Therefore this paper which is based onthe freshness model established by Zhang and Shao-chuan[12] takes the transportation time and the transport distanceas the variables into account We form a new freshnessformula

120601119895119896 = (1 minus 120579119896)sumℎisin119867sum119894isin119868 sum119895isin119869[1205821(119897ℎ119894V+119905119894119895)+1205822(119897ℎ119894+119897119894119895)]119911119894119895 (4)

where the transit time weight is 1205821 the transport distanceweight is 1205822 and the weight is determined according to thespecific transportation distance and the transportation timeFor the convenience of follow-up study in this article 1205821 =1205822 = 05

Fresh goods corruption costs

1205754 = sum119896isin119870

119903119896 (1 minus 120601119895119896) (5)

(5) The freshness of fresh goods (120591119895119896)120591119895119896 = sum119895isin119869sum119896isin119870 119911119895119896120601119895119896sum119895isin119869sum119896isin119870 119911119895119896 (6)

(6) The distribution center service time (120583119895)

120583119895 = sum119894isin119868sum119895isin119869 119911119894119895120596 (119905119894119895)sum119894isin119868sum119895isin119869 119911119894119895 (7)

Scientific Programming 5

120596(119905119894119895) is the consumer satisfaction time function Weuse the satisfaction formula introduced to the literature inYunfeng et al [30]

120596 (119905119894119895) =

1 119905119894119895 le 119879119895min

( 119879119895max minus 119905119894119895119879119895max minus 119879119895min

)120574

119879119895min lt 119905119894119895 le 119879119895max

0 119905119894119895 ge 119879119895max(8)

In summary the models of e-commerce distribution centerlocations are as follows

min 120575 = 1205751 + 1205752 + 1205753 + 1205754 (9)

max 120591119895119896 (10)

max 120583119895 (11)

st sum119894isin119868

119889ℎ119894 le 119880ℎforallℎ isin 119867

(12)

sumℎisin119867

119889ℎ119894 le 119873119894119910119894sum119895isin119869

119889119894119895 le 119873119894119910119894forall119894 isin 119868

(13)

sum119894isin119868

119910119894 le 119908 (14)

sum119894isin119868

119911119894119895 = 1forall119895 isin 119869

(15)

sum119894isin119868

119889119894119895 ge 119889119895forall119895 isin 119869

(16)

119911119894119895 le 119910119894119911ℎ119894 le 119910119894forall119894 isin 119868 forall119895 isin 119869

(17)

119889ℎ119894 ge 0119889119894119895 ge 0 (18)

119910119894 119911ℎ119894 119911119894119895 isin 0 1forall119894 isin 119868 forall119895 isin 119869 (19)

The objective function (9) indicates that the total cost isto be minimized The objective function (10) indicates themaximum freshness of fresh goods The objective function(11) indicates the maximum accuracy of the distributioncenter service time

Constraint (12) is the supply constraint of the supplier Itensures that the total amount of products transported from

supplier ℎ does not exceed the maximum supply capacityConstraints (13) are the distribution center 119894 inventory con-straints and they enforce that the storage of the total freshproduct does not exceed the maximum inventory capacityConstraint (14) represents the number of new distributioncenter constraints Constraint (15) ensures that each customerhas only one candidate distribution center to deliver to himor her Constraint (16) indicates that the volume of freshfoods delivered to the customer cannot be less than thecustomer demand due to possible cargo damage Constraint(17) ensures that the selected distribution center can providedelivery Equations (18) and (19) are constrained by decisionvariables

In the calculation the multiobjective function is trans-formed into a single objective function by the main objectivemethod to select themain objective function according to theenterprisersquos strategic plan If the business goal is to minimizethe total cost and the freshness and the distribution centerservice time only need to achieve a consumer satisfactionthreshold then consumer satisfaction does not have to bemaximized but consumer satisfaction is transformed intoa constraint In this paper the main objective function ischosen to be the minimum total cost and the satisfaction ofthe consumer is set as a constraint

120591119895119896 ge 120572119895119896120583119895 ge 120573119895 (20)

Constraint (20) requires that the freshness of the productmust reach the customer satisfaction threshold and thesatisfaction degree of the distribution center service timemust meet the customer satisfaction threshold for time

In the abovementioned distribution center locationmodel it is assumed that the demand 119889119895 is known and thetotal cost of the decision method can be obtained from theobjective function (9) However in real life there is a greatdeal of uncertainty in the demand for fresh goods so we needto use a robust optimizationmethod to optimize the selectionof locations for distribution centers

342 LocationMathematicalModel underUncertainDemandThe abovementioned distribution center location model isconverted into an equivalent auxiliary model by using robustoptimization The uncertainty of demand is at the coreof obtaining the equivalent auxiliary model This paperuses a series of discrete scenarios to describe the possiblerequirements of the customer

The specific demand of each location is unknown and isconsidered to vary in a closed and bounded box This is acommon description of the uncertainty method

Assuming that the demand scenario is 119904 where 119904 =1 2 119878 is the probability that the demand scenario 119904 ofcustomer 119895 satisfies the ellipsoid uncertainty set The generalform of the box can be specified as follows

119901119895119904 isin Ω = 1199010119895119904 + 119876119906 119890119879119876119906 = 01199010119895119904 + 119876119906 ge 0 119906 le 1 (21)

6 Scientific Programming

where 1199010119895119904 is the most probable probability distribution ofdemand points 119876 isin 119877119899119898times119899119898 is the scope of the zoom119906 denotes the Euclidean norm for perturbation 119890119879119876119906 =0 1199010119895119904 + 119876119906 ge 0 is to ensure that the demand scenarioprobability 119901119895119904 is a probability distribution

Assuming that the demand of each customer is indepen-dent of each other and does not interfere with each otherand the total cost of the site under the demand scenario119904 of customer 119895 is 120575119895119904 the cost of a distribution center isdetermined as follows

120575119894119895 = sum119904isin119878

120575119894119895119904119901119895119904 (22)

The total expected cost for all distribution centers isdetermined as follows

119864 (120575119894) = sum119895isin119869

120575119894119895 = sum119895isin119869

sum119904isin119878

120575119894119895119904119901119895119904 = sum119895isin119869

119901119879119895 120575119895

120575119895 = (1205751198951 1205751198952 120575119895119904)119879 119901119895 = (1199011198951 1199011198952 119901119895119904)119879

(23)

The total cost of the distribution center is transformed

min 119864 (120575) = minsum119895isin119869

119901119879119895 120575119895 (24)

The robust correspondence model of (19) is expressed as

min max119901119895119904isinΩ

119864 (120575) = minmax119901119895119904isinΩ

sum119895isin119869

119901119879119895 120575119895 (25)

The above model is equivalent to

min 120603 (26)

st max119901119895119904isinΩ

sum119895isin119869

119901119879119895 120575119895 le 120603 (27)

119901119895119904 satisfies the demand uncertain set (21) then the leftside of formula (27) is

max119901119895119904isinΩ

sum119895isin119869

119901119879119895 120575119895 = max119901119895119904isinΩ

sum119895isin119869

[(1199010119895119904)119879 120575119895 + (119876119906)119879 120575119895]

= sum119895isin119869

(1199010119895119904)119879 120575119895 + max119901119895119904isinΩ

(119876119906)119879 120575119895(28)

Because 119906 le 1max119901119895119904isinΩ

(119876119906)119879 120575119895 = max119901119895119904isinΩ

119876119879120575119895 (29)

Equation (27) is converted to

sum119895isin119869

(1199010119895119904)119879 120575119895 + max119901119895119904isinΩ

119876119879120575119895 le 120603 (30)

In summary the optimization objective of the robustoptimizationmodel ismin120603 and composed of the constraints(30) and (12) to (20)Themodel has good robustness throughthe robust optimization of the model which can meet theuncertain demand of the customer and ensure the economicfeasibility of the location selection scheme

35 Improved Fruit FlyOptimizationAlgorithm (IFOA) Afterthe above two-step modeling this paper establishes a modelof the distribution center of fresh goods e-commerce underuncertain demand The next important problem is the solu-tion of themodelThe location problem in the uncertain situ-ation is anNP-hard problemThe traditional solutionmethodis complicated and the required amount of is prohibitive forfinding a solution Therefore a heuristic algorithm is used tosolve the problem

FOA is suitable for solving the optimization problemwith complex constraints and strong correlation betweenthe constituent elements of the solution [31] It is widelyused in many classical optimization fields such as efficienttruss optimization [32] gasification process operation opti-mization [33] and analysis of service satisfaction [34] TheFOA algorithm is easy to combine with other methods hasstrong robustness and is suitable for robustly optimizing thelocation of distribution centers Therefore FOA is used tosolve the problem in this paper

351 Fruit Fly Optimization Algorithm (FOA) FOA is out-lined as follows

Step 1 Initialize parameters including the maximumnumber of evaluations (maxgen) and the size of fruitflies (sizepop) and initialize the position of the flies(119883 axis 119884 axis)

Step 2 Randomly initialize the flight direction and distanceof the individual flies where Random Value is the distance inthe search

119883119894 = 119883 axis + Random Value119884119894 = 119884 axis + Random Value (31)

Step 3 The distance of each fly from the origin point and thesmell concentration judgment value is defined as follows

Dist119894 = radic1199091198942 + 1199101198942119878119894 = 1

Dist119894 (32)

Step 4 Based on 119878119894 the smell concentration of flies denotedby Smell119894 is calculated as follows

Smell119894 = function (119878119894) (33)

Step 5 Find the fruit flies with the best smell concentrationand allow the flies to fly to the optimal position

[bestSmell bestindex] = min (Smell119894)Smellbest = bestSmell

119909 axis = 119883 (bestindex)119910 axis = 119884 (bestindex)

(34)

Step 6 Stop the search if the maximum evaluation number isreached otherwise repeat Steps 2ndash5

Scientific Programming 7

Table 1 Test function

Test function Range Optimal Peak

min 1198911 = minusexp(minus05 sdot119899sum119894=1

1199091198942) [minus1 1] minus1 Single

min 1198912 =sin2 (radicsum119899119894=1 1199091198942) minus 05(1 + 0001 (sum119899119894=1 1199091198942))2 + 05 [minus100 100] 0 Multiple

Table 2 Mean and standard deviation of function test

Function Result FOA IFOA

1198911(119909) Mean 30546 times 10minus6 minus1Std 75382 times 10minus6 0

1198912(119909) Mean 31266 times 10minus6 467 times 10minus4Std 86307 times 10minus8 2328 times 10minus3

FOA has great ability to achieve global optimization andhigh convergence accuracy and has great research value in thefield of engineering However the original FOA uses a fixedsearch step and cannot take both global search capabilitiesand local search capabilities into account thus affecting theconvergence rate and search ability Additionally it is easyfor FOA to focus on a local optimum leading to prematureconvergence This paper focuses on the shortcomings of thealgorithm and improves FOAThe purpose of improving theFOA is to make it solve the location model better

352 Improved Fruit Fly Optimization Algorithm (IFOA)In this paper an improved fruit fly optimization algorithm(IFOA) is proposed The search step size is dynamicallyadjusted by introducing the weighting functionThe purposeof dynamic adjustment is to divide the search into two partsThe first part contains a large search step in a large area for aglobal search to ensure that the algorithmconsiders the globaloptimum The second part contains a smaller step search toensure local search capabilities

The fruit fly individual random search expression is asfollows

119883119894 = 119883 axis + 120595 sdot rand ( ) 119884119894 = 119884 axis + 120595 sdot rand ( ) (35)

where 120595 represents the weighted function

120595 = exp(minus 10038161003816100381610038161003816100381610038161003816Smell119894 minus Smell119894minus1

Smell119894

10038161003816100381610038161003816100381610038161003816120577) (36)

where Smell119894 is the 119894th optimal fitness value When the ratiochange is large it indicates that the fly group is searching fora new space and that the weighting function is conducive toa global search When the ratio change is small the fruit flygroup has shifted to a local search and the weight functionis reduced 120577 gt 0 and as 120577 increases fruit fly search abilityincreases which prevents the algorithms from concentratingon a local optimum It can be adjusted according to the actualproblem In addition to the random search expression theother IFOA algorithm step expression is consistent with FOA

353 Test Function To test and analyze the performanceof the improved algorithm the following two classic testfunctions were used to test FOA and IFOA respectivelyFunction form range theoretical extremes and peak areshown in Table 1

The specific initialization parameter is set to sizepop =20 maxgen = 100 We randomly initialize the fliesrsquo popula-tion position The results of the functional tests are shown inTable 2 and the optimization process is shown in Figure 2

From the test results in Table 2 and optimization processIFOA has stronger capabilities of global search local searchand higher convergence accuracy than FOA Under the sameconditions IFOA results are superior to FOA in termsof both mean and standard deviation Under the sameconvergence accuracy the number of valid iterations of IFOAis less than that of FOA which indicates that IFOA convergesfaster Therefore IFOA effectively improves the convergenceprecision and convergence speed of FOA

36 The Calculation Process of Model

(1) Collect the relevant data needed to establish thedistribution center model (as shown in Section 33)

(2) Convert the distribution center model under uncer-tain demand to a tractable equivalent model by usingrobust optimization

(3) IFOA is used to solve the mathematical model

(1) Set the initial parameters including the maxi-mum number of evaluations (maxgen) and thesize of the fruit flies (sizepop) and the initialposition of the flies (119883 axis 119884 axis)

(2) Randomly setting the flight direction and dis-tance of the individual flies the fruit fly individ-ual random search expression is as follows

119883119894 = 119883 axis + 120595 sdot rand () 119884119894 = 119884 axis + 120595 sdot rand () (37)

(3) According to the fitness function formula theindividual fruit fly is calculated to find the

8 Scientific Programming

Table 3 Distance between supplier ℎ and distribution center 119894 (km)

1198681 1198682 1198683 1198684 1198685 1198686 1198687 11986881198671 1431 2912 19945 12093 7738 8814 3214 79831198672 7382 9424 11886 4712 4500 1204 6527 109651198673 13223 11025 10594 3544 9126 6395 7580 6324

0 10 20 30 40 50 60 70 80 90 100minus1

minus0998

minus0996

minus0994

minus0992

minus099

minus0988

minus0986

minus0984

Iteration number

Smel

l

IFOAFOA

0

0002

0004

0006

0008

001

0012

0014

Smel

l

f1(x)

0 10 20 30 40 50 60 70 80 90 100Iteration number

IFOAFOA

f2(x)

Figure 2 Optimization process of FOA and IFOA

position and optimal value of the individual andthe global optimal individual

(4) Find the fruit flies with the best smell concen-tration and allow the flies to fly to the optimalposition

(5) Stop the search if the maximum evaluationnumber is reached otherwise repeat

(6) According to the IFOA optimal location resultsthen find the corresponding best location of thedistribution center and the optimal distributionpath

4 Computational Results

Experiments are proposed in this part to prove the effective-ness and feasibility of the location model Both deterministicand uncertain demand scenarios are considered and then acomparison and analysis of the results of the two situationsis providedThe numerical calculation problem is consideredto occur in a developed city where a fresh goods e-commercefirm chooses to rent a certain number of distribution centerswithin an appropriate area The area of suppliers is 3 and thearea of customers is 10 The firm chooses to rent 3 locationsfrom a set of 8 candidate distribution centers

The distance between the supplier and the candidatedistribution center and the distance between the candidatedistribution center and the demand point are obtained by

using the Euclidean theorem The details are shown inTables 3 and 4 The tables consider the different qualitiesof each candidate distribution center such as the locationtransportation economy and other conditions Fixed costsoperating costs and the largest inventory are also different asshown in Table 5 The maximum supply capacity of supplierℎ is shown in Table 6

The average traveling speed is 45 kmh for the distributionvehicles in the region the average unit freight from thesupplier to the distribution center is 15 yuan(tsdotkm) and thefreight rate from the distribution center to the demand pointis 18 yuan(tsdotkm) To simplify the follow-up calculation thenumerical calculations only consider the distribution of twofresh goods using the corruption coefficients of 015 and008 and the unit prices of 4 yuankg and 6 yuankg Theaverage satisfaction threshold for customer satisfaction is075 and the average satisfaction threshold for freshness is07 If the delivery vehicle arrives late the compensation feeis 50 yuan(hsdott) The demand point time window is shown inTable 7

We consider cases where demand is both deterministicand uncertain The calculation and comparative analysisof two cases can be conducted more directly to verifywhether the model can help the fresh goods e-commerceto suppress the uncertainty interference by demand Themethod used to predict the consumer demand is the multi-variate autoregressive integrated moving average (AMIMA)model in this paper Fresh e-commerce is characterized

Scientific Programming 9

Table 4 Distance between distribution center 119894 and customer 119895 (km)

1198681 1198682 1198683 1198684 1198685 1198686 1198687 11986881198691 14200 4134 24550 16717 8919 11733 7560 144361198692 5420 9642 20535 14220 5903 8628 10072 180711198693 11610 1170 19564 11682 5178 7156 2469 102011198694 6525 18398 13761 12419 12180 11123 16497 214241198695 4827 7716 17279 10536 2282 4850 7000 145791198696 9904 15932 6296 4810 10720 7694 12857 146731198697 22649 13509 20341 14670 16589 15631 12035 48871198698 10718 3383 17310 9420 4161 5215 721 89051198699 12879 19474 3981 7506 14322 11287 16319 1711411986910 15277 14586 7910 3984 12248 9166 11140 8238

Table 5 Fixed costs operating costs and maximum inventory

Candidate distribution centers 1198681 1198682 1198683 1198684 1198685 1198686 1198687 1198688Fixed costs (million) 145 138 123 148 129 123 138 136Operating costs (million) 007 006 006 009 005 006 007 006Maximum inventoryt 1000 900 700 1100 1000 900 1200 800

Table 6 The maximum supply capacity of supplier

Supplier 1198671 1198672 1198673Themaximum supply capacityt 8800 7900 6300

Table 7 Time window and determined demand of customer

Customer (119879119895min 119879119895 119879119895max) Demand (t)1198691 (2 25 3) 2001198692 (3 4 5) 4001198693 (1 15 2) 3501198694 (1 2 25) 2501198695 (2 3 4) 1501198696 (3 35 4) 3501198697 (15 25 3) 3001198698 (2 3 45) 1801198699 (15 25 3) 35011986910 (3 4 5) 300

by consumers ordering through the Internet so fresh e-commerce companies can collect customer information andorder information (eg customersrsquo purchasing frequencypurchasing preferences and position distribution) Thenthe fresh e-commerce company can use this informationto classify consumers and predict consumer demand Theautoregressive part of the multiple ARIMAmodel representsa linear combination of past values while themoving averagepart of the multiple ARIMAmodel is a linear combination ofpast forecasting errorsThe advantage of themultiple ARIMAmodel is that it improves prediction accuracy facilitatesstatistics and reduces the cost of prediction Moreover it cancombine product cost changes with demand uncertainty topredict consumer demand [35] In view of this the multi-variate ARIMA model is suitable to predict the consumerdemand for fresh e-commerce Although the AMIMAmodel

can more accurately predict the uncertainty of demand thesize of fresh e-commercersquos consumers is small and widelydistributed so there is still uncertainty in demand To learnmore about the multivariate ARIMA model studies [35 36]are suggested The deterministic demand for each customeris shown in Table 7

The affected factors of uncertain supply involve envi-ronmental factors (eg the natural environment economicenvironment and political environment) and the abilities ofsuppliers (eg production capacity equipment capacity) [37]First the planting period for fresh foods is the quarter or yearas a unit the period is longer than for other products Fresh e-commerce can be investigated in advance through the Inter-net and then the product cultivation of the fresh food and thefield investigation can be planned accordingly Second thesuppliers of fresh electricity providers are typically farmersand fresh food bases around the region These suppliersare less affected by global economic changes and politicalchanges The selection diversity of suppliers also allows freshe-commerce companies to evaluate and select suppliers inadvance In addition the equipment failure problem has lessof an effect on fresh e-commerce because fresh productscan be delivered to the distribution center though simplepretreatment packaging In summary the supply of fresh e-commerce is uncertain but fresh e-commerce companies areless affected by these uncertain factors due to the specialnature of fresh foods The current delivery mode of freshproducts is from a mono type and large batch distributionto a multitype delivery mode and small batch distributionEach time an order is made the consumer evaluates thefresh electricity service (eg Amazon Fresh and MotionOptimization) For the majority of instances the perishablenature of a product results in the supply process having alower variability than the demand process [38] Thereforethis paper focuses on the location model for distributioncenters under uncertain demand

10 Scientific Programming

0 009 014027033

071093

119

165 175191

0

0005

001

0015

002

0025

0 01 02 03 04 05 06 07 08 09 1

The i

ncre

ase r

atio

The value of a

Figure 3 The increase ratio of the total cost of uncertain demand

For the case of uncertainty we assume that the demandfor each demand point is 119904 = 5 The number of scenariosfor each demand point can be different from each other Thevalue of the demand scenario is determined by the surveyand then the five cases are generated randomly by Matlab 83as the demand scenario of the demand point 119895 The demandscenario of the 10 demandpoints can be obtained by repeatingthe process ten times

The discrete demand probability distribution is 1199010119895119904 119869 =119895 | 119895 = 1 2 119899For 1199010119895119904 in the range (0 1) the simulations are randomly

generated between the 10 numbers normalized and repeatedten times in order to get all the demand points in theuncertain demand scenarioTheprobability demand scenarioof customer 119895 (119901119895119904) meets the uncertainty set Let thedecentralized matrix be 119876 = 119886119868 where 119886 is a nonnegativeparameter and 119868 is an identity matrix

In the experiment let 119886 = 05 and 119886 = 08 respectivelyCalculate 119901119895119904

The specific initialization parameter is set to maxgen =100 sizepop = 20 The program is implemented in Matlab83 and run on a computer with 26GHz Intel i5-4210MCPU 4GB of RAM andWindows 10The distribution centerdecision-making program and the total cost are shown inTable 8

For the deterministic demand situation the optimal deci-sion is to choose distribution center 119868211986851198686 from the candidatelist The total cost is 7208 million For the uncertain demandsituation when 119886 = 01 to 119886 = 04 the optimal decision isto choose distribution centers 119868211986851198686 The distribution rangeis constant but the cost increases When 119886 = 05 to 119886 = 07the optimal decision is to choose distribution centers 119868211986851198686but the distribution range is different from the deterministicdemand situation When 119886 = 08 to 119886 = 1 the optimaldecision is to choose distribution centers 119868511986861198687 The increaseratio of the total cost in the case of uncertainty is comparedto the total cost in the demand determination as shownin Figure 3 Enterprises in the decision-making before theconsumer demand should be the historical data for statisticaland analysis determine the variation range of parameter119886 and make decisions based on cost and self-conditions(Figure 3)

Then using FOA to solve themodel and initial parametersand operating environment equally with IFOA the results are

Table 8 The decision-making program and the total cost ofdistribution center

The value of 119886 Decision-makingprogram and

distribution rangeCost (RMB)

119886 = 0 1198682 1198691 1198693 11986977208563141198685 1198692 1198695 11986981198686 1198694 1198696 1198699 11986910

119886 = 01 1198682 1198691 1198693 11986977215050851198685 1198692 1198695 11986981198686 1198694 1198696 1198699 11986910

119886 = 02 1198682 1198691 1198693 11986977218655131198685 1198692 1198695 11986981198686 1198694 1198696 1198699 11986910

119886 = 03 1198682 1198691 1198693 11986977228026261198685 1198692 1198695 11986981198686 1198694 1198696 1198699 11986910

119886 = 04 1198682 1198691 1198693 11986977232351401198685 1198692 1198695 11986981198686 1198694 1198696 1198699 11986910

119886 = 05 1198682 1198691 1198693 11986977259452741198685 1198692 1198694 1198695 11986981198686 1198696 1198699 11986910

119886 = 06 1198682 1198691 1198693 11986977275602781198685 1198692 1198694 1198695 11986981198686 1198696 1198699 11986910

119886 = 07 1198682 1198691 1198693 11986977294345041198685 1198692 1198694 1198695 11986981198686 1198696 1198699 11986910

119886 = 08 1198685 1198692 11986957327583631198686 1198694 1198696 1198699 119869101198687 1198691 1198693 1198697 1198698

119886 = 09 1198685 1198692 11986957334712991198686 1198694 1198696 1198699 119869101198687 1198691 1198693 1198697 1198698

119886 = 1 1198685 1198692 11986957346246701198686 1198694 1198696 1198699 119869101198687 1198691 1198693 1198697 1198698

shown in Table 9 the difference value of IFOA and FOA isshown in Figure 4 and the optimization process of FOA andIFOA is shown in Figure 5 (select 119886 = 05)

From the test results in Table 9 and Figures 4 and 5under the same conditions IFOA results are superior to FOAthe convergence accuracy is more accurate and the optimalresults are better Under the same convergence accuracythe number of valid iterations of IFOA is less than that ofFOA which indicates that IFOA converges faster ThereforeIFOA effectively improves the convergence precision andconvergence speed of FOAThe applicability of IFOA is moreextensive

Scientific Programming 11

Table 9 The results of FOA and IFOA

The value of 119886 IFOA optimal FOA optimal119886 = 0 720856314 720874332119886 = 01 721505085 721515326119886 = 02 721865513 721881176119886 = 03 722802626 72285562119886 = 04 723235140 723309877119886 = 05 725945274 726005691119886 = 06 727560278 727613354119886 = 07 729434504 729495412119886 = 08 732758363 732827122119886 = 09 733471299 733549837119886 = 1 734624670 734714368

18018 10241 15663

52994

7473760417

5307660908

6875978538

89698

000100002000030000400005000060000700008000090000

100000

0 01 02 03 04 05 06 07 08 09 1

The d

iffer

ent v

alue

The value of a

Figure 4 The difference value of IFOA and FOA

0 10 20 30 40 50 60 70 80 90 1007

75

8

85

9

95

Iteration number

Cos

t

IFOAFOA

times106

Figure 5 Optimization process of FOA and IFOA (119886 = 05)

5 Conclusions

The location of distribution centers is a complex optimizationproblem To solve the problem of unreasonable networklayout and poor interpretation of customer demand and highcost of distribution this paper optimizes the location ofdistribution centers minimizes the total cost of distributionand establishes a fast and secure distribution center networksystem The conclusions of this paper are summarized asfollows

In this paper a distribution center model is established toreduce the total cost of the enterpriseThemodel is combinedwith the inherent characteristics of fresh goods e-commercetaking into account the principles of distribution centerselection service levels and freshness constraints Due to theincrease in the number of fresh goods e-commerce enter-prises with more intense competition consumer demand ismore and more uncertain Robust optimization is used tooptimize the distribution center model which makes themodel more robust

An improved fruit fly optimization algorithm (IFOA) isproposed in this paper The search step size is dynamicallyadjusted by introducing a weighting function IFOA willserve to solve the established model However the applica-bility of IFOA is more general In this paper we validatethe uncertain demand model by using an example and weprove that the model of distribution centers is valid and caneffectively handle the uncertainty of demand

This paper considers the influence of uncertain demandon the location of distribution centers for fresh goods Itenriches the fresh goods e-commerce distribution centermodel and provides a theoretical basis for a scientific methodof selecting the locations of fresh e-commerce distributioncenters The applicability of the proposed model is mean-ingful and useful for the selection of fresh e-commercedistribution center locations The shortcomings of this paperis that it only considers the uncertainty of customer demandand does not take into account other factors of uncertaintysuch as uncertain delivery weather conditions and uncertaincorruption rate

It is worth noting that some aspects of the model needto be improved For example we will pay more attentionto a variety of uncertain factors so that the model is moresuitable formore complex situations Because the distributioncenter will be related to the distribution of fresh productscoupled with the international awareness of environmentalprotection strengthened gradually the future will take intoaccount the impacts of low-carbon environmental aspects ofthe distribution center location model

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

This research was sponsored by Project of National SocialScience Foundation of China (15BGL202) project of theplanning subject of ldquothe 12th Five-Year Planrdquo in NationalScience and Technology for the Rural Development inChina Demonstration of Key Technology and Equipment forSafe Distribution of Agricultural Logistics (2015BAD18B01)Project of Beijing Philosophy and Social Science (17GBL013)Project of Beijing Municipal Commission of Education(SM201410011002) Project of Innovation Ability Promotion(PXM2016 014213 000033) 2017 Beijing Technology andBusiness University postgraduate student research abilityenhancing project

12 Scientific Programming

References

[1] RAccorsi AGallo andRManzini ldquoA climate driven decision-support model for the distribution of perishable productsrdquoJournal of Cleaner Production vol 165 pp 917ndash929 2017

[2] E Morganti and J Gonzalez-Feliu ldquoCity logistics for perishableproducts The case of the Parmarsquos Food Hubrdquo Case Studies onTransport Policy vol 3 no 2 pp 120ndash128 2015

[3] J A Orjuela-Castro L A Sanabria-Coronado and Peralta-Lozano A M ldquoCoupling facility location models in the supplychain of perishable fruitsrdquo Research in Transportation Businessamp Management 2017

[4] M Merakli and H Yaman ldquoRobust intermodal hub loca-tion under polyhedral demand uncertaintyrdquo TransportationResearch Part B Methodological vol 86 pp 66ndash85 2016

[5] M a Schuster Puga and J-S Tancrez ldquoA heuristic algorithmfor solving large location-inventory problems with demanduncertaintyrdquo European Journal of Operational Research vol 259no 2 pp 413ndash423 2017

[6] A Hiassat A Diabat and I Rahwan ldquoA genetic algorithmapproach for location-inventory-routing problem with perish-able productsrdquo Journal of Manufacturing Systems vol 42 pp93ndash103 2017

[7] K Govindan A Jafarian R Khodaverdi and K DevikaldquoTwo-echelon multiple-vehicle location-routing problem withtime windows for optimization of sustainable supply chainnetwork of perishable foodrdquo International Journal of ProductionEconomics vol 152 pp 9ndash28 2014

[8] Z Drezner and C H Scott ldquoLocation of a distribution centerfor a perishable productrdquo Mathematical Methods of OperationsResearch vol 78 no 3 pp 301ndash314 2013

[9] S M Seyedhosseini and S M Ghoreyshi ldquoAn integrated modelfor production and distribution planning of perishable prod-ucts with inventory and routing considerationsrdquo MathematicalProblems in Engineering vol 2014 Article ID 475606 10 pages2014

[10] M de Keizer R Akkerman M Grunow J M Bloemhof RHaijema and J G van der Vorst ldquoLogistics network designfor perishable products with heterogeneous quality decayrdquoEuropean Journal of Operational Research vol 262 no 2 pp535ndash549 2017

[11] H Yang L I Hong DUWei et al ldquoResearch on location selec-tion of perishable dairy products distribution center based ontwo-stage distributionrdquoComputer Engineering andApplicationsvol 23 pp 239ndash245 2015

[12] J Zhang and F U Shao-chuan ldquoStudy on location of fresh fooddistribution center with demand influenced by the freshnessrdquoChinese Journal of Management Science vol 19 no 10 pp 473ndash476 2011

[13] T Wu H Shen and C Zhu ldquoA multi-period location modelwith transportation economies-of-scale and perishable inven-toryrdquo International Journal of Production Economics vol 169 pp343ndash349 2015

[14] M Musavi and A Bozorgi-Amiri ldquoA multi-objective sus-tainable hub location-scheduling problem for perishable foodsupply chainrdquo Computers amp Industrial Engineering 2017

[15] M Rezaei-Malek R Tavakkoli-Moghaddam B Zahiri and ABozorgi-Amiri ldquoAn interactive approach for designing a robustdisaster relief logistics network with perishable commoditiesrdquoComputers amp Industrial Engineering vol 94 pp 201ndash215 2016

[16] K Khalili-Damghani A-R Abtahi andA Ghasemi ldquoA new bi-objective location-routing problem for distribution of perish-able products evolutionary computation approachrdquo Journal ofMathematical Modelling and Algorithms in Operations Researchvol 14 no 3 pp 287ndash312 2015

[17] Y Zhang Y Jiang M Zhong N Geng and D Chen ldquoRobustOptimization on Regional WCO-for-Biodiesel Supply Chainunder Supply and Demand Uncertaintiesrdquo Scientific Program-ming vol 2016 Article ID 1087845 15 pages 2016

[18] R Qiu and Y Wang ldquoSupply chain network design underdemand uncertainty and supply disruptions a distributionallyrobust optimization approachrdquo Scientific Programming vol2016 Article ID 3848520 15 pages 2016

[19] A Ben-Tal E Hazan T Koren and S Mannor ldquoOracle-basedrobust optimization via online learningrdquo Operations Researchvol 63 no 3 pp 628ndash638 2015

[20] M Melamed A Ben-Tal and B Golany ldquoOn the averageperformance of the adjustable RO and its use as an offlinetool for multi-period production planning under uncertaintyrdquoComputational Management Science vol 13 no 2 pp 293ndash3152016

[21] A Ghodratnama R Tavakkoli-Moghaddam and A AzaronldquoRobust and fuzzy goal programming optimization approachesfor a novel multi-objective hub location-allocation problem Asupply chain overviewrdquoApplied SoftComputing vol 37 pp 255ndash276 2015

[22] F Habibzadeh Boukani B Farhang Moghaddam and M SPishvaee ldquoRobust optimization approach to capacitated singleand multiple allocation hub location problemsrdquo Computationalamp Applied Mathematics vol 35 no 1 pp 45ndash60 2016

[23] A Jakubovskis ldquoStrategic facility location capacity acquisitionand technology choice decisions under demand uncertaintyrobust vs non-robust optimization approachesrdquo European Jour-nal of Operational Research vol 260 no 3 pp 1095ndash1104 2017

[24] H A Eiselt and V Marianov ldquoA bi-objective model for thelocation of landfills formunicipal solidwasterdquoEuropean Journalof Operational Research vol 235 no 1 pp 187ndash194 2014

[25] M G Bardossy and S Raghavan ldquoRobust Optimization forthe Connected Facility Location Problemrdquo Electronic Notes inDiscrete Mathematics vol 44 pp 149ndash154 2013

[26] V de Rosa E Hartmann M Gebhard and J WollenweberldquoRobust capacitated facility location model for acquisitionsunder uncertaintyrdquoComputers amp Industrial Engineering vol 72pp 206ndash216 2014

[27] M Ehrgott J Ide and A Schoobel ldquoMinmax robustness formulti-objective optimization problemsrdquo European Journal ofOperational Research vol 239 no 1 pp 17ndash31 2014

[28] X-F Xu J Hao Y-R Deng and YWang ldquoDesign optimizationof resource combination for collaborative logistics networkunder uncertaintyrdquo Applied Soft Computing vol 56 pp 684ndash691 2017

[29] E D Majewski M Wirtz M Lampe and etal ldquoRobust multi-objective optimization for sustainable design of distributedenergy supply systemsrdquoComputersampChemical Engineering vol102 pp 26ndash39 2016

[30] M Yunfeng Y Chao M Zhang and H Chunyan ldquoTime-satisfaction-based maximal covering location problemrdquo Chi-nese Journal of Management Science vol 2 pp 45ndash51 2006

[31] W-T Pan ldquoA new fruit fly optimization algorithm takingthe financial distress model as an examplerdquo Knowledge-BasedSystems vol 26 pp 69ndash74 2012

Scientific Programming 13

[32] S Kanarachos J Griffin and M E Fitzpatrick ldquoEfficient trussoptimization using the contrast-based fruit fly optimizationalgorithmrdquo Computers amp Structures vol 182 pp 137ndash148 2017

[33] J Niu W Zhong Y Liang N Luo and F Qian ldquoFruit flyoptimization algorithm based on differential evolution andits application on gasification process operation optimizationrdquoKnowledge-Based Systems vol 88 pp 253ndash263 2015

[34] S-M Lin ldquoAnalysis of service satisfaction in web auctionlogistics service using a combination of Fruit fly optimizationalgorithm and general regression neural networkrdquoNeural Com-puting and Applications vol 22 no 3-4 pp 783ndash791 2013

[35] J Huber A Gossmann andH Stuckenschmidt ldquoCluster-basedhierarchical demand forecasting for perishable goodsrdquo ExpertSystems with Applications vol 76 pp 140ndash151 2017

[36] M Shukla and S Jharkharia ldquoApplicability of ARIMA modelsin wholesale vegetable market An investigationrdquo InternationalJournal of Information Systems and Supply Chain Managementvol 6 no 3 pp 105ndash119 2013

[37] C Sun and X Luo ldquoThe influencing factors and countermea-sures of supply uncertainty in supply chainrdquo Economic ResearchGuide vol 11 pp 146-147 2013

[38] S Minner and S Transchel ldquoOrder variability in perish-able product supply chainsrdquo European Journal of OperationalResearch vol 260 no 1 pp 93ndash107 2017

Submit your manuscripts athttpswwwhindawicom

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Applied Computational Intelligence and Soft Computing

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in

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4 Scientific Programming

119897119894119895 Distance between distribution center 119894 and cus-tomer 119895V Average speed of vehicle

119862ℎ119894 Transportation cost per unit from supplier ℎ todistribution center 119894119862119894119895 Transportation cost per unit from distributioncenter 119894 to customer 119895119860 119894 Fixed cost of distribution center 119894119861119894 Operating cost of distribution center 119894119891119894119895 Penalty costs of vehicle arriving late to customer 119895119908 The largest number of new distribution centersavailable to rent

119903119896 The average selling price of the variety 119896 of freshgoods

119905119894119895 Time of vehicle from distribution center 119894 tocustomer 119895119879119895 The serve time that customer 119895 requires from thedelivery center

119879119895maxThe shortest waiting time that customer 119895 is notdissatisfied

119879119895min The longest waiting time that customer 119895 isdissatisfied

120572119895119896 The freshness satisfaction threshold for customer119895 of variety 119896 of fresh goods

120573119895 The time satisfaction threshold for customer 119895Decision Variables

119889ℎ119894 The transport quantity of goods from supplier ℎto distribution center 119894119889119894119895 The transport quantity of goods from distributioncenter 119894 to customer 119895119889119895 The demand of customer 119895119910119894 Binary variable that takes the value 1 if distributioncenter 119894 is selected119911ℎ119894 Binary variable that takes the value 1 if distribu-tion center 119894 is supplied by supplier ℎ119911119894119895 Binary variable that takes the value 1 if customer 119895is supplied by distribution center 119894119911119895119896 Binary variable that takes the value 1 if fresh food119896 is supplied to customer 119895

34 Distribution Center Location Mathematical Model Thispaper constructs the locationmodel of the distribution centerunder the condition of determinate customer demand thenintroduces the demand uncertainty function and optimizesthe model using the robust optimization method

341 Location Mathematical Model under DeterminateDemand The total cost of the distribution center model isthe minimum total cost which is composed of fixed costsoperating expenses transportation costs delayed penaltycosts and fresh goods corruption costs for distribution cen-tersThe consumer satisfactionmodel includes themaximumfreshness of fresh goods and the maximum accuracy of thedistribution center service time

(1) Fixed costs and operating expenses (1205751)1205751 = sum119894isin119868

119860 119894119910119894 +sum119894isin119868

119861119894119910119894 (1)

(2) Transportation costs (1205752)1205752 = sumℎisin119867

sum119894isin119868

119862ℎ119894119897ℎ119894119889ℎ119894 +sum119894isin119868

sum119895isin119869

119862119894119895119897119894119895119889119894119895 (2)

(3) Delayed penalty costs (1205753)

1205753 = 119891119894119895 (119905119894119895 minus 119879119895)0

119905119894119895 ge 119879119895119905119894119895 lt 119879119895 (3)

(4) Fresh goods corruption costs (1205754)Fresh goods corruption costs can be expressed in terms

of freshness Consumers care about the freshness of productsas visual indicators of their quality Product transport timeand mileage have a large impact on the freshness of certainperishable products Therefore this paper which is based onthe freshness model established by Zhang and Shao-chuan[12] takes the transportation time and the transport distanceas the variables into account We form a new freshnessformula

120601119895119896 = (1 minus 120579119896)sumℎisin119867sum119894isin119868 sum119895isin119869[1205821(119897ℎ119894V+119905119894119895)+1205822(119897ℎ119894+119897119894119895)]119911119894119895 (4)

where the transit time weight is 1205821 the transport distanceweight is 1205822 and the weight is determined according to thespecific transportation distance and the transportation timeFor the convenience of follow-up study in this article 1205821 =1205822 = 05

Fresh goods corruption costs

1205754 = sum119896isin119870

119903119896 (1 minus 120601119895119896) (5)

(5) The freshness of fresh goods (120591119895119896)120591119895119896 = sum119895isin119869sum119896isin119870 119911119895119896120601119895119896sum119895isin119869sum119896isin119870 119911119895119896 (6)

(6) The distribution center service time (120583119895)

120583119895 = sum119894isin119868sum119895isin119869 119911119894119895120596 (119905119894119895)sum119894isin119868sum119895isin119869 119911119894119895 (7)

Scientific Programming 5

120596(119905119894119895) is the consumer satisfaction time function Weuse the satisfaction formula introduced to the literature inYunfeng et al [30]

120596 (119905119894119895) =

1 119905119894119895 le 119879119895min

( 119879119895max minus 119905119894119895119879119895max minus 119879119895min

)120574

119879119895min lt 119905119894119895 le 119879119895max

0 119905119894119895 ge 119879119895max(8)

In summary the models of e-commerce distribution centerlocations are as follows

min 120575 = 1205751 + 1205752 + 1205753 + 1205754 (9)

max 120591119895119896 (10)

max 120583119895 (11)

st sum119894isin119868

119889ℎ119894 le 119880ℎforallℎ isin 119867

(12)

sumℎisin119867

119889ℎ119894 le 119873119894119910119894sum119895isin119869

119889119894119895 le 119873119894119910119894forall119894 isin 119868

(13)

sum119894isin119868

119910119894 le 119908 (14)

sum119894isin119868

119911119894119895 = 1forall119895 isin 119869

(15)

sum119894isin119868

119889119894119895 ge 119889119895forall119895 isin 119869

(16)

119911119894119895 le 119910119894119911ℎ119894 le 119910119894forall119894 isin 119868 forall119895 isin 119869

(17)

119889ℎ119894 ge 0119889119894119895 ge 0 (18)

119910119894 119911ℎ119894 119911119894119895 isin 0 1forall119894 isin 119868 forall119895 isin 119869 (19)

The objective function (9) indicates that the total cost isto be minimized The objective function (10) indicates themaximum freshness of fresh goods The objective function(11) indicates the maximum accuracy of the distributioncenter service time

Constraint (12) is the supply constraint of the supplier Itensures that the total amount of products transported from

supplier ℎ does not exceed the maximum supply capacityConstraints (13) are the distribution center 119894 inventory con-straints and they enforce that the storage of the total freshproduct does not exceed the maximum inventory capacityConstraint (14) represents the number of new distributioncenter constraints Constraint (15) ensures that each customerhas only one candidate distribution center to deliver to himor her Constraint (16) indicates that the volume of freshfoods delivered to the customer cannot be less than thecustomer demand due to possible cargo damage Constraint(17) ensures that the selected distribution center can providedelivery Equations (18) and (19) are constrained by decisionvariables

In the calculation the multiobjective function is trans-formed into a single objective function by the main objectivemethod to select themain objective function according to theenterprisersquos strategic plan If the business goal is to minimizethe total cost and the freshness and the distribution centerservice time only need to achieve a consumer satisfactionthreshold then consumer satisfaction does not have to bemaximized but consumer satisfaction is transformed intoa constraint In this paper the main objective function ischosen to be the minimum total cost and the satisfaction ofthe consumer is set as a constraint

120591119895119896 ge 120572119895119896120583119895 ge 120573119895 (20)

Constraint (20) requires that the freshness of the productmust reach the customer satisfaction threshold and thesatisfaction degree of the distribution center service timemust meet the customer satisfaction threshold for time

In the abovementioned distribution center locationmodel it is assumed that the demand 119889119895 is known and thetotal cost of the decision method can be obtained from theobjective function (9) However in real life there is a greatdeal of uncertainty in the demand for fresh goods so we needto use a robust optimizationmethod to optimize the selectionof locations for distribution centers

342 LocationMathematicalModel underUncertainDemandThe abovementioned distribution center location model isconverted into an equivalent auxiliary model by using robustoptimization The uncertainty of demand is at the coreof obtaining the equivalent auxiliary model This paperuses a series of discrete scenarios to describe the possiblerequirements of the customer

The specific demand of each location is unknown and isconsidered to vary in a closed and bounded box This is acommon description of the uncertainty method

Assuming that the demand scenario is 119904 where 119904 =1 2 119878 is the probability that the demand scenario 119904 ofcustomer 119895 satisfies the ellipsoid uncertainty set The generalform of the box can be specified as follows

119901119895119904 isin Ω = 1199010119895119904 + 119876119906 119890119879119876119906 = 01199010119895119904 + 119876119906 ge 0 119906 le 1 (21)

6 Scientific Programming

where 1199010119895119904 is the most probable probability distribution ofdemand points 119876 isin 119877119899119898times119899119898 is the scope of the zoom119906 denotes the Euclidean norm for perturbation 119890119879119876119906 =0 1199010119895119904 + 119876119906 ge 0 is to ensure that the demand scenarioprobability 119901119895119904 is a probability distribution

Assuming that the demand of each customer is indepen-dent of each other and does not interfere with each otherand the total cost of the site under the demand scenario119904 of customer 119895 is 120575119895119904 the cost of a distribution center isdetermined as follows

120575119894119895 = sum119904isin119878

120575119894119895119904119901119895119904 (22)

The total expected cost for all distribution centers isdetermined as follows

119864 (120575119894) = sum119895isin119869

120575119894119895 = sum119895isin119869

sum119904isin119878

120575119894119895119904119901119895119904 = sum119895isin119869

119901119879119895 120575119895

120575119895 = (1205751198951 1205751198952 120575119895119904)119879 119901119895 = (1199011198951 1199011198952 119901119895119904)119879

(23)

The total cost of the distribution center is transformed

min 119864 (120575) = minsum119895isin119869

119901119879119895 120575119895 (24)

The robust correspondence model of (19) is expressed as

min max119901119895119904isinΩ

119864 (120575) = minmax119901119895119904isinΩ

sum119895isin119869

119901119879119895 120575119895 (25)

The above model is equivalent to

min 120603 (26)

st max119901119895119904isinΩ

sum119895isin119869

119901119879119895 120575119895 le 120603 (27)

119901119895119904 satisfies the demand uncertain set (21) then the leftside of formula (27) is

max119901119895119904isinΩ

sum119895isin119869

119901119879119895 120575119895 = max119901119895119904isinΩ

sum119895isin119869

[(1199010119895119904)119879 120575119895 + (119876119906)119879 120575119895]

= sum119895isin119869

(1199010119895119904)119879 120575119895 + max119901119895119904isinΩ

(119876119906)119879 120575119895(28)

Because 119906 le 1max119901119895119904isinΩ

(119876119906)119879 120575119895 = max119901119895119904isinΩ

119876119879120575119895 (29)

Equation (27) is converted to

sum119895isin119869

(1199010119895119904)119879 120575119895 + max119901119895119904isinΩ

119876119879120575119895 le 120603 (30)

In summary the optimization objective of the robustoptimizationmodel ismin120603 and composed of the constraints(30) and (12) to (20)Themodel has good robustness throughthe robust optimization of the model which can meet theuncertain demand of the customer and ensure the economicfeasibility of the location selection scheme

35 Improved Fruit FlyOptimizationAlgorithm (IFOA) Afterthe above two-step modeling this paper establishes a modelof the distribution center of fresh goods e-commerce underuncertain demand The next important problem is the solu-tion of themodelThe location problem in the uncertain situ-ation is anNP-hard problemThe traditional solutionmethodis complicated and the required amount of is prohibitive forfinding a solution Therefore a heuristic algorithm is used tosolve the problem

FOA is suitable for solving the optimization problemwith complex constraints and strong correlation betweenthe constituent elements of the solution [31] It is widelyused in many classical optimization fields such as efficienttruss optimization [32] gasification process operation opti-mization [33] and analysis of service satisfaction [34] TheFOA algorithm is easy to combine with other methods hasstrong robustness and is suitable for robustly optimizing thelocation of distribution centers Therefore FOA is used tosolve the problem in this paper

351 Fruit Fly Optimization Algorithm (FOA) FOA is out-lined as follows

Step 1 Initialize parameters including the maximumnumber of evaluations (maxgen) and the size of fruitflies (sizepop) and initialize the position of the flies(119883 axis 119884 axis)

Step 2 Randomly initialize the flight direction and distanceof the individual flies where Random Value is the distance inthe search

119883119894 = 119883 axis + Random Value119884119894 = 119884 axis + Random Value (31)

Step 3 The distance of each fly from the origin point and thesmell concentration judgment value is defined as follows

Dist119894 = radic1199091198942 + 1199101198942119878119894 = 1

Dist119894 (32)

Step 4 Based on 119878119894 the smell concentration of flies denotedby Smell119894 is calculated as follows

Smell119894 = function (119878119894) (33)

Step 5 Find the fruit flies with the best smell concentrationand allow the flies to fly to the optimal position

[bestSmell bestindex] = min (Smell119894)Smellbest = bestSmell

119909 axis = 119883 (bestindex)119910 axis = 119884 (bestindex)

(34)

Step 6 Stop the search if the maximum evaluation number isreached otherwise repeat Steps 2ndash5

Scientific Programming 7

Table 1 Test function

Test function Range Optimal Peak

min 1198911 = minusexp(minus05 sdot119899sum119894=1

1199091198942) [minus1 1] minus1 Single

min 1198912 =sin2 (radicsum119899119894=1 1199091198942) minus 05(1 + 0001 (sum119899119894=1 1199091198942))2 + 05 [minus100 100] 0 Multiple

Table 2 Mean and standard deviation of function test

Function Result FOA IFOA

1198911(119909) Mean 30546 times 10minus6 minus1Std 75382 times 10minus6 0

1198912(119909) Mean 31266 times 10minus6 467 times 10minus4Std 86307 times 10minus8 2328 times 10minus3

FOA has great ability to achieve global optimization andhigh convergence accuracy and has great research value in thefield of engineering However the original FOA uses a fixedsearch step and cannot take both global search capabilitiesand local search capabilities into account thus affecting theconvergence rate and search ability Additionally it is easyfor FOA to focus on a local optimum leading to prematureconvergence This paper focuses on the shortcomings of thealgorithm and improves FOAThe purpose of improving theFOA is to make it solve the location model better

352 Improved Fruit Fly Optimization Algorithm (IFOA)In this paper an improved fruit fly optimization algorithm(IFOA) is proposed The search step size is dynamicallyadjusted by introducing the weighting functionThe purposeof dynamic adjustment is to divide the search into two partsThe first part contains a large search step in a large area for aglobal search to ensure that the algorithmconsiders the globaloptimum The second part contains a smaller step search toensure local search capabilities

The fruit fly individual random search expression is asfollows

119883119894 = 119883 axis + 120595 sdot rand ( ) 119884119894 = 119884 axis + 120595 sdot rand ( ) (35)

where 120595 represents the weighted function

120595 = exp(minus 10038161003816100381610038161003816100381610038161003816Smell119894 minus Smell119894minus1

Smell119894

10038161003816100381610038161003816100381610038161003816120577) (36)

where Smell119894 is the 119894th optimal fitness value When the ratiochange is large it indicates that the fly group is searching fora new space and that the weighting function is conducive toa global search When the ratio change is small the fruit flygroup has shifted to a local search and the weight functionis reduced 120577 gt 0 and as 120577 increases fruit fly search abilityincreases which prevents the algorithms from concentratingon a local optimum It can be adjusted according to the actualproblem In addition to the random search expression theother IFOA algorithm step expression is consistent with FOA

353 Test Function To test and analyze the performanceof the improved algorithm the following two classic testfunctions were used to test FOA and IFOA respectivelyFunction form range theoretical extremes and peak areshown in Table 1

The specific initialization parameter is set to sizepop =20 maxgen = 100 We randomly initialize the fliesrsquo popula-tion position The results of the functional tests are shown inTable 2 and the optimization process is shown in Figure 2

From the test results in Table 2 and optimization processIFOA has stronger capabilities of global search local searchand higher convergence accuracy than FOA Under the sameconditions IFOA results are superior to FOA in termsof both mean and standard deviation Under the sameconvergence accuracy the number of valid iterations of IFOAis less than that of FOA which indicates that IFOA convergesfaster Therefore IFOA effectively improves the convergenceprecision and convergence speed of FOA

36 The Calculation Process of Model

(1) Collect the relevant data needed to establish thedistribution center model (as shown in Section 33)

(2) Convert the distribution center model under uncer-tain demand to a tractable equivalent model by usingrobust optimization

(3) IFOA is used to solve the mathematical model

(1) Set the initial parameters including the maxi-mum number of evaluations (maxgen) and thesize of the fruit flies (sizepop) and the initialposition of the flies (119883 axis 119884 axis)

(2) Randomly setting the flight direction and dis-tance of the individual flies the fruit fly individ-ual random search expression is as follows

119883119894 = 119883 axis + 120595 sdot rand () 119884119894 = 119884 axis + 120595 sdot rand () (37)

(3) According to the fitness function formula theindividual fruit fly is calculated to find the

8 Scientific Programming

Table 3 Distance between supplier ℎ and distribution center 119894 (km)

1198681 1198682 1198683 1198684 1198685 1198686 1198687 11986881198671 1431 2912 19945 12093 7738 8814 3214 79831198672 7382 9424 11886 4712 4500 1204 6527 109651198673 13223 11025 10594 3544 9126 6395 7580 6324

0 10 20 30 40 50 60 70 80 90 100minus1

minus0998

minus0996

minus0994

minus0992

minus099

minus0988

minus0986

minus0984

Iteration number

Smel

l

IFOAFOA

0

0002

0004

0006

0008

001

0012

0014

Smel

l

f1(x)

0 10 20 30 40 50 60 70 80 90 100Iteration number

IFOAFOA

f2(x)

Figure 2 Optimization process of FOA and IFOA

position and optimal value of the individual andthe global optimal individual

(4) Find the fruit flies with the best smell concen-tration and allow the flies to fly to the optimalposition

(5) Stop the search if the maximum evaluationnumber is reached otherwise repeat

(6) According to the IFOA optimal location resultsthen find the corresponding best location of thedistribution center and the optimal distributionpath

4 Computational Results

Experiments are proposed in this part to prove the effective-ness and feasibility of the location model Both deterministicand uncertain demand scenarios are considered and then acomparison and analysis of the results of the two situationsis providedThe numerical calculation problem is consideredto occur in a developed city where a fresh goods e-commercefirm chooses to rent a certain number of distribution centerswithin an appropriate area The area of suppliers is 3 and thearea of customers is 10 The firm chooses to rent 3 locationsfrom a set of 8 candidate distribution centers

The distance between the supplier and the candidatedistribution center and the distance between the candidatedistribution center and the demand point are obtained by

using the Euclidean theorem The details are shown inTables 3 and 4 The tables consider the different qualitiesof each candidate distribution center such as the locationtransportation economy and other conditions Fixed costsoperating costs and the largest inventory are also different asshown in Table 5 The maximum supply capacity of supplierℎ is shown in Table 6

The average traveling speed is 45 kmh for the distributionvehicles in the region the average unit freight from thesupplier to the distribution center is 15 yuan(tsdotkm) and thefreight rate from the distribution center to the demand pointis 18 yuan(tsdotkm) To simplify the follow-up calculation thenumerical calculations only consider the distribution of twofresh goods using the corruption coefficients of 015 and008 and the unit prices of 4 yuankg and 6 yuankg Theaverage satisfaction threshold for customer satisfaction is075 and the average satisfaction threshold for freshness is07 If the delivery vehicle arrives late the compensation feeis 50 yuan(hsdott) The demand point time window is shown inTable 7

We consider cases where demand is both deterministicand uncertain The calculation and comparative analysisof two cases can be conducted more directly to verifywhether the model can help the fresh goods e-commerceto suppress the uncertainty interference by demand Themethod used to predict the consumer demand is the multi-variate autoregressive integrated moving average (AMIMA)model in this paper Fresh e-commerce is characterized

Scientific Programming 9

Table 4 Distance between distribution center 119894 and customer 119895 (km)

1198681 1198682 1198683 1198684 1198685 1198686 1198687 11986881198691 14200 4134 24550 16717 8919 11733 7560 144361198692 5420 9642 20535 14220 5903 8628 10072 180711198693 11610 1170 19564 11682 5178 7156 2469 102011198694 6525 18398 13761 12419 12180 11123 16497 214241198695 4827 7716 17279 10536 2282 4850 7000 145791198696 9904 15932 6296 4810 10720 7694 12857 146731198697 22649 13509 20341 14670 16589 15631 12035 48871198698 10718 3383 17310 9420 4161 5215 721 89051198699 12879 19474 3981 7506 14322 11287 16319 1711411986910 15277 14586 7910 3984 12248 9166 11140 8238

Table 5 Fixed costs operating costs and maximum inventory

Candidate distribution centers 1198681 1198682 1198683 1198684 1198685 1198686 1198687 1198688Fixed costs (million) 145 138 123 148 129 123 138 136Operating costs (million) 007 006 006 009 005 006 007 006Maximum inventoryt 1000 900 700 1100 1000 900 1200 800

Table 6 The maximum supply capacity of supplier

Supplier 1198671 1198672 1198673Themaximum supply capacityt 8800 7900 6300

Table 7 Time window and determined demand of customer

Customer (119879119895min 119879119895 119879119895max) Demand (t)1198691 (2 25 3) 2001198692 (3 4 5) 4001198693 (1 15 2) 3501198694 (1 2 25) 2501198695 (2 3 4) 1501198696 (3 35 4) 3501198697 (15 25 3) 3001198698 (2 3 45) 1801198699 (15 25 3) 35011986910 (3 4 5) 300

by consumers ordering through the Internet so fresh e-commerce companies can collect customer information andorder information (eg customersrsquo purchasing frequencypurchasing preferences and position distribution) Thenthe fresh e-commerce company can use this informationto classify consumers and predict consumer demand Theautoregressive part of the multiple ARIMAmodel representsa linear combination of past values while themoving averagepart of the multiple ARIMAmodel is a linear combination ofpast forecasting errorsThe advantage of themultiple ARIMAmodel is that it improves prediction accuracy facilitatesstatistics and reduces the cost of prediction Moreover it cancombine product cost changes with demand uncertainty topredict consumer demand [35] In view of this the multi-variate ARIMA model is suitable to predict the consumerdemand for fresh e-commerce Although the AMIMAmodel

can more accurately predict the uncertainty of demand thesize of fresh e-commercersquos consumers is small and widelydistributed so there is still uncertainty in demand To learnmore about the multivariate ARIMA model studies [35 36]are suggested The deterministic demand for each customeris shown in Table 7

The affected factors of uncertain supply involve envi-ronmental factors (eg the natural environment economicenvironment and political environment) and the abilities ofsuppliers (eg production capacity equipment capacity) [37]First the planting period for fresh foods is the quarter or yearas a unit the period is longer than for other products Fresh e-commerce can be investigated in advance through the Inter-net and then the product cultivation of the fresh food and thefield investigation can be planned accordingly Second thesuppliers of fresh electricity providers are typically farmersand fresh food bases around the region These suppliersare less affected by global economic changes and politicalchanges The selection diversity of suppliers also allows freshe-commerce companies to evaluate and select suppliers inadvance In addition the equipment failure problem has lessof an effect on fresh e-commerce because fresh productscan be delivered to the distribution center though simplepretreatment packaging In summary the supply of fresh e-commerce is uncertain but fresh e-commerce companies areless affected by these uncertain factors due to the specialnature of fresh foods The current delivery mode of freshproducts is from a mono type and large batch distributionto a multitype delivery mode and small batch distributionEach time an order is made the consumer evaluates thefresh electricity service (eg Amazon Fresh and MotionOptimization) For the majority of instances the perishablenature of a product results in the supply process having alower variability than the demand process [38] Thereforethis paper focuses on the location model for distributioncenters under uncertain demand

10 Scientific Programming

0 009 014027033

071093

119

165 175191

0

0005

001

0015

002

0025

0 01 02 03 04 05 06 07 08 09 1

The i

ncre

ase r

atio

The value of a

Figure 3 The increase ratio of the total cost of uncertain demand

For the case of uncertainty we assume that the demandfor each demand point is 119904 = 5 The number of scenariosfor each demand point can be different from each other Thevalue of the demand scenario is determined by the surveyand then the five cases are generated randomly by Matlab 83as the demand scenario of the demand point 119895 The demandscenario of the 10 demandpoints can be obtained by repeatingthe process ten times

The discrete demand probability distribution is 1199010119895119904 119869 =119895 | 119895 = 1 2 119899For 1199010119895119904 in the range (0 1) the simulations are randomly

generated between the 10 numbers normalized and repeatedten times in order to get all the demand points in theuncertain demand scenarioTheprobability demand scenarioof customer 119895 (119901119895119904) meets the uncertainty set Let thedecentralized matrix be 119876 = 119886119868 where 119886 is a nonnegativeparameter and 119868 is an identity matrix

In the experiment let 119886 = 05 and 119886 = 08 respectivelyCalculate 119901119895119904

The specific initialization parameter is set to maxgen =100 sizepop = 20 The program is implemented in Matlab83 and run on a computer with 26GHz Intel i5-4210MCPU 4GB of RAM andWindows 10The distribution centerdecision-making program and the total cost are shown inTable 8

For the deterministic demand situation the optimal deci-sion is to choose distribution center 119868211986851198686 from the candidatelist The total cost is 7208 million For the uncertain demandsituation when 119886 = 01 to 119886 = 04 the optimal decision isto choose distribution centers 119868211986851198686 The distribution rangeis constant but the cost increases When 119886 = 05 to 119886 = 07the optimal decision is to choose distribution centers 119868211986851198686but the distribution range is different from the deterministicdemand situation When 119886 = 08 to 119886 = 1 the optimaldecision is to choose distribution centers 119868511986861198687 The increaseratio of the total cost in the case of uncertainty is comparedto the total cost in the demand determination as shownin Figure 3 Enterprises in the decision-making before theconsumer demand should be the historical data for statisticaland analysis determine the variation range of parameter119886 and make decisions based on cost and self-conditions(Figure 3)

Then using FOA to solve themodel and initial parametersand operating environment equally with IFOA the results are

Table 8 The decision-making program and the total cost ofdistribution center

The value of 119886 Decision-makingprogram and

distribution rangeCost (RMB)

119886 = 0 1198682 1198691 1198693 11986977208563141198685 1198692 1198695 11986981198686 1198694 1198696 1198699 11986910

119886 = 01 1198682 1198691 1198693 11986977215050851198685 1198692 1198695 11986981198686 1198694 1198696 1198699 11986910

119886 = 02 1198682 1198691 1198693 11986977218655131198685 1198692 1198695 11986981198686 1198694 1198696 1198699 11986910

119886 = 03 1198682 1198691 1198693 11986977228026261198685 1198692 1198695 11986981198686 1198694 1198696 1198699 11986910

119886 = 04 1198682 1198691 1198693 11986977232351401198685 1198692 1198695 11986981198686 1198694 1198696 1198699 11986910

119886 = 05 1198682 1198691 1198693 11986977259452741198685 1198692 1198694 1198695 11986981198686 1198696 1198699 11986910

119886 = 06 1198682 1198691 1198693 11986977275602781198685 1198692 1198694 1198695 11986981198686 1198696 1198699 11986910

119886 = 07 1198682 1198691 1198693 11986977294345041198685 1198692 1198694 1198695 11986981198686 1198696 1198699 11986910

119886 = 08 1198685 1198692 11986957327583631198686 1198694 1198696 1198699 119869101198687 1198691 1198693 1198697 1198698

119886 = 09 1198685 1198692 11986957334712991198686 1198694 1198696 1198699 119869101198687 1198691 1198693 1198697 1198698

119886 = 1 1198685 1198692 11986957346246701198686 1198694 1198696 1198699 119869101198687 1198691 1198693 1198697 1198698

shown in Table 9 the difference value of IFOA and FOA isshown in Figure 4 and the optimization process of FOA andIFOA is shown in Figure 5 (select 119886 = 05)

From the test results in Table 9 and Figures 4 and 5under the same conditions IFOA results are superior to FOAthe convergence accuracy is more accurate and the optimalresults are better Under the same convergence accuracythe number of valid iterations of IFOA is less than that ofFOA which indicates that IFOA converges faster ThereforeIFOA effectively improves the convergence precision andconvergence speed of FOAThe applicability of IFOA is moreextensive

Scientific Programming 11

Table 9 The results of FOA and IFOA

The value of 119886 IFOA optimal FOA optimal119886 = 0 720856314 720874332119886 = 01 721505085 721515326119886 = 02 721865513 721881176119886 = 03 722802626 72285562119886 = 04 723235140 723309877119886 = 05 725945274 726005691119886 = 06 727560278 727613354119886 = 07 729434504 729495412119886 = 08 732758363 732827122119886 = 09 733471299 733549837119886 = 1 734624670 734714368

18018 10241 15663

52994

7473760417

5307660908

6875978538

89698

000100002000030000400005000060000700008000090000

100000

0 01 02 03 04 05 06 07 08 09 1

The d

iffer

ent v

alue

The value of a

Figure 4 The difference value of IFOA and FOA

0 10 20 30 40 50 60 70 80 90 1007

75

8

85

9

95

Iteration number

Cos

t

IFOAFOA

times106

Figure 5 Optimization process of FOA and IFOA (119886 = 05)

5 Conclusions

The location of distribution centers is a complex optimizationproblem To solve the problem of unreasonable networklayout and poor interpretation of customer demand and highcost of distribution this paper optimizes the location ofdistribution centers minimizes the total cost of distributionand establishes a fast and secure distribution center networksystem The conclusions of this paper are summarized asfollows

In this paper a distribution center model is established toreduce the total cost of the enterpriseThemodel is combinedwith the inherent characteristics of fresh goods e-commercetaking into account the principles of distribution centerselection service levels and freshness constraints Due to theincrease in the number of fresh goods e-commerce enter-prises with more intense competition consumer demand ismore and more uncertain Robust optimization is used tooptimize the distribution center model which makes themodel more robust

An improved fruit fly optimization algorithm (IFOA) isproposed in this paper The search step size is dynamicallyadjusted by introducing a weighting function IFOA willserve to solve the established model However the applica-bility of IFOA is more general In this paper we validatethe uncertain demand model by using an example and weprove that the model of distribution centers is valid and caneffectively handle the uncertainty of demand

This paper considers the influence of uncertain demandon the location of distribution centers for fresh goods Itenriches the fresh goods e-commerce distribution centermodel and provides a theoretical basis for a scientific methodof selecting the locations of fresh e-commerce distributioncenters The applicability of the proposed model is mean-ingful and useful for the selection of fresh e-commercedistribution center locations The shortcomings of this paperis that it only considers the uncertainty of customer demandand does not take into account other factors of uncertaintysuch as uncertain delivery weather conditions and uncertaincorruption rate

It is worth noting that some aspects of the model needto be improved For example we will pay more attentionto a variety of uncertain factors so that the model is moresuitable formore complex situations Because the distributioncenter will be related to the distribution of fresh productscoupled with the international awareness of environmentalprotection strengthened gradually the future will take intoaccount the impacts of low-carbon environmental aspects ofthe distribution center location model

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

This research was sponsored by Project of National SocialScience Foundation of China (15BGL202) project of theplanning subject of ldquothe 12th Five-Year Planrdquo in NationalScience and Technology for the Rural Development inChina Demonstration of Key Technology and Equipment forSafe Distribution of Agricultural Logistics (2015BAD18B01)Project of Beijing Philosophy and Social Science (17GBL013)Project of Beijing Municipal Commission of Education(SM201410011002) Project of Innovation Ability Promotion(PXM2016 014213 000033) 2017 Beijing Technology andBusiness University postgraduate student research abilityenhancing project

12 Scientific Programming

References

[1] RAccorsi AGallo andRManzini ldquoA climate driven decision-support model for the distribution of perishable productsrdquoJournal of Cleaner Production vol 165 pp 917ndash929 2017

[2] E Morganti and J Gonzalez-Feliu ldquoCity logistics for perishableproducts The case of the Parmarsquos Food Hubrdquo Case Studies onTransport Policy vol 3 no 2 pp 120ndash128 2015

[3] J A Orjuela-Castro L A Sanabria-Coronado and Peralta-Lozano A M ldquoCoupling facility location models in the supplychain of perishable fruitsrdquo Research in Transportation Businessamp Management 2017

[4] M Merakli and H Yaman ldquoRobust intermodal hub loca-tion under polyhedral demand uncertaintyrdquo TransportationResearch Part B Methodological vol 86 pp 66ndash85 2016

[5] M a Schuster Puga and J-S Tancrez ldquoA heuristic algorithmfor solving large location-inventory problems with demanduncertaintyrdquo European Journal of Operational Research vol 259no 2 pp 413ndash423 2017

[6] A Hiassat A Diabat and I Rahwan ldquoA genetic algorithmapproach for location-inventory-routing problem with perish-able productsrdquo Journal of Manufacturing Systems vol 42 pp93ndash103 2017

[7] K Govindan A Jafarian R Khodaverdi and K DevikaldquoTwo-echelon multiple-vehicle location-routing problem withtime windows for optimization of sustainable supply chainnetwork of perishable foodrdquo International Journal of ProductionEconomics vol 152 pp 9ndash28 2014

[8] Z Drezner and C H Scott ldquoLocation of a distribution centerfor a perishable productrdquo Mathematical Methods of OperationsResearch vol 78 no 3 pp 301ndash314 2013

[9] S M Seyedhosseini and S M Ghoreyshi ldquoAn integrated modelfor production and distribution planning of perishable prod-ucts with inventory and routing considerationsrdquo MathematicalProblems in Engineering vol 2014 Article ID 475606 10 pages2014

[10] M de Keizer R Akkerman M Grunow J M Bloemhof RHaijema and J G van der Vorst ldquoLogistics network designfor perishable products with heterogeneous quality decayrdquoEuropean Journal of Operational Research vol 262 no 2 pp535ndash549 2017

[11] H Yang L I Hong DUWei et al ldquoResearch on location selec-tion of perishable dairy products distribution center based ontwo-stage distributionrdquoComputer Engineering andApplicationsvol 23 pp 239ndash245 2015

[12] J Zhang and F U Shao-chuan ldquoStudy on location of fresh fooddistribution center with demand influenced by the freshnessrdquoChinese Journal of Management Science vol 19 no 10 pp 473ndash476 2011

[13] T Wu H Shen and C Zhu ldquoA multi-period location modelwith transportation economies-of-scale and perishable inven-toryrdquo International Journal of Production Economics vol 169 pp343ndash349 2015

[14] M Musavi and A Bozorgi-Amiri ldquoA multi-objective sus-tainable hub location-scheduling problem for perishable foodsupply chainrdquo Computers amp Industrial Engineering 2017

[15] M Rezaei-Malek R Tavakkoli-Moghaddam B Zahiri and ABozorgi-Amiri ldquoAn interactive approach for designing a robustdisaster relief logistics network with perishable commoditiesrdquoComputers amp Industrial Engineering vol 94 pp 201ndash215 2016

[16] K Khalili-Damghani A-R Abtahi andA Ghasemi ldquoA new bi-objective location-routing problem for distribution of perish-able products evolutionary computation approachrdquo Journal ofMathematical Modelling and Algorithms in Operations Researchvol 14 no 3 pp 287ndash312 2015

[17] Y Zhang Y Jiang M Zhong N Geng and D Chen ldquoRobustOptimization on Regional WCO-for-Biodiesel Supply Chainunder Supply and Demand Uncertaintiesrdquo Scientific Program-ming vol 2016 Article ID 1087845 15 pages 2016

[18] R Qiu and Y Wang ldquoSupply chain network design underdemand uncertainty and supply disruptions a distributionallyrobust optimization approachrdquo Scientific Programming vol2016 Article ID 3848520 15 pages 2016

[19] A Ben-Tal E Hazan T Koren and S Mannor ldquoOracle-basedrobust optimization via online learningrdquo Operations Researchvol 63 no 3 pp 628ndash638 2015

[20] M Melamed A Ben-Tal and B Golany ldquoOn the averageperformance of the adjustable RO and its use as an offlinetool for multi-period production planning under uncertaintyrdquoComputational Management Science vol 13 no 2 pp 293ndash3152016

[21] A Ghodratnama R Tavakkoli-Moghaddam and A AzaronldquoRobust and fuzzy goal programming optimization approachesfor a novel multi-objective hub location-allocation problem Asupply chain overviewrdquoApplied SoftComputing vol 37 pp 255ndash276 2015

[22] F Habibzadeh Boukani B Farhang Moghaddam and M SPishvaee ldquoRobust optimization approach to capacitated singleand multiple allocation hub location problemsrdquo Computationalamp Applied Mathematics vol 35 no 1 pp 45ndash60 2016

[23] A Jakubovskis ldquoStrategic facility location capacity acquisitionand technology choice decisions under demand uncertaintyrobust vs non-robust optimization approachesrdquo European Jour-nal of Operational Research vol 260 no 3 pp 1095ndash1104 2017

[24] H A Eiselt and V Marianov ldquoA bi-objective model for thelocation of landfills formunicipal solidwasterdquoEuropean Journalof Operational Research vol 235 no 1 pp 187ndash194 2014

[25] M G Bardossy and S Raghavan ldquoRobust Optimization forthe Connected Facility Location Problemrdquo Electronic Notes inDiscrete Mathematics vol 44 pp 149ndash154 2013

[26] V de Rosa E Hartmann M Gebhard and J WollenweberldquoRobust capacitated facility location model for acquisitionsunder uncertaintyrdquoComputers amp Industrial Engineering vol 72pp 206ndash216 2014

[27] M Ehrgott J Ide and A Schoobel ldquoMinmax robustness formulti-objective optimization problemsrdquo European Journal ofOperational Research vol 239 no 1 pp 17ndash31 2014

[28] X-F Xu J Hao Y-R Deng and YWang ldquoDesign optimizationof resource combination for collaborative logistics networkunder uncertaintyrdquo Applied Soft Computing vol 56 pp 684ndash691 2017

[29] E D Majewski M Wirtz M Lampe and etal ldquoRobust multi-objective optimization for sustainable design of distributedenergy supply systemsrdquoComputersampChemical Engineering vol102 pp 26ndash39 2016

[30] M Yunfeng Y Chao M Zhang and H Chunyan ldquoTime-satisfaction-based maximal covering location problemrdquo Chi-nese Journal of Management Science vol 2 pp 45ndash51 2006

[31] W-T Pan ldquoA new fruit fly optimization algorithm takingthe financial distress model as an examplerdquo Knowledge-BasedSystems vol 26 pp 69ndash74 2012

Scientific Programming 13

[32] S Kanarachos J Griffin and M E Fitzpatrick ldquoEfficient trussoptimization using the contrast-based fruit fly optimizationalgorithmrdquo Computers amp Structures vol 182 pp 137ndash148 2017

[33] J Niu W Zhong Y Liang N Luo and F Qian ldquoFruit flyoptimization algorithm based on differential evolution andits application on gasification process operation optimizationrdquoKnowledge-Based Systems vol 88 pp 253ndash263 2015

[34] S-M Lin ldquoAnalysis of service satisfaction in web auctionlogistics service using a combination of Fruit fly optimizationalgorithm and general regression neural networkrdquoNeural Com-puting and Applications vol 22 no 3-4 pp 783ndash791 2013

[35] J Huber A Gossmann andH Stuckenschmidt ldquoCluster-basedhierarchical demand forecasting for perishable goodsrdquo ExpertSystems with Applications vol 76 pp 140ndash151 2017

[36] M Shukla and S Jharkharia ldquoApplicability of ARIMA modelsin wholesale vegetable market An investigationrdquo InternationalJournal of Information Systems and Supply Chain Managementvol 6 no 3 pp 105ndash119 2013

[37] C Sun and X Luo ldquoThe influencing factors and countermea-sures of supply uncertainty in supply chainrdquo Economic ResearchGuide vol 11 pp 146-147 2013

[38] S Minner and S Transchel ldquoOrder variability in perish-able product supply chainsrdquo European Journal of OperationalResearch vol 260 no 1 pp 93ndash107 2017

Submit your manuscripts athttpswwwhindawicom

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Applied Computational Intelligence and Soft Computing

thinspAdvancesthinspinthinsp

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HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014

Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Electrical and Computer Engineering

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httpwwwhindawicom Volume 2014

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International Journal of

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RoboticsJournal of

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Computational Intelligence and Neuroscience

Industrial EngineeringJournal of

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Scientific Programming 5

120596(119905119894119895) is the consumer satisfaction time function Weuse the satisfaction formula introduced to the literature inYunfeng et al [30]

120596 (119905119894119895) =

1 119905119894119895 le 119879119895min

( 119879119895max minus 119905119894119895119879119895max minus 119879119895min

)120574

119879119895min lt 119905119894119895 le 119879119895max

0 119905119894119895 ge 119879119895max(8)

In summary the models of e-commerce distribution centerlocations are as follows

min 120575 = 1205751 + 1205752 + 1205753 + 1205754 (9)

max 120591119895119896 (10)

max 120583119895 (11)

st sum119894isin119868

119889ℎ119894 le 119880ℎforallℎ isin 119867

(12)

sumℎisin119867

119889ℎ119894 le 119873119894119910119894sum119895isin119869

119889119894119895 le 119873119894119910119894forall119894 isin 119868

(13)

sum119894isin119868

119910119894 le 119908 (14)

sum119894isin119868

119911119894119895 = 1forall119895 isin 119869

(15)

sum119894isin119868

119889119894119895 ge 119889119895forall119895 isin 119869

(16)

119911119894119895 le 119910119894119911ℎ119894 le 119910119894forall119894 isin 119868 forall119895 isin 119869

(17)

119889ℎ119894 ge 0119889119894119895 ge 0 (18)

119910119894 119911ℎ119894 119911119894119895 isin 0 1forall119894 isin 119868 forall119895 isin 119869 (19)

The objective function (9) indicates that the total cost isto be minimized The objective function (10) indicates themaximum freshness of fresh goods The objective function(11) indicates the maximum accuracy of the distributioncenter service time

Constraint (12) is the supply constraint of the supplier Itensures that the total amount of products transported from

supplier ℎ does not exceed the maximum supply capacityConstraints (13) are the distribution center 119894 inventory con-straints and they enforce that the storage of the total freshproduct does not exceed the maximum inventory capacityConstraint (14) represents the number of new distributioncenter constraints Constraint (15) ensures that each customerhas only one candidate distribution center to deliver to himor her Constraint (16) indicates that the volume of freshfoods delivered to the customer cannot be less than thecustomer demand due to possible cargo damage Constraint(17) ensures that the selected distribution center can providedelivery Equations (18) and (19) are constrained by decisionvariables

In the calculation the multiobjective function is trans-formed into a single objective function by the main objectivemethod to select themain objective function according to theenterprisersquos strategic plan If the business goal is to minimizethe total cost and the freshness and the distribution centerservice time only need to achieve a consumer satisfactionthreshold then consumer satisfaction does not have to bemaximized but consumer satisfaction is transformed intoa constraint In this paper the main objective function ischosen to be the minimum total cost and the satisfaction ofthe consumer is set as a constraint

120591119895119896 ge 120572119895119896120583119895 ge 120573119895 (20)

Constraint (20) requires that the freshness of the productmust reach the customer satisfaction threshold and thesatisfaction degree of the distribution center service timemust meet the customer satisfaction threshold for time

In the abovementioned distribution center locationmodel it is assumed that the demand 119889119895 is known and thetotal cost of the decision method can be obtained from theobjective function (9) However in real life there is a greatdeal of uncertainty in the demand for fresh goods so we needto use a robust optimizationmethod to optimize the selectionof locations for distribution centers

342 LocationMathematicalModel underUncertainDemandThe abovementioned distribution center location model isconverted into an equivalent auxiliary model by using robustoptimization The uncertainty of demand is at the coreof obtaining the equivalent auxiliary model This paperuses a series of discrete scenarios to describe the possiblerequirements of the customer

The specific demand of each location is unknown and isconsidered to vary in a closed and bounded box This is acommon description of the uncertainty method

Assuming that the demand scenario is 119904 where 119904 =1 2 119878 is the probability that the demand scenario 119904 ofcustomer 119895 satisfies the ellipsoid uncertainty set The generalform of the box can be specified as follows

119901119895119904 isin Ω = 1199010119895119904 + 119876119906 119890119879119876119906 = 01199010119895119904 + 119876119906 ge 0 119906 le 1 (21)

6 Scientific Programming

where 1199010119895119904 is the most probable probability distribution ofdemand points 119876 isin 119877119899119898times119899119898 is the scope of the zoom119906 denotes the Euclidean norm for perturbation 119890119879119876119906 =0 1199010119895119904 + 119876119906 ge 0 is to ensure that the demand scenarioprobability 119901119895119904 is a probability distribution

Assuming that the demand of each customer is indepen-dent of each other and does not interfere with each otherand the total cost of the site under the demand scenario119904 of customer 119895 is 120575119895119904 the cost of a distribution center isdetermined as follows

120575119894119895 = sum119904isin119878

120575119894119895119904119901119895119904 (22)

The total expected cost for all distribution centers isdetermined as follows

119864 (120575119894) = sum119895isin119869

120575119894119895 = sum119895isin119869

sum119904isin119878

120575119894119895119904119901119895119904 = sum119895isin119869

119901119879119895 120575119895

120575119895 = (1205751198951 1205751198952 120575119895119904)119879 119901119895 = (1199011198951 1199011198952 119901119895119904)119879

(23)

The total cost of the distribution center is transformed

min 119864 (120575) = minsum119895isin119869

119901119879119895 120575119895 (24)

The robust correspondence model of (19) is expressed as

min max119901119895119904isinΩ

119864 (120575) = minmax119901119895119904isinΩ

sum119895isin119869

119901119879119895 120575119895 (25)

The above model is equivalent to

min 120603 (26)

st max119901119895119904isinΩ

sum119895isin119869

119901119879119895 120575119895 le 120603 (27)

119901119895119904 satisfies the demand uncertain set (21) then the leftside of formula (27) is

max119901119895119904isinΩ

sum119895isin119869

119901119879119895 120575119895 = max119901119895119904isinΩ

sum119895isin119869

[(1199010119895119904)119879 120575119895 + (119876119906)119879 120575119895]

= sum119895isin119869

(1199010119895119904)119879 120575119895 + max119901119895119904isinΩ

(119876119906)119879 120575119895(28)

Because 119906 le 1max119901119895119904isinΩ

(119876119906)119879 120575119895 = max119901119895119904isinΩ

119876119879120575119895 (29)

Equation (27) is converted to

sum119895isin119869

(1199010119895119904)119879 120575119895 + max119901119895119904isinΩ

119876119879120575119895 le 120603 (30)

In summary the optimization objective of the robustoptimizationmodel ismin120603 and composed of the constraints(30) and (12) to (20)Themodel has good robustness throughthe robust optimization of the model which can meet theuncertain demand of the customer and ensure the economicfeasibility of the location selection scheme

35 Improved Fruit FlyOptimizationAlgorithm (IFOA) Afterthe above two-step modeling this paper establishes a modelof the distribution center of fresh goods e-commerce underuncertain demand The next important problem is the solu-tion of themodelThe location problem in the uncertain situ-ation is anNP-hard problemThe traditional solutionmethodis complicated and the required amount of is prohibitive forfinding a solution Therefore a heuristic algorithm is used tosolve the problem

FOA is suitable for solving the optimization problemwith complex constraints and strong correlation betweenthe constituent elements of the solution [31] It is widelyused in many classical optimization fields such as efficienttruss optimization [32] gasification process operation opti-mization [33] and analysis of service satisfaction [34] TheFOA algorithm is easy to combine with other methods hasstrong robustness and is suitable for robustly optimizing thelocation of distribution centers Therefore FOA is used tosolve the problem in this paper

351 Fruit Fly Optimization Algorithm (FOA) FOA is out-lined as follows

Step 1 Initialize parameters including the maximumnumber of evaluations (maxgen) and the size of fruitflies (sizepop) and initialize the position of the flies(119883 axis 119884 axis)

Step 2 Randomly initialize the flight direction and distanceof the individual flies where Random Value is the distance inthe search

119883119894 = 119883 axis + Random Value119884119894 = 119884 axis + Random Value (31)

Step 3 The distance of each fly from the origin point and thesmell concentration judgment value is defined as follows

Dist119894 = radic1199091198942 + 1199101198942119878119894 = 1

Dist119894 (32)

Step 4 Based on 119878119894 the smell concentration of flies denotedby Smell119894 is calculated as follows

Smell119894 = function (119878119894) (33)

Step 5 Find the fruit flies with the best smell concentrationand allow the flies to fly to the optimal position

[bestSmell bestindex] = min (Smell119894)Smellbest = bestSmell

119909 axis = 119883 (bestindex)119910 axis = 119884 (bestindex)

(34)

Step 6 Stop the search if the maximum evaluation number isreached otherwise repeat Steps 2ndash5

Scientific Programming 7

Table 1 Test function

Test function Range Optimal Peak

min 1198911 = minusexp(minus05 sdot119899sum119894=1

1199091198942) [minus1 1] minus1 Single

min 1198912 =sin2 (radicsum119899119894=1 1199091198942) minus 05(1 + 0001 (sum119899119894=1 1199091198942))2 + 05 [minus100 100] 0 Multiple

Table 2 Mean and standard deviation of function test

Function Result FOA IFOA

1198911(119909) Mean 30546 times 10minus6 minus1Std 75382 times 10minus6 0

1198912(119909) Mean 31266 times 10minus6 467 times 10minus4Std 86307 times 10minus8 2328 times 10minus3

FOA has great ability to achieve global optimization andhigh convergence accuracy and has great research value in thefield of engineering However the original FOA uses a fixedsearch step and cannot take both global search capabilitiesand local search capabilities into account thus affecting theconvergence rate and search ability Additionally it is easyfor FOA to focus on a local optimum leading to prematureconvergence This paper focuses on the shortcomings of thealgorithm and improves FOAThe purpose of improving theFOA is to make it solve the location model better

352 Improved Fruit Fly Optimization Algorithm (IFOA)In this paper an improved fruit fly optimization algorithm(IFOA) is proposed The search step size is dynamicallyadjusted by introducing the weighting functionThe purposeof dynamic adjustment is to divide the search into two partsThe first part contains a large search step in a large area for aglobal search to ensure that the algorithmconsiders the globaloptimum The second part contains a smaller step search toensure local search capabilities

The fruit fly individual random search expression is asfollows

119883119894 = 119883 axis + 120595 sdot rand ( ) 119884119894 = 119884 axis + 120595 sdot rand ( ) (35)

where 120595 represents the weighted function

120595 = exp(minus 10038161003816100381610038161003816100381610038161003816Smell119894 minus Smell119894minus1

Smell119894

10038161003816100381610038161003816100381610038161003816120577) (36)

where Smell119894 is the 119894th optimal fitness value When the ratiochange is large it indicates that the fly group is searching fora new space and that the weighting function is conducive toa global search When the ratio change is small the fruit flygroup has shifted to a local search and the weight functionis reduced 120577 gt 0 and as 120577 increases fruit fly search abilityincreases which prevents the algorithms from concentratingon a local optimum It can be adjusted according to the actualproblem In addition to the random search expression theother IFOA algorithm step expression is consistent with FOA

353 Test Function To test and analyze the performanceof the improved algorithm the following two classic testfunctions were used to test FOA and IFOA respectivelyFunction form range theoretical extremes and peak areshown in Table 1

The specific initialization parameter is set to sizepop =20 maxgen = 100 We randomly initialize the fliesrsquo popula-tion position The results of the functional tests are shown inTable 2 and the optimization process is shown in Figure 2

From the test results in Table 2 and optimization processIFOA has stronger capabilities of global search local searchand higher convergence accuracy than FOA Under the sameconditions IFOA results are superior to FOA in termsof both mean and standard deviation Under the sameconvergence accuracy the number of valid iterations of IFOAis less than that of FOA which indicates that IFOA convergesfaster Therefore IFOA effectively improves the convergenceprecision and convergence speed of FOA

36 The Calculation Process of Model

(1) Collect the relevant data needed to establish thedistribution center model (as shown in Section 33)

(2) Convert the distribution center model under uncer-tain demand to a tractable equivalent model by usingrobust optimization

(3) IFOA is used to solve the mathematical model

(1) Set the initial parameters including the maxi-mum number of evaluations (maxgen) and thesize of the fruit flies (sizepop) and the initialposition of the flies (119883 axis 119884 axis)

(2) Randomly setting the flight direction and dis-tance of the individual flies the fruit fly individ-ual random search expression is as follows

119883119894 = 119883 axis + 120595 sdot rand () 119884119894 = 119884 axis + 120595 sdot rand () (37)

(3) According to the fitness function formula theindividual fruit fly is calculated to find the

8 Scientific Programming

Table 3 Distance between supplier ℎ and distribution center 119894 (km)

1198681 1198682 1198683 1198684 1198685 1198686 1198687 11986881198671 1431 2912 19945 12093 7738 8814 3214 79831198672 7382 9424 11886 4712 4500 1204 6527 109651198673 13223 11025 10594 3544 9126 6395 7580 6324

0 10 20 30 40 50 60 70 80 90 100minus1

minus0998

minus0996

minus0994

minus0992

minus099

minus0988

minus0986

minus0984

Iteration number

Smel

l

IFOAFOA

0

0002

0004

0006

0008

001

0012

0014

Smel

l

f1(x)

0 10 20 30 40 50 60 70 80 90 100Iteration number

IFOAFOA

f2(x)

Figure 2 Optimization process of FOA and IFOA

position and optimal value of the individual andthe global optimal individual

(4) Find the fruit flies with the best smell concen-tration and allow the flies to fly to the optimalposition

(5) Stop the search if the maximum evaluationnumber is reached otherwise repeat

(6) According to the IFOA optimal location resultsthen find the corresponding best location of thedistribution center and the optimal distributionpath

4 Computational Results

Experiments are proposed in this part to prove the effective-ness and feasibility of the location model Both deterministicand uncertain demand scenarios are considered and then acomparison and analysis of the results of the two situationsis providedThe numerical calculation problem is consideredto occur in a developed city where a fresh goods e-commercefirm chooses to rent a certain number of distribution centerswithin an appropriate area The area of suppliers is 3 and thearea of customers is 10 The firm chooses to rent 3 locationsfrom a set of 8 candidate distribution centers

The distance between the supplier and the candidatedistribution center and the distance between the candidatedistribution center and the demand point are obtained by

using the Euclidean theorem The details are shown inTables 3 and 4 The tables consider the different qualitiesof each candidate distribution center such as the locationtransportation economy and other conditions Fixed costsoperating costs and the largest inventory are also different asshown in Table 5 The maximum supply capacity of supplierℎ is shown in Table 6

The average traveling speed is 45 kmh for the distributionvehicles in the region the average unit freight from thesupplier to the distribution center is 15 yuan(tsdotkm) and thefreight rate from the distribution center to the demand pointis 18 yuan(tsdotkm) To simplify the follow-up calculation thenumerical calculations only consider the distribution of twofresh goods using the corruption coefficients of 015 and008 and the unit prices of 4 yuankg and 6 yuankg Theaverage satisfaction threshold for customer satisfaction is075 and the average satisfaction threshold for freshness is07 If the delivery vehicle arrives late the compensation feeis 50 yuan(hsdott) The demand point time window is shown inTable 7

We consider cases where demand is both deterministicand uncertain The calculation and comparative analysisof two cases can be conducted more directly to verifywhether the model can help the fresh goods e-commerceto suppress the uncertainty interference by demand Themethod used to predict the consumer demand is the multi-variate autoregressive integrated moving average (AMIMA)model in this paper Fresh e-commerce is characterized

Scientific Programming 9

Table 4 Distance between distribution center 119894 and customer 119895 (km)

1198681 1198682 1198683 1198684 1198685 1198686 1198687 11986881198691 14200 4134 24550 16717 8919 11733 7560 144361198692 5420 9642 20535 14220 5903 8628 10072 180711198693 11610 1170 19564 11682 5178 7156 2469 102011198694 6525 18398 13761 12419 12180 11123 16497 214241198695 4827 7716 17279 10536 2282 4850 7000 145791198696 9904 15932 6296 4810 10720 7694 12857 146731198697 22649 13509 20341 14670 16589 15631 12035 48871198698 10718 3383 17310 9420 4161 5215 721 89051198699 12879 19474 3981 7506 14322 11287 16319 1711411986910 15277 14586 7910 3984 12248 9166 11140 8238

Table 5 Fixed costs operating costs and maximum inventory

Candidate distribution centers 1198681 1198682 1198683 1198684 1198685 1198686 1198687 1198688Fixed costs (million) 145 138 123 148 129 123 138 136Operating costs (million) 007 006 006 009 005 006 007 006Maximum inventoryt 1000 900 700 1100 1000 900 1200 800

Table 6 The maximum supply capacity of supplier

Supplier 1198671 1198672 1198673Themaximum supply capacityt 8800 7900 6300

Table 7 Time window and determined demand of customer

Customer (119879119895min 119879119895 119879119895max) Demand (t)1198691 (2 25 3) 2001198692 (3 4 5) 4001198693 (1 15 2) 3501198694 (1 2 25) 2501198695 (2 3 4) 1501198696 (3 35 4) 3501198697 (15 25 3) 3001198698 (2 3 45) 1801198699 (15 25 3) 35011986910 (3 4 5) 300

by consumers ordering through the Internet so fresh e-commerce companies can collect customer information andorder information (eg customersrsquo purchasing frequencypurchasing preferences and position distribution) Thenthe fresh e-commerce company can use this informationto classify consumers and predict consumer demand Theautoregressive part of the multiple ARIMAmodel representsa linear combination of past values while themoving averagepart of the multiple ARIMAmodel is a linear combination ofpast forecasting errorsThe advantage of themultiple ARIMAmodel is that it improves prediction accuracy facilitatesstatistics and reduces the cost of prediction Moreover it cancombine product cost changes with demand uncertainty topredict consumer demand [35] In view of this the multi-variate ARIMA model is suitable to predict the consumerdemand for fresh e-commerce Although the AMIMAmodel

can more accurately predict the uncertainty of demand thesize of fresh e-commercersquos consumers is small and widelydistributed so there is still uncertainty in demand To learnmore about the multivariate ARIMA model studies [35 36]are suggested The deterministic demand for each customeris shown in Table 7

The affected factors of uncertain supply involve envi-ronmental factors (eg the natural environment economicenvironment and political environment) and the abilities ofsuppliers (eg production capacity equipment capacity) [37]First the planting period for fresh foods is the quarter or yearas a unit the period is longer than for other products Fresh e-commerce can be investigated in advance through the Inter-net and then the product cultivation of the fresh food and thefield investigation can be planned accordingly Second thesuppliers of fresh electricity providers are typically farmersand fresh food bases around the region These suppliersare less affected by global economic changes and politicalchanges The selection diversity of suppliers also allows freshe-commerce companies to evaluate and select suppliers inadvance In addition the equipment failure problem has lessof an effect on fresh e-commerce because fresh productscan be delivered to the distribution center though simplepretreatment packaging In summary the supply of fresh e-commerce is uncertain but fresh e-commerce companies areless affected by these uncertain factors due to the specialnature of fresh foods The current delivery mode of freshproducts is from a mono type and large batch distributionto a multitype delivery mode and small batch distributionEach time an order is made the consumer evaluates thefresh electricity service (eg Amazon Fresh and MotionOptimization) For the majority of instances the perishablenature of a product results in the supply process having alower variability than the demand process [38] Thereforethis paper focuses on the location model for distributioncenters under uncertain demand

10 Scientific Programming

0 009 014027033

071093

119

165 175191

0

0005

001

0015

002

0025

0 01 02 03 04 05 06 07 08 09 1

The i

ncre

ase r

atio

The value of a

Figure 3 The increase ratio of the total cost of uncertain demand

For the case of uncertainty we assume that the demandfor each demand point is 119904 = 5 The number of scenariosfor each demand point can be different from each other Thevalue of the demand scenario is determined by the surveyand then the five cases are generated randomly by Matlab 83as the demand scenario of the demand point 119895 The demandscenario of the 10 demandpoints can be obtained by repeatingthe process ten times

The discrete demand probability distribution is 1199010119895119904 119869 =119895 | 119895 = 1 2 119899For 1199010119895119904 in the range (0 1) the simulations are randomly

generated between the 10 numbers normalized and repeatedten times in order to get all the demand points in theuncertain demand scenarioTheprobability demand scenarioof customer 119895 (119901119895119904) meets the uncertainty set Let thedecentralized matrix be 119876 = 119886119868 where 119886 is a nonnegativeparameter and 119868 is an identity matrix

In the experiment let 119886 = 05 and 119886 = 08 respectivelyCalculate 119901119895119904

The specific initialization parameter is set to maxgen =100 sizepop = 20 The program is implemented in Matlab83 and run on a computer with 26GHz Intel i5-4210MCPU 4GB of RAM andWindows 10The distribution centerdecision-making program and the total cost are shown inTable 8

For the deterministic demand situation the optimal deci-sion is to choose distribution center 119868211986851198686 from the candidatelist The total cost is 7208 million For the uncertain demandsituation when 119886 = 01 to 119886 = 04 the optimal decision isto choose distribution centers 119868211986851198686 The distribution rangeis constant but the cost increases When 119886 = 05 to 119886 = 07the optimal decision is to choose distribution centers 119868211986851198686but the distribution range is different from the deterministicdemand situation When 119886 = 08 to 119886 = 1 the optimaldecision is to choose distribution centers 119868511986861198687 The increaseratio of the total cost in the case of uncertainty is comparedto the total cost in the demand determination as shownin Figure 3 Enterprises in the decision-making before theconsumer demand should be the historical data for statisticaland analysis determine the variation range of parameter119886 and make decisions based on cost and self-conditions(Figure 3)

Then using FOA to solve themodel and initial parametersand operating environment equally with IFOA the results are

Table 8 The decision-making program and the total cost ofdistribution center

The value of 119886 Decision-makingprogram and

distribution rangeCost (RMB)

119886 = 0 1198682 1198691 1198693 11986977208563141198685 1198692 1198695 11986981198686 1198694 1198696 1198699 11986910

119886 = 01 1198682 1198691 1198693 11986977215050851198685 1198692 1198695 11986981198686 1198694 1198696 1198699 11986910

119886 = 02 1198682 1198691 1198693 11986977218655131198685 1198692 1198695 11986981198686 1198694 1198696 1198699 11986910

119886 = 03 1198682 1198691 1198693 11986977228026261198685 1198692 1198695 11986981198686 1198694 1198696 1198699 11986910

119886 = 04 1198682 1198691 1198693 11986977232351401198685 1198692 1198695 11986981198686 1198694 1198696 1198699 11986910

119886 = 05 1198682 1198691 1198693 11986977259452741198685 1198692 1198694 1198695 11986981198686 1198696 1198699 11986910

119886 = 06 1198682 1198691 1198693 11986977275602781198685 1198692 1198694 1198695 11986981198686 1198696 1198699 11986910

119886 = 07 1198682 1198691 1198693 11986977294345041198685 1198692 1198694 1198695 11986981198686 1198696 1198699 11986910

119886 = 08 1198685 1198692 11986957327583631198686 1198694 1198696 1198699 119869101198687 1198691 1198693 1198697 1198698

119886 = 09 1198685 1198692 11986957334712991198686 1198694 1198696 1198699 119869101198687 1198691 1198693 1198697 1198698

119886 = 1 1198685 1198692 11986957346246701198686 1198694 1198696 1198699 119869101198687 1198691 1198693 1198697 1198698

shown in Table 9 the difference value of IFOA and FOA isshown in Figure 4 and the optimization process of FOA andIFOA is shown in Figure 5 (select 119886 = 05)

From the test results in Table 9 and Figures 4 and 5under the same conditions IFOA results are superior to FOAthe convergence accuracy is more accurate and the optimalresults are better Under the same convergence accuracythe number of valid iterations of IFOA is less than that ofFOA which indicates that IFOA converges faster ThereforeIFOA effectively improves the convergence precision andconvergence speed of FOAThe applicability of IFOA is moreextensive

Scientific Programming 11

Table 9 The results of FOA and IFOA

The value of 119886 IFOA optimal FOA optimal119886 = 0 720856314 720874332119886 = 01 721505085 721515326119886 = 02 721865513 721881176119886 = 03 722802626 72285562119886 = 04 723235140 723309877119886 = 05 725945274 726005691119886 = 06 727560278 727613354119886 = 07 729434504 729495412119886 = 08 732758363 732827122119886 = 09 733471299 733549837119886 = 1 734624670 734714368

18018 10241 15663

52994

7473760417

5307660908

6875978538

89698

000100002000030000400005000060000700008000090000

100000

0 01 02 03 04 05 06 07 08 09 1

The d

iffer

ent v

alue

The value of a

Figure 4 The difference value of IFOA and FOA

0 10 20 30 40 50 60 70 80 90 1007

75

8

85

9

95

Iteration number

Cos

t

IFOAFOA

times106

Figure 5 Optimization process of FOA and IFOA (119886 = 05)

5 Conclusions

The location of distribution centers is a complex optimizationproblem To solve the problem of unreasonable networklayout and poor interpretation of customer demand and highcost of distribution this paper optimizes the location ofdistribution centers minimizes the total cost of distributionand establishes a fast and secure distribution center networksystem The conclusions of this paper are summarized asfollows

In this paper a distribution center model is established toreduce the total cost of the enterpriseThemodel is combinedwith the inherent characteristics of fresh goods e-commercetaking into account the principles of distribution centerselection service levels and freshness constraints Due to theincrease in the number of fresh goods e-commerce enter-prises with more intense competition consumer demand ismore and more uncertain Robust optimization is used tooptimize the distribution center model which makes themodel more robust

An improved fruit fly optimization algorithm (IFOA) isproposed in this paper The search step size is dynamicallyadjusted by introducing a weighting function IFOA willserve to solve the established model However the applica-bility of IFOA is more general In this paper we validatethe uncertain demand model by using an example and weprove that the model of distribution centers is valid and caneffectively handle the uncertainty of demand

This paper considers the influence of uncertain demandon the location of distribution centers for fresh goods Itenriches the fresh goods e-commerce distribution centermodel and provides a theoretical basis for a scientific methodof selecting the locations of fresh e-commerce distributioncenters The applicability of the proposed model is mean-ingful and useful for the selection of fresh e-commercedistribution center locations The shortcomings of this paperis that it only considers the uncertainty of customer demandand does not take into account other factors of uncertaintysuch as uncertain delivery weather conditions and uncertaincorruption rate

It is worth noting that some aspects of the model needto be improved For example we will pay more attentionto a variety of uncertain factors so that the model is moresuitable formore complex situations Because the distributioncenter will be related to the distribution of fresh productscoupled with the international awareness of environmentalprotection strengthened gradually the future will take intoaccount the impacts of low-carbon environmental aspects ofthe distribution center location model

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

This research was sponsored by Project of National SocialScience Foundation of China (15BGL202) project of theplanning subject of ldquothe 12th Five-Year Planrdquo in NationalScience and Technology for the Rural Development inChina Demonstration of Key Technology and Equipment forSafe Distribution of Agricultural Logistics (2015BAD18B01)Project of Beijing Philosophy and Social Science (17GBL013)Project of Beijing Municipal Commission of Education(SM201410011002) Project of Innovation Ability Promotion(PXM2016 014213 000033) 2017 Beijing Technology andBusiness University postgraduate student research abilityenhancing project

12 Scientific Programming

References

[1] RAccorsi AGallo andRManzini ldquoA climate driven decision-support model for the distribution of perishable productsrdquoJournal of Cleaner Production vol 165 pp 917ndash929 2017

[2] E Morganti and J Gonzalez-Feliu ldquoCity logistics for perishableproducts The case of the Parmarsquos Food Hubrdquo Case Studies onTransport Policy vol 3 no 2 pp 120ndash128 2015

[3] J A Orjuela-Castro L A Sanabria-Coronado and Peralta-Lozano A M ldquoCoupling facility location models in the supplychain of perishable fruitsrdquo Research in Transportation Businessamp Management 2017

[4] M Merakli and H Yaman ldquoRobust intermodal hub loca-tion under polyhedral demand uncertaintyrdquo TransportationResearch Part B Methodological vol 86 pp 66ndash85 2016

[5] M a Schuster Puga and J-S Tancrez ldquoA heuristic algorithmfor solving large location-inventory problems with demanduncertaintyrdquo European Journal of Operational Research vol 259no 2 pp 413ndash423 2017

[6] A Hiassat A Diabat and I Rahwan ldquoA genetic algorithmapproach for location-inventory-routing problem with perish-able productsrdquo Journal of Manufacturing Systems vol 42 pp93ndash103 2017

[7] K Govindan A Jafarian R Khodaverdi and K DevikaldquoTwo-echelon multiple-vehicle location-routing problem withtime windows for optimization of sustainable supply chainnetwork of perishable foodrdquo International Journal of ProductionEconomics vol 152 pp 9ndash28 2014

[8] Z Drezner and C H Scott ldquoLocation of a distribution centerfor a perishable productrdquo Mathematical Methods of OperationsResearch vol 78 no 3 pp 301ndash314 2013

[9] S M Seyedhosseini and S M Ghoreyshi ldquoAn integrated modelfor production and distribution planning of perishable prod-ucts with inventory and routing considerationsrdquo MathematicalProblems in Engineering vol 2014 Article ID 475606 10 pages2014

[10] M de Keizer R Akkerman M Grunow J M Bloemhof RHaijema and J G van der Vorst ldquoLogistics network designfor perishable products with heterogeneous quality decayrdquoEuropean Journal of Operational Research vol 262 no 2 pp535ndash549 2017

[11] H Yang L I Hong DUWei et al ldquoResearch on location selec-tion of perishable dairy products distribution center based ontwo-stage distributionrdquoComputer Engineering andApplicationsvol 23 pp 239ndash245 2015

[12] J Zhang and F U Shao-chuan ldquoStudy on location of fresh fooddistribution center with demand influenced by the freshnessrdquoChinese Journal of Management Science vol 19 no 10 pp 473ndash476 2011

[13] T Wu H Shen and C Zhu ldquoA multi-period location modelwith transportation economies-of-scale and perishable inven-toryrdquo International Journal of Production Economics vol 169 pp343ndash349 2015

[14] M Musavi and A Bozorgi-Amiri ldquoA multi-objective sus-tainable hub location-scheduling problem for perishable foodsupply chainrdquo Computers amp Industrial Engineering 2017

[15] M Rezaei-Malek R Tavakkoli-Moghaddam B Zahiri and ABozorgi-Amiri ldquoAn interactive approach for designing a robustdisaster relief logistics network with perishable commoditiesrdquoComputers amp Industrial Engineering vol 94 pp 201ndash215 2016

[16] K Khalili-Damghani A-R Abtahi andA Ghasemi ldquoA new bi-objective location-routing problem for distribution of perish-able products evolutionary computation approachrdquo Journal ofMathematical Modelling and Algorithms in Operations Researchvol 14 no 3 pp 287ndash312 2015

[17] Y Zhang Y Jiang M Zhong N Geng and D Chen ldquoRobustOptimization on Regional WCO-for-Biodiesel Supply Chainunder Supply and Demand Uncertaintiesrdquo Scientific Program-ming vol 2016 Article ID 1087845 15 pages 2016

[18] R Qiu and Y Wang ldquoSupply chain network design underdemand uncertainty and supply disruptions a distributionallyrobust optimization approachrdquo Scientific Programming vol2016 Article ID 3848520 15 pages 2016

[19] A Ben-Tal E Hazan T Koren and S Mannor ldquoOracle-basedrobust optimization via online learningrdquo Operations Researchvol 63 no 3 pp 628ndash638 2015

[20] M Melamed A Ben-Tal and B Golany ldquoOn the averageperformance of the adjustable RO and its use as an offlinetool for multi-period production planning under uncertaintyrdquoComputational Management Science vol 13 no 2 pp 293ndash3152016

[21] A Ghodratnama R Tavakkoli-Moghaddam and A AzaronldquoRobust and fuzzy goal programming optimization approachesfor a novel multi-objective hub location-allocation problem Asupply chain overviewrdquoApplied SoftComputing vol 37 pp 255ndash276 2015

[22] F Habibzadeh Boukani B Farhang Moghaddam and M SPishvaee ldquoRobust optimization approach to capacitated singleand multiple allocation hub location problemsrdquo Computationalamp Applied Mathematics vol 35 no 1 pp 45ndash60 2016

[23] A Jakubovskis ldquoStrategic facility location capacity acquisitionand technology choice decisions under demand uncertaintyrobust vs non-robust optimization approachesrdquo European Jour-nal of Operational Research vol 260 no 3 pp 1095ndash1104 2017

[24] H A Eiselt and V Marianov ldquoA bi-objective model for thelocation of landfills formunicipal solidwasterdquoEuropean Journalof Operational Research vol 235 no 1 pp 187ndash194 2014

[25] M G Bardossy and S Raghavan ldquoRobust Optimization forthe Connected Facility Location Problemrdquo Electronic Notes inDiscrete Mathematics vol 44 pp 149ndash154 2013

[26] V de Rosa E Hartmann M Gebhard and J WollenweberldquoRobust capacitated facility location model for acquisitionsunder uncertaintyrdquoComputers amp Industrial Engineering vol 72pp 206ndash216 2014

[27] M Ehrgott J Ide and A Schoobel ldquoMinmax robustness formulti-objective optimization problemsrdquo European Journal ofOperational Research vol 239 no 1 pp 17ndash31 2014

[28] X-F Xu J Hao Y-R Deng and YWang ldquoDesign optimizationof resource combination for collaborative logistics networkunder uncertaintyrdquo Applied Soft Computing vol 56 pp 684ndash691 2017

[29] E D Majewski M Wirtz M Lampe and etal ldquoRobust multi-objective optimization for sustainable design of distributedenergy supply systemsrdquoComputersampChemical Engineering vol102 pp 26ndash39 2016

[30] M Yunfeng Y Chao M Zhang and H Chunyan ldquoTime-satisfaction-based maximal covering location problemrdquo Chi-nese Journal of Management Science vol 2 pp 45ndash51 2006

[31] W-T Pan ldquoA new fruit fly optimization algorithm takingthe financial distress model as an examplerdquo Knowledge-BasedSystems vol 26 pp 69ndash74 2012

Scientific Programming 13

[32] S Kanarachos J Griffin and M E Fitzpatrick ldquoEfficient trussoptimization using the contrast-based fruit fly optimizationalgorithmrdquo Computers amp Structures vol 182 pp 137ndash148 2017

[33] J Niu W Zhong Y Liang N Luo and F Qian ldquoFruit flyoptimization algorithm based on differential evolution andits application on gasification process operation optimizationrdquoKnowledge-Based Systems vol 88 pp 253ndash263 2015

[34] S-M Lin ldquoAnalysis of service satisfaction in web auctionlogistics service using a combination of Fruit fly optimizationalgorithm and general regression neural networkrdquoNeural Com-puting and Applications vol 22 no 3-4 pp 783ndash791 2013

[35] J Huber A Gossmann andH Stuckenschmidt ldquoCluster-basedhierarchical demand forecasting for perishable goodsrdquo ExpertSystems with Applications vol 76 pp 140ndash151 2017

[36] M Shukla and S Jharkharia ldquoApplicability of ARIMA modelsin wholesale vegetable market An investigationrdquo InternationalJournal of Information Systems and Supply Chain Managementvol 6 no 3 pp 105ndash119 2013

[37] C Sun and X Luo ldquoThe influencing factors and countermea-sures of supply uncertainty in supply chainrdquo Economic ResearchGuide vol 11 pp 146-147 2013

[38] S Minner and S Transchel ldquoOrder variability in perish-able product supply chainsrdquo European Journal of OperationalResearch vol 260 no 1 pp 93ndash107 2017

Submit your manuscripts athttpswwwhindawicom

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6 Scientific Programming

where 1199010119895119904 is the most probable probability distribution ofdemand points 119876 isin 119877119899119898times119899119898 is the scope of the zoom119906 denotes the Euclidean norm for perturbation 119890119879119876119906 =0 1199010119895119904 + 119876119906 ge 0 is to ensure that the demand scenarioprobability 119901119895119904 is a probability distribution

Assuming that the demand of each customer is indepen-dent of each other and does not interfere with each otherand the total cost of the site under the demand scenario119904 of customer 119895 is 120575119895119904 the cost of a distribution center isdetermined as follows

120575119894119895 = sum119904isin119878

120575119894119895119904119901119895119904 (22)

The total expected cost for all distribution centers isdetermined as follows

119864 (120575119894) = sum119895isin119869

120575119894119895 = sum119895isin119869

sum119904isin119878

120575119894119895119904119901119895119904 = sum119895isin119869

119901119879119895 120575119895

120575119895 = (1205751198951 1205751198952 120575119895119904)119879 119901119895 = (1199011198951 1199011198952 119901119895119904)119879

(23)

The total cost of the distribution center is transformed

min 119864 (120575) = minsum119895isin119869

119901119879119895 120575119895 (24)

The robust correspondence model of (19) is expressed as

min max119901119895119904isinΩ

119864 (120575) = minmax119901119895119904isinΩ

sum119895isin119869

119901119879119895 120575119895 (25)

The above model is equivalent to

min 120603 (26)

st max119901119895119904isinΩ

sum119895isin119869

119901119879119895 120575119895 le 120603 (27)

119901119895119904 satisfies the demand uncertain set (21) then the leftside of formula (27) is

max119901119895119904isinΩ

sum119895isin119869

119901119879119895 120575119895 = max119901119895119904isinΩ

sum119895isin119869

[(1199010119895119904)119879 120575119895 + (119876119906)119879 120575119895]

= sum119895isin119869

(1199010119895119904)119879 120575119895 + max119901119895119904isinΩ

(119876119906)119879 120575119895(28)

Because 119906 le 1max119901119895119904isinΩ

(119876119906)119879 120575119895 = max119901119895119904isinΩ

119876119879120575119895 (29)

Equation (27) is converted to

sum119895isin119869

(1199010119895119904)119879 120575119895 + max119901119895119904isinΩ

119876119879120575119895 le 120603 (30)

In summary the optimization objective of the robustoptimizationmodel ismin120603 and composed of the constraints(30) and (12) to (20)Themodel has good robustness throughthe robust optimization of the model which can meet theuncertain demand of the customer and ensure the economicfeasibility of the location selection scheme

35 Improved Fruit FlyOptimizationAlgorithm (IFOA) Afterthe above two-step modeling this paper establishes a modelof the distribution center of fresh goods e-commerce underuncertain demand The next important problem is the solu-tion of themodelThe location problem in the uncertain situ-ation is anNP-hard problemThe traditional solutionmethodis complicated and the required amount of is prohibitive forfinding a solution Therefore a heuristic algorithm is used tosolve the problem

FOA is suitable for solving the optimization problemwith complex constraints and strong correlation betweenthe constituent elements of the solution [31] It is widelyused in many classical optimization fields such as efficienttruss optimization [32] gasification process operation opti-mization [33] and analysis of service satisfaction [34] TheFOA algorithm is easy to combine with other methods hasstrong robustness and is suitable for robustly optimizing thelocation of distribution centers Therefore FOA is used tosolve the problem in this paper

351 Fruit Fly Optimization Algorithm (FOA) FOA is out-lined as follows

Step 1 Initialize parameters including the maximumnumber of evaluations (maxgen) and the size of fruitflies (sizepop) and initialize the position of the flies(119883 axis 119884 axis)

Step 2 Randomly initialize the flight direction and distanceof the individual flies where Random Value is the distance inthe search

119883119894 = 119883 axis + Random Value119884119894 = 119884 axis + Random Value (31)

Step 3 The distance of each fly from the origin point and thesmell concentration judgment value is defined as follows

Dist119894 = radic1199091198942 + 1199101198942119878119894 = 1

Dist119894 (32)

Step 4 Based on 119878119894 the smell concentration of flies denotedby Smell119894 is calculated as follows

Smell119894 = function (119878119894) (33)

Step 5 Find the fruit flies with the best smell concentrationand allow the flies to fly to the optimal position

[bestSmell bestindex] = min (Smell119894)Smellbest = bestSmell

119909 axis = 119883 (bestindex)119910 axis = 119884 (bestindex)

(34)

Step 6 Stop the search if the maximum evaluation number isreached otherwise repeat Steps 2ndash5

Scientific Programming 7

Table 1 Test function

Test function Range Optimal Peak

min 1198911 = minusexp(minus05 sdot119899sum119894=1

1199091198942) [minus1 1] minus1 Single

min 1198912 =sin2 (radicsum119899119894=1 1199091198942) minus 05(1 + 0001 (sum119899119894=1 1199091198942))2 + 05 [minus100 100] 0 Multiple

Table 2 Mean and standard deviation of function test

Function Result FOA IFOA

1198911(119909) Mean 30546 times 10minus6 minus1Std 75382 times 10minus6 0

1198912(119909) Mean 31266 times 10minus6 467 times 10minus4Std 86307 times 10minus8 2328 times 10minus3

FOA has great ability to achieve global optimization andhigh convergence accuracy and has great research value in thefield of engineering However the original FOA uses a fixedsearch step and cannot take both global search capabilitiesand local search capabilities into account thus affecting theconvergence rate and search ability Additionally it is easyfor FOA to focus on a local optimum leading to prematureconvergence This paper focuses on the shortcomings of thealgorithm and improves FOAThe purpose of improving theFOA is to make it solve the location model better

352 Improved Fruit Fly Optimization Algorithm (IFOA)In this paper an improved fruit fly optimization algorithm(IFOA) is proposed The search step size is dynamicallyadjusted by introducing the weighting functionThe purposeof dynamic adjustment is to divide the search into two partsThe first part contains a large search step in a large area for aglobal search to ensure that the algorithmconsiders the globaloptimum The second part contains a smaller step search toensure local search capabilities

The fruit fly individual random search expression is asfollows

119883119894 = 119883 axis + 120595 sdot rand ( ) 119884119894 = 119884 axis + 120595 sdot rand ( ) (35)

where 120595 represents the weighted function

120595 = exp(minus 10038161003816100381610038161003816100381610038161003816Smell119894 minus Smell119894minus1

Smell119894

10038161003816100381610038161003816100381610038161003816120577) (36)

where Smell119894 is the 119894th optimal fitness value When the ratiochange is large it indicates that the fly group is searching fora new space and that the weighting function is conducive toa global search When the ratio change is small the fruit flygroup has shifted to a local search and the weight functionis reduced 120577 gt 0 and as 120577 increases fruit fly search abilityincreases which prevents the algorithms from concentratingon a local optimum It can be adjusted according to the actualproblem In addition to the random search expression theother IFOA algorithm step expression is consistent with FOA

353 Test Function To test and analyze the performanceof the improved algorithm the following two classic testfunctions were used to test FOA and IFOA respectivelyFunction form range theoretical extremes and peak areshown in Table 1

The specific initialization parameter is set to sizepop =20 maxgen = 100 We randomly initialize the fliesrsquo popula-tion position The results of the functional tests are shown inTable 2 and the optimization process is shown in Figure 2

From the test results in Table 2 and optimization processIFOA has stronger capabilities of global search local searchand higher convergence accuracy than FOA Under the sameconditions IFOA results are superior to FOA in termsof both mean and standard deviation Under the sameconvergence accuracy the number of valid iterations of IFOAis less than that of FOA which indicates that IFOA convergesfaster Therefore IFOA effectively improves the convergenceprecision and convergence speed of FOA

36 The Calculation Process of Model

(1) Collect the relevant data needed to establish thedistribution center model (as shown in Section 33)

(2) Convert the distribution center model under uncer-tain demand to a tractable equivalent model by usingrobust optimization

(3) IFOA is used to solve the mathematical model

(1) Set the initial parameters including the maxi-mum number of evaluations (maxgen) and thesize of the fruit flies (sizepop) and the initialposition of the flies (119883 axis 119884 axis)

(2) Randomly setting the flight direction and dis-tance of the individual flies the fruit fly individ-ual random search expression is as follows

119883119894 = 119883 axis + 120595 sdot rand () 119884119894 = 119884 axis + 120595 sdot rand () (37)

(3) According to the fitness function formula theindividual fruit fly is calculated to find the

8 Scientific Programming

Table 3 Distance between supplier ℎ and distribution center 119894 (km)

1198681 1198682 1198683 1198684 1198685 1198686 1198687 11986881198671 1431 2912 19945 12093 7738 8814 3214 79831198672 7382 9424 11886 4712 4500 1204 6527 109651198673 13223 11025 10594 3544 9126 6395 7580 6324

0 10 20 30 40 50 60 70 80 90 100minus1

minus0998

minus0996

minus0994

minus0992

minus099

minus0988

minus0986

minus0984

Iteration number

Smel

l

IFOAFOA

0

0002

0004

0006

0008

001

0012

0014

Smel

l

f1(x)

0 10 20 30 40 50 60 70 80 90 100Iteration number

IFOAFOA

f2(x)

Figure 2 Optimization process of FOA and IFOA

position and optimal value of the individual andthe global optimal individual

(4) Find the fruit flies with the best smell concen-tration and allow the flies to fly to the optimalposition

(5) Stop the search if the maximum evaluationnumber is reached otherwise repeat

(6) According to the IFOA optimal location resultsthen find the corresponding best location of thedistribution center and the optimal distributionpath

4 Computational Results

Experiments are proposed in this part to prove the effective-ness and feasibility of the location model Both deterministicand uncertain demand scenarios are considered and then acomparison and analysis of the results of the two situationsis providedThe numerical calculation problem is consideredto occur in a developed city where a fresh goods e-commercefirm chooses to rent a certain number of distribution centerswithin an appropriate area The area of suppliers is 3 and thearea of customers is 10 The firm chooses to rent 3 locationsfrom a set of 8 candidate distribution centers

The distance between the supplier and the candidatedistribution center and the distance between the candidatedistribution center and the demand point are obtained by

using the Euclidean theorem The details are shown inTables 3 and 4 The tables consider the different qualitiesof each candidate distribution center such as the locationtransportation economy and other conditions Fixed costsoperating costs and the largest inventory are also different asshown in Table 5 The maximum supply capacity of supplierℎ is shown in Table 6

The average traveling speed is 45 kmh for the distributionvehicles in the region the average unit freight from thesupplier to the distribution center is 15 yuan(tsdotkm) and thefreight rate from the distribution center to the demand pointis 18 yuan(tsdotkm) To simplify the follow-up calculation thenumerical calculations only consider the distribution of twofresh goods using the corruption coefficients of 015 and008 and the unit prices of 4 yuankg and 6 yuankg Theaverage satisfaction threshold for customer satisfaction is075 and the average satisfaction threshold for freshness is07 If the delivery vehicle arrives late the compensation feeis 50 yuan(hsdott) The demand point time window is shown inTable 7

We consider cases where demand is both deterministicand uncertain The calculation and comparative analysisof two cases can be conducted more directly to verifywhether the model can help the fresh goods e-commerceto suppress the uncertainty interference by demand Themethod used to predict the consumer demand is the multi-variate autoregressive integrated moving average (AMIMA)model in this paper Fresh e-commerce is characterized

Scientific Programming 9

Table 4 Distance between distribution center 119894 and customer 119895 (km)

1198681 1198682 1198683 1198684 1198685 1198686 1198687 11986881198691 14200 4134 24550 16717 8919 11733 7560 144361198692 5420 9642 20535 14220 5903 8628 10072 180711198693 11610 1170 19564 11682 5178 7156 2469 102011198694 6525 18398 13761 12419 12180 11123 16497 214241198695 4827 7716 17279 10536 2282 4850 7000 145791198696 9904 15932 6296 4810 10720 7694 12857 146731198697 22649 13509 20341 14670 16589 15631 12035 48871198698 10718 3383 17310 9420 4161 5215 721 89051198699 12879 19474 3981 7506 14322 11287 16319 1711411986910 15277 14586 7910 3984 12248 9166 11140 8238

Table 5 Fixed costs operating costs and maximum inventory

Candidate distribution centers 1198681 1198682 1198683 1198684 1198685 1198686 1198687 1198688Fixed costs (million) 145 138 123 148 129 123 138 136Operating costs (million) 007 006 006 009 005 006 007 006Maximum inventoryt 1000 900 700 1100 1000 900 1200 800

Table 6 The maximum supply capacity of supplier

Supplier 1198671 1198672 1198673Themaximum supply capacityt 8800 7900 6300

Table 7 Time window and determined demand of customer

Customer (119879119895min 119879119895 119879119895max) Demand (t)1198691 (2 25 3) 2001198692 (3 4 5) 4001198693 (1 15 2) 3501198694 (1 2 25) 2501198695 (2 3 4) 1501198696 (3 35 4) 3501198697 (15 25 3) 3001198698 (2 3 45) 1801198699 (15 25 3) 35011986910 (3 4 5) 300

by consumers ordering through the Internet so fresh e-commerce companies can collect customer information andorder information (eg customersrsquo purchasing frequencypurchasing preferences and position distribution) Thenthe fresh e-commerce company can use this informationto classify consumers and predict consumer demand Theautoregressive part of the multiple ARIMAmodel representsa linear combination of past values while themoving averagepart of the multiple ARIMAmodel is a linear combination ofpast forecasting errorsThe advantage of themultiple ARIMAmodel is that it improves prediction accuracy facilitatesstatistics and reduces the cost of prediction Moreover it cancombine product cost changes with demand uncertainty topredict consumer demand [35] In view of this the multi-variate ARIMA model is suitable to predict the consumerdemand for fresh e-commerce Although the AMIMAmodel

can more accurately predict the uncertainty of demand thesize of fresh e-commercersquos consumers is small and widelydistributed so there is still uncertainty in demand To learnmore about the multivariate ARIMA model studies [35 36]are suggested The deterministic demand for each customeris shown in Table 7

The affected factors of uncertain supply involve envi-ronmental factors (eg the natural environment economicenvironment and political environment) and the abilities ofsuppliers (eg production capacity equipment capacity) [37]First the planting period for fresh foods is the quarter or yearas a unit the period is longer than for other products Fresh e-commerce can be investigated in advance through the Inter-net and then the product cultivation of the fresh food and thefield investigation can be planned accordingly Second thesuppliers of fresh electricity providers are typically farmersand fresh food bases around the region These suppliersare less affected by global economic changes and politicalchanges The selection diversity of suppliers also allows freshe-commerce companies to evaluate and select suppliers inadvance In addition the equipment failure problem has lessof an effect on fresh e-commerce because fresh productscan be delivered to the distribution center though simplepretreatment packaging In summary the supply of fresh e-commerce is uncertain but fresh e-commerce companies areless affected by these uncertain factors due to the specialnature of fresh foods The current delivery mode of freshproducts is from a mono type and large batch distributionto a multitype delivery mode and small batch distributionEach time an order is made the consumer evaluates thefresh electricity service (eg Amazon Fresh and MotionOptimization) For the majority of instances the perishablenature of a product results in the supply process having alower variability than the demand process [38] Thereforethis paper focuses on the location model for distributioncenters under uncertain demand

10 Scientific Programming

0 009 014027033

071093

119

165 175191

0

0005

001

0015

002

0025

0 01 02 03 04 05 06 07 08 09 1

The i

ncre

ase r

atio

The value of a

Figure 3 The increase ratio of the total cost of uncertain demand

For the case of uncertainty we assume that the demandfor each demand point is 119904 = 5 The number of scenariosfor each demand point can be different from each other Thevalue of the demand scenario is determined by the surveyand then the five cases are generated randomly by Matlab 83as the demand scenario of the demand point 119895 The demandscenario of the 10 demandpoints can be obtained by repeatingthe process ten times

The discrete demand probability distribution is 1199010119895119904 119869 =119895 | 119895 = 1 2 119899For 1199010119895119904 in the range (0 1) the simulations are randomly

generated between the 10 numbers normalized and repeatedten times in order to get all the demand points in theuncertain demand scenarioTheprobability demand scenarioof customer 119895 (119901119895119904) meets the uncertainty set Let thedecentralized matrix be 119876 = 119886119868 where 119886 is a nonnegativeparameter and 119868 is an identity matrix

In the experiment let 119886 = 05 and 119886 = 08 respectivelyCalculate 119901119895119904

The specific initialization parameter is set to maxgen =100 sizepop = 20 The program is implemented in Matlab83 and run on a computer with 26GHz Intel i5-4210MCPU 4GB of RAM andWindows 10The distribution centerdecision-making program and the total cost are shown inTable 8

For the deterministic demand situation the optimal deci-sion is to choose distribution center 119868211986851198686 from the candidatelist The total cost is 7208 million For the uncertain demandsituation when 119886 = 01 to 119886 = 04 the optimal decision isto choose distribution centers 119868211986851198686 The distribution rangeis constant but the cost increases When 119886 = 05 to 119886 = 07the optimal decision is to choose distribution centers 119868211986851198686but the distribution range is different from the deterministicdemand situation When 119886 = 08 to 119886 = 1 the optimaldecision is to choose distribution centers 119868511986861198687 The increaseratio of the total cost in the case of uncertainty is comparedto the total cost in the demand determination as shownin Figure 3 Enterprises in the decision-making before theconsumer demand should be the historical data for statisticaland analysis determine the variation range of parameter119886 and make decisions based on cost and self-conditions(Figure 3)

Then using FOA to solve themodel and initial parametersand operating environment equally with IFOA the results are

Table 8 The decision-making program and the total cost ofdistribution center

The value of 119886 Decision-makingprogram and

distribution rangeCost (RMB)

119886 = 0 1198682 1198691 1198693 11986977208563141198685 1198692 1198695 11986981198686 1198694 1198696 1198699 11986910

119886 = 01 1198682 1198691 1198693 11986977215050851198685 1198692 1198695 11986981198686 1198694 1198696 1198699 11986910

119886 = 02 1198682 1198691 1198693 11986977218655131198685 1198692 1198695 11986981198686 1198694 1198696 1198699 11986910

119886 = 03 1198682 1198691 1198693 11986977228026261198685 1198692 1198695 11986981198686 1198694 1198696 1198699 11986910

119886 = 04 1198682 1198691 1198693 11986977232351401198685 1198692 1198695 11986981198686 1198694 1198696 1198699 11986910

119886 = 05 1198682 1198691 1198693 11986977259452741198685 1198692 1198694 1198695 11986981198686 1198696 1198699 11986910

119886 = 06 1198682 1198691 1198693 11986977275602781198685 1198692 1198694 1198695 11986981198686 1198696 1198699 11986910

119886 = 07 1198682 1198691 1198693 11986977294345041198685 1198692 1198694 1198695 11986981198686 1198696 1198699 11986910

119886 = 08 1198685 1198692 11986957327583631198686 1198694 1198696 1198699 119869101198687 1198691 1198693 1198697 1198698

119886 = 09 1198685 1198692 11986957334712991198686 1198694 1198696 1198699 119869101198687 1198691 1198693 1198697 1198698

119886 = 1 1198685 1198692 11986957346246701198686 1198694 1198696 1198699 119869101198687 1198691 1198693 1198697 1198698

shown in Table 9 the difference value of IFOA and FOA isshown in Figure 4 and the optimization process of FOA andIFOA is shown in Figure 5 (select 119886 = 05)

From the test results in Table 9 and Figures 4 and 5under the same conditions IFOA results are superior to FOAthe convergence accuracy is more accurate and the optimalresults are better Under the same convergence accuracythe number of valid iterations of IFOA is less than that ofFOA which indicates that IFOA converges faster ThereforeIFOA effectively improves the convergence precision andconvergence speed of FOAThe applicability of IFOA is moreextensive

Scientific Programming 11

Table 9 The results of FOA and IFOA

The value of 119886 IFOA optimal FOA optimal119886 = 0 720856314 720874332119886 = 01 721505085 721515326119886 = 02 721865513 721881176119886 = 03 722802626 72285562119886 = 04 723235140 723309877119886 = 05 725945274 726005691119886 = 06 727560278 727613354119886 = 07 729434504 729495412119886 = 08 732758363 732827122119886 = 09 733471299 733549837119886 = 1 734624670 734714368

18018 10241 15663

52994

7473760417

5307660908

6875978538

89698

000100002000030000400005000060000700008000090000

100000

0 01 02 03 04 05 06 07 08 09 1

The d

iffer

ent v

alue

The value of a

Figure 4 The difference value of IFOA and FOA

0 10 20 30 40 50 60 70 80 90 1007

75

8

85

9

95

Iteration number

Cos

t

IFOAFOA

times106

Figure 5 Optimization process of FOA and IFOA (119886 = 05)

5 Conclusions

The location of distribution centers is a complex optimizationproblem To solve the problem of unreasonable networklayout and poor interpretation of customer demand and highcost of distribution this paper optimizes the location ofdistribution centers minimizes the total cost of distributionand establishes a fast and secure distribution center networksystem The conclusions of this paper are summarized asfollows

In this paper a distribution center model is established toreduce the total cost of the enterpriseThemodel is combinedwith the inherent characteristics of fresh goods e-commercetaking into account the principles of distribution centerselection service levels and freshness constraints Due to theincrease in the number of fresh goods e-commerce enter-prises with more intense competition consumer demand ismore and more uncertain Robust optimization is used tooptimize the distribution center model which makes themodel more robust

An improved fruit fly optimization algorithm (IFOA) isproposed in this paper The search step size is dynamicallyadjusted by introducing a weighting function IFOA willserve to solve the established model However the applica-bility of IFOA is more general In this paper we validatethe uncertain demand model by using an example and weprove that the model of distribution centers is valid and caneffectively handle the uncertainty of demand

This paper considers the influence of uncertain demandon the location of distribution centers for fresh goods Itenriches the fresh goods e-commerce distribution centermodel and provides a theoretical basis for a scientific methodof selecting the locations of fresh e-commerce distributioncenters The applicability of the proposed model is mean-ingful and useful for the selection of fresh e-commercedistribution center locations The shortcomings of this paperis that it only considers the uncertainty of customer demandand does not take into account other factors of uncertaintysuch as uncertain delivery weather conditions and uncertaincorruption rate

It is worth noting that some aspects of the model needto be improved For example we will pay more attentionto a variety of uncertain factors so that the model is moresuitable formore complex situations Because the distributioncenter will be related to the distribution of fresh productscoupled with the international awareness of environmentalprotection strengthened gradually the future will take intoaccount the impacts of low-carbon environmental aspects ofthe distribution center location model

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

This research was sponsored by Project of National SocialScience Foundation of China (15BGL202) project of theplanning subject of ldquothe 12th Five-Year Planrdquo in NationalScience and Technology for the Rural Development inChina Demonstration of Key Technology and Equipment forSafe Distribution of Agricultural Logistics (2015BAD18B01)Project of Beijing Philosophy and Social Science (17GBL013)Project of Beijing Municipal Commission of Education(SM201410011002) Project of Innovation Ability Promotion(PXM2016 014213 000033) 2017 Beijing Technology andBusiness University postgraduate student research abilityenhancing project

12 Scientific Programming

References

[1] RAccorsi AGallo andRManzini ldquoA climate driven decision-support model for the distribution of perishable productsrdquoJournal of Cleaner Production vol 165 pp 917ndash929 2017

[2] E Morganti and J Gonzalez-Feliu ldquoCity logistics for perishableproducts The case of the Parmarsquos Food Hubrdquo Case Studies onTransport Policy vol 3 no 2 pp 120ndash128 2015

[3] J A Orjuela-Castro L A Sanabria-Coronado and Peralta-Lozano A M ldquoCoupling facility location models in the supplychain of perishable fruitsrdquo Research in Transportation Businessamp Management 2017

[4] M Merakli and H Yaman ldquoRobust intermodal hub loca-tion under polyhedral demand uncertaintyrdquo TransportationResearch Part B Methodological vol 86 pp 66ndash85 2016

[5] M a Schuster Puga and J-S Tancrez ldquoA heuristic algorithmfor solving large location-inventory problems with demanduncertaintyrdquo European Journal of Operational Research vol 259no 2 pp 413ndash423 2017

[6] A Hiassat A Diabat and I Rahwan ldquoA genetic algorithmapproach for location-inventory-routing problem with perish-able productsrdquo Journal of Manufacturing Systems vol 42 pp93ndash103 2017

[7] K Govindan A Jafarian R Khodaverdi and K DevikaldquoTwo-echelon multiple-vehicle location-routing problem withtime windows for optimization of sustainable supply chainnetwork of perishable foodrdquo International Journal of ProductionEconomics vol 152 pp 9ndash28 2014

[8] Z Drezner and C H Scott ldquoLocation of a distribution centerfor a perishable productrdquo Mathematical Methods of OperationsResearch vol 78 no 3 pp 301ndash314 2013

[9] S M Seyedhosseini and S M Ghoreyshi ldquoAn integrated modelfor production and distribution planning of perishable prod-ucts with inventory and routing considerationsrdquo MathematicalProblems in Engineering vol 2014 Article ID 475606 10 pages2014

[10] M de Keizer R Akkerman M Grunow J M Bloemhof RHaijema and J G van der Vorst ldquoLogistics network designfor perishable products with heterogeneous quality decayrdquoEuropean Journal of Operational Research vol 262 no 2 pp535ndash549 2017

[11] H Yang L I Hong DUWei et al ldquoResearch on location selec-tion of perishable dairy products distribution center based ontwo-stage distributionrdquoComputer Engineering andApplicationsvol 23 pp 239ndash245 2015

[12] J Zhang and F U Shao-chuan ldquoStudy on location of fresh fooddistribution center with demand influenced by the freshnessrdquoChinese Journal of Management Science vol 19 no 10 pp 473ndash476 2011

[13] T Wu H Shen and C Zhu ldquoA multi-period location modelwith transportation economies-of-scale and perishable inven-toryrdquo International Journal of Production Economics vol 169 pp343ndash349 2015

[14] M Musavi and A Bozorgi-Amiri ldquoA multi-objective sus-tainable hub location-scheduling problem for perishable foodsupply chainrdquo Computers amp Industrial Engineering 2017

[15] M Rezaei-Malek R Tavakkoli-Moghaddam B Zahiri and ABozorgi-Amiri ldquoAn interactive approach for designing a robustdisaster relief logistics network with perishable commoditiesrdquoComputers amp Industrial Engineering vol 94 pp 201ndash215 2016

[16] K Khalili-Damghani A-R Abtahi andA Ghasemi ldquoA new bi-objective location-routing problem for distribution of perish-able products evolutionary computation approachrdquo Journal ofMathematical Modelling and Algorithms in Operations Researchvol 14 no 3 pp 287ndash312 2015

[17] Y Zhang Y Jiang M Zhong N Geng and D Chen ldquoRobustOptimization on Regional WCO-for-Biodiesel Supply Chainunder Supply and Demand Uncertaintiesrdquo Scientific Program-ming vol 2016 Article ID 1087845 15 pages 2016

[18] R Qiu and Y Wang ldquoSupply chain network design underdemand uncertainty and supply disruptions a distributionallyrobust optimization approachrdquo Scientific Programming vol2016 Article ID 3848520 15 pages 2016

[19] A Ben-Tal E Hazan T Koren and S Mannor ldquoOracle-basedrobust optimization via online learningrdquo Operations Researchvol 63 no 3 pp 628ndash638 2015

[20] M Melamed A Ben-Tal and B Golany ldquoOn the averageperformance of the adjustable RO and its use as an offlinetool for multi-period production planning under uncertaintyrdquoComputational Management Science vol 13 no 2 pp 293ndash3152016

[21] A Ghodratnama R Tavakkoli-Moghaddam and A AzaronldquoRobust and fuzzy goal programming optimization approachesfor a novel multi-objective hub location-allocation problem Asupply chain overviewrdquoApplied SoftComputing vol 37 pp 255ndash276 2015

[22] F Habibzadeh Boukani B Farhang Moghaddam and M SPishvaee ldquoRobust optimization approach to capacitated singleand multiple allocation hub location problemsrdquo Computationalamp Applied Mathematics vol 35 no 1 pp 45ndash60 2016

[23] A Jakubovskis ldquoStrategic facility location capacity acquisitionand technology choice decisions under demand uncertaintyrobust vs non-robust optimization approachesrdquo European Jour-nal of Operational Research vol 260 no 3 pp 1095ndash1104 2017

[24] H A Eiselt and V Marianov ldquoA bi-objective model for thelocation of landfills formunicipal solidwasterdquoEuropean Journalof Operational Research vol 235 no 1 pp 187ndash194 2014

[25] M G Bardossy and S Raghavan ldquoRobust Optimization forthe Connected Facility Location Problemrdquo Electronic Notes inDiscrete Mathematics vol 44 pp 149ndash154 2013

[26] V de Rosa E Hartmann M Gebhard and J WollenweberldquoRobust capacitated facility location model for acquisitionsunder uncertaintyrdquoComputers amp Industrial Engineering vol 72pp 206ndash216 2014

[27] M Ehrgott J Ide and A Schoobel ldquoMinmax robustness formulti-objective optimization problemsrdquo European Journal ofOperational Research vol 239 no 1 pp 17ndash31 2014

[28] X-F Xu J Hao Y-R Deng and YWang ldquoDesign optimizationof resource combination for collaborative logistics networkunder uncertaintyrdquo Applied Soft Computing vol 56 pp 684ndash691 2017

[29] E D Majewski M Wirtz M Lampe and etal ldquoRobust multi-objective optimization for sustainable design of distributedenergy supply systemsrdquoComputersampChemical Engineering vol102 pp 26ndash39 2016

[30] M Yunfeng Y Chao M Zhang and H Chunyan ldquoTime-satisfaction-based maximal covering location problemrdquo Chi-nese Journal of Management Science vol 2 pp 45ndash51 2006

[31] W-T Pan ldquoA new fruit fly optimization algorithm takingthe financial distress model as an examplerdquo Knowledge-BasedSystems vol 26 pp 69ndash74 2012

Scientific Programming 13

[32] S Kanarachos J Griffin and M E Fitzpatrick ldquoEfficient trussoptimization using the contrast-based fruit fly optimizationalgorithmrdquo Computers amp Structures vol 182 pp 137ndash148 2017

[33] J Niu W Zhong Y Liang N Luo and F Qian ldquoFruit flyoptimization algorithm based on differential evolution andits application on gasification process operation optimizationrdquoKnowledge-Based Systems vol 88 pp 253ndash263 2015

[34] S-M Lin ldquoAnalysis of service satisfaction in web auctionlogistics service using a combination of Fruit fly optimizationalgorithm and general regression neural networkrdquoNeural Com-puting and Applications vol 22 no 3-4 pp 783ndash791 2013

[35] J Huber A Gossmann andH Stuckenschmidt ldquoCluster-basedhierarchical demand forecasting for perishable goodsrdquo ExpertSystems with Applications vol 76 pp 140ndash151 2017

[36] M Shukla and S Jharkharia ldquoApplicability of ARIMA modelsin wholesale vegetable market An investigationrdquo InternationalJournal of Information Systems and Supply Chain Managementvol 6 no 3 pp 105ndash119 2013

[37] C Sun and X Luo ldquoThe influencing factors and countermea-sures of supply uncertainty in supply chainrdquo Economic ResearchGuide vol 11 pp 146-147 2013

[38] S Minner and S Transchel ldquoOrder variability in perish-able product supply chainsrdquo European Journal of OperationalResearch vol 260 no 1 pp 93ndash107 2017

Submit your manuscripts athttpswwwhindawicom

Computer Games Technology

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Distributed Sensor Networks

International Journal of

Advances in

FuzzySystems

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014

International Journal of

ReconfigurableComputing

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 201

Applied Computational Intelligence and Soft Computing

thinspAdvancesthinspinthinsp

Artificial Intelligence

HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014

Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Hindawi Publishing Corporation

httpwwwhindawicom Volume 2014

Advances in

Multimedia

International Journal of

Biomedical Imaging

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 201

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Computational Intelligence and Neuroscience

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Scientific Programming 7

Table 1 Test function

Test function Range Optimal Peak

min 1198911 = minusexp(minus05 sdot119899sum119894=1

1199091198942) [minus1 1] minus1 Single

min 1198912 =sin2 (radicsum119899119894=1 1199091198942) minus 05(1 + 0001 (sum119899119894=1 1199091198942))2 + 05 [minus100 100] 0 Multiple

Table 2 Mean and standard deviation of function test

Function Result FOA IFOA

1198911(119909) Mean 30546 times 10minus6 minus1Std 75382 times 10minus6 0

1198912(119909) Mean 31266 times 10minus6 467 times 10minus4Std 86307 times 10minus8 2328 times 10minus3

FOA has great ability to achieve global optimization andhigh convergence accuracy and has great research value in thefield of engineering However the original FOA uses a fixedsearch step and cannot take both global search capabilitiesand local search capabilities into account thus affecting theconvergence rate and search ability Additionally it is easyfor FOA to focus on a local optimum leading to prematureconvergence This paper focuses on the shortcomings of thealgorithm and improves FOAThe purpose of improving theFOA is to make it solve the location model better

352 Improved Fruit Fly Optimization Algorithm (IFOA)In this paper an improved fruit fly optimization algorithm(IFOA) is proposed The search step size is dynamicallyadjusted by introducing the weighting functionThe purposeof dynamic adjustment is to divide the search into two partsThe first part contains a large search step in a large area for aglobal search to ensure that the algorithmconsiders the globaloptimum The second part contains a smaller step search toensure local search capabilities

The fruit fly individual random search expression is asfollows

119883119894 = 119883 axis + 120595 sdot rand ( ) 119884119894 = 119884 axis + 120595 sdot rand ( ) (35)

where 120595 represents the weighted function

120595 = exp(minus 10038161003816100381610038161003816100381610038161003816Smell119894 minus Smell119894minus1

Smell119894

10038161003816100381610038161003816100381610038161003816120577) (36)

where Smell119894 is the 119894th optimal fitness value When the ratiochange is large it indicates that the fly group is searching fora new space and that the weighting function is conducive toa global search When the ratio change is small the fruit flygroup has shifted to a local search and the weight functionis reduced 120577 gt 0 and as 120577 increases fruit fly search abilityincreases which prevents the algorithms from concentratingon a local optimum It can be adjusted according to the actualproblem In addition to the random search expression theother IFOA algorithm step expression is consistent with FOA

353 Test Function To test and analyze the performanceof the improved algorithm the following two classic testfunctions were used to test FOA and IFOA respectivelyFunction form range theoretical extremes and peak areshown in Table 1

The specific initialization parameter is set to sizepop =20 maxgen = 100 We randomly initialize the fliesrsquo popula-tion position The results of the functional tests are shown inTable 2 and the optimization process is shown in Figure 2

From the test results in Table 2 and optimization processIFOA has stronger capabilities of global search local searchand higher convergence accuracy than FOA Under the sameconditions IFOA results are superior to FOA in termsof both mean and standard deviation Under the sameconvergence accuracy the number of valid iterations of IFOAis less than that of FOA which indicates that IFOA convergesfaster Therefore IFOA effectively improves the convergenceprecision and convergence speed of FOA

36 The Calculation Process of Model

(1) Collect the relevant data needed to establish thedistribution center model (as shown in Section 33)

(2) Convert the distribution center model under uncer-tain demand to a tractable equivalent model by usingrobust optimization

(3) IFOA is used to solve the mathematical model

(1) Set the initial parameters including the maxi-mum number of evaluations (maxgen) and thesize of the fruit flies (sizepop) and the initialposition of the flies (119883 axis 119884 axis)

(2) Randomly setting the flight direction and dis-tance of the individual flies the fruit fly individ-ual random search expression is as follows

119883119894 = 119883 axis + 120595 sdot rand () 119884119894 = 119884 axis + 120595 sdot rand () (37)

(3) According to the fitness function formula theindividual fruit fly is calculated to find the

8 Scientific Programming

Table 3 Distance between supplier ℎ and distribution center 119894 (km)

1198681 1198682 1198683 1198684 1198685 1198686 1198687 11986881198671 1431 2912 19945 12093 7738 8814 3214 79831198672 7382 9424 11886 4712 4500 1204 6527 109651198673 13223 11025 10594 3544 9126 6395 7580 6324

0 10 20 30 40 50 60 70 80 90 100minus1

minus0998

minus0996

minus0994

minus0992

minus099

minus0988

minus0986

minus0984

Iteration number

Smel

l

IFOAFOA

0

0002

0004

0006

0008

001

0012

0014

Smel

l

f1(x)

0 10 20 30 40 50 60 70 80 90 100Iteration number

IFOAFOA

f2(x)

Figure 2 Optimization process of FOA and IFOA

position and optimal value of the individual andthe global optimal individual

(4) Find the fruit flies with the best smell concen-tration and allow the flies to fly to the optimalposition

(5) Stop the search if the maximum evaluationnumber is reached otherwise repeat

(6) According to the IFOA optimal location resultsthen find the corresponding best location of thedistribution center and the optimal distributionpath

4 Computational Results

Experiments are proposed in this part to prove the effective-ness and feasibility of the location model Both deterministicand uncertain demand scenarios are considered and then acomparison and analysis of the results of the two situationsis providedThe numerical calculation problem is consideredto occur in a developed city where a fresh goods e-commercefirm chooses to rent a certain number of distribution centerswithin an appropriate area The area of suppliers is 3 and thearea of customers is 10 The firm chooses to rent 3 locationsfrom a set of 8 candidate distribution centers

The distance between the supplier and the candidatedistribution center and the distance between the candidatedistribution center and the demand point are obtained by

using the Euclidean theorem The details are shown inTables 3 and 4 The tables consider the different qualitiesof each candidate distribution center such as the locationtransportation economy and other conditions Fixed costsoperating costs and the largest inventory are also different asshown in Table 5 The maximum supply capacity of supplierℎ is shown in Table 6

The average traveling speed is 45 kmh for the distributionvehicles in the region the average unit freight from thesupplier to the distribution center is 15 yuan(tsdotkm) and thefreight rate from the distribution center to the demand pointis 18 yuan(tsdotkm) To simplify the follow-up calculation thenumerical calculations only consider the distribution of twofresh goods using the corruption coefficients of 015 and008 and the unit prices of 4 yuankg and 6 yuankg Theaverage satisfaction threshold for customer satisfaction is075 and the average satisfaction threshold for freshness is07 If the delivery vehicle arrives late the compensation feeis 50 yuan(hsdott) The demand point time window is shown inTable 7

We consider cases where demand is both deterministicand uncertain The calculation and comparative analysisof two cases can be conducted more directly to verifywhether the model can help the fresh goods e-commerceto suppress the uncertainty interference by demand Themethod used to predict the consumer demand is the multi-variate autoregressive integrated moving average (AMIMA)model in this paper Fresh e-commerce is characterized

Scientific Programming 9

Table 4 Distance between distribution center 119894 and customer 119895 (km)

1198681 1198682 1198683 1198684 1198685 1198686 1198687 11986881198691 14200 4134 24550 16717 8919 11733 7560 144361198692 5420 9642 20535 14220 5903 8628 10072 180711198693 11610 1170 19564 11682 5178 7156 2469 102011198694 6525 18398 13761 12419 12180 11123 16497 214241198695 4827 7716 17279 10536 2282 4850 7000 145791198696 9904 15932 6296 4810 10720 7694 12857 146731198697 22649 13509 20341 14670 16589 15631 12035 48871198698 10718 3383 17310 9420 4161 5215 721 89051198699 12879 19474 3981 7506 14322 11287 16319 1711411986910 15277 14586 7910 3984 12248 9166 11140 8238

Table 5 Fixed costs operating costs and maximum inventory

Candidate distribution centers 1198681 1198682 1198683 1198684 1198685 1198686 1198687 1198688Fixed costs (million) 145 138 123 148 129 123 138 136Operating costs (million) 007 006 006 009 005 006 007 006Maximum inventoryt 1000 900 700 1100 1000 900 1200 800

Table 6 The maximum supply capacity of supplier

Supplier 1198671 1198672 1198673Themaximum supply capacityt 8800 7900 6300

Table 7 Time window and determined demand of customer

Customer (119879119895min 119879119895 119879119895max) Demand (t)1198691 (2 25 3) 2001198692 (3 4 5) 4001198693 (1 15 2) 3501198694 (1 2 25) 2501198695 (2 3 4) 1501198696 (3 35 4) 3501198697 (15 25 3) 3001198698 (2 3 45) 1801198699 (15 25 3) 35011986910 (3 4 5) 300

by consumers ordering through the Internet so fresh e-commerce companies can collect customer information andorder information (eg customersrsquo purchasing frequencypurchasing preferences and position distribution) Thenthe fresh e-commerce company can use this informationto classify consumers and predict consumer demand Theautoregressive part of the multiple ARIMAmodel representsa linear combination of past values while themoving averagepart of the multiple ARIMAmodel is a linear combination ofpast forecasting errorsThe advantage of themultiple ARIMAmodel is that it improves prediction accuracy facilitatesstatistics and reduces the cost of prediction Moreover it cancombine product cost changes with demand uncertainty topredict consumer demand [35] In view of this the multi-variate ARIMA model is suitable to predict the consumerdemand for fresh e-commerce Although the AMIMAmodel

can more accurately predict the uncertainty of demand thesize of fresh e-commercersquos consumers is small and widelydistributed so there is still uncertainty in demand To learnmore about the multivariate ARIMA model studies [35 36]are suggested The deterministic demand for each customeris shown in Table 7

The affected factors of uncertain supply involve envi-ronmental factors (eg the natural environment economicenvironment and political environment) and the abilities ofsuppliers (eg production capacity equipment capacity) [37]First the planting period for fresh foods is the quarter or yearas a unit the period is longer than for other products Fresh e-commerce can be investigated in advance through the Inter-net and then the product cultivation of the fresh food and thefield investigation can be planned accordingly Second thesuppliers of fresh electricity providers are typically farmersand fresh food bases around the region These suppliersare less affected by global economic changes and politicalchanges The selection diversity of suppliers also allows freshe-commerce companies to evaluate and select suppliers inadvance In addition the equipment failure problem has lessof an effect on fresh e-commerce because fresh productscan be delivered to the distribution center though simplepretreatment packaging In summary the supply of fresh e-commerce is uncertain but fresh e-commerce companies areless affected by these uncertain factors due to the specialnature of fresh foods The current delivery mode of freshproducts is from a mono type and large batch distributionto a multitype delivery mode and small batch distributionEach time an order is made the consumer evaluates thefresh electricity service (eg Amazon Fresh and MotionOptimization) For the majority of instances the perishablenature of a product results in the supply process having alower variability than the demand process [38] Thereforethis paper focuses on the location model for distributioncenters under uncertain demand

10 Scientific Programming

0 009 014027033

071093

119

165 175191

0

0005

001

0015

002

0025

0 01 02 03 04 05 06 07 08 09 1

The i

ncre

ase r

atio

The value of a

Figure 3 The increase ratio of the total cost of uncertain demand

For the case of uncertainty we assume that the demandfor each demand point is 119904 = 5 The number of scenariosfor each demand point can be different from each other Thevalue of the demand scenario is determined by the surveyand then the five cases are generated randomly by Matlab 83as the demand scenario of the demand point 119895 The demandscenario of the 10 demandpoints can be obtained by repeatingthe process ten times

The discrete demand probability distribution is 1199010119895119904 119869 =119895 | 119895 = 1 2 119899For 1199010119895119904 in the range (0 1) the simulations are randomly

generated between the 10 numbers normalized and repeatedten times in order to get all the demand points in theuncertain demand scenarioTheprobability demand scenarioof customer 119895 (119901119895119904) meets the uncertainty set Let thedecentralized matrix be 119876 = 119886119868 where 119886 is a nonnegativeparameter and 119868 is an identity matrix

In the experiment let 119886 = 05 and 119886 = 08 respectivelyCalculate 119901119895119904

The specific initialization parameter is set to maxgen =100 sizepop = 20 The program is implemented in Matlab83 and run on a computer with 26GHz Intel i5-4210MCPU 4GB of RAM andWindows 10The distribution centerdecision-making program and the total cost are shown inTable 8

For the deterministic demand situation the optimal deci-sion is to choose distribution center 119868211986851198686 from the candidatelist The total cost is 7208 million For the uncertain demandsituation when 119886 = 01 to 119886 = 04 the optimal decision isto choose distribution centers 119868211986851198686 The distribution rangeis constant but the cost increases When 119886 = 05 to 119886 = 07the optimal decision is to choose distribution centers 119868211986851198686but the distribution range is different from the deterministicdemand situation When 119886 = 08 to 119886 = 1 the optimaldecision is to choose distribution centers 119868511986861198687 The increaseratio of the total cost in the case of uncertainty is comparedto the total cost in the demand determination as shownin Figure 3 Enterprises in the decision-making before theconsumer demand should be the historical data for statisticaland analysis determine the variation range of parameter119886 and make decisions based on cost and self-conditions(Figure 3)

Then using FOA to solve themodel and initial parametersand operating environment equally with IFOA the results are

Table 8 The decision-making program and the total cost ofdistribution center

The value of 119886 Decision-makingprogram and

distribution rangeCost (RMB)

119886 = 0 1198682 1198691 1198693 11986977208563141198685 1198692 1198695 11986981198686 1198694 1198696 1198699 11986910

119886 = 01 1198682 1198691 1198693 11986977215050851198685 1198692 1198695 11986981198686 1198694 1198696 1198699 11986910

119886 = 02 1198682 1198691 1198693 11986977218655131198685 1198692 1198695 11986981198686 1198694 1198696 1198699 11986910

119886 = 03 1198682 1198691 1198693 11986977228026261198685 1198692 1198695 11986981198686 1198694 1198696 1198699 11986910

119886 = 04 1198682 1198691 1198693 11986977232351401198685 1198692 1198695 11986981198686 1198694 1198696 1198699 11986910

119886 = 05 1198682 1198691 1198693 11986977259452741198685 1198692 1198694 1198695 11986981198686 1198696 1198699 11986910

119886 = 06 1198682 1198691 1198693 11986977275602781198685 1198692 1198694 1198695 11986981198686 1198696 1198699 11986910

119886 = 07 1198682 1198691 1198693 11986977294345041198685 1198692 1198694 1198695 11986981198686 1198696 1198699 11986910

119886 = 08 1198685 1198692 11986957327583631198686 1198694 1198696 1198699 119869101198687 1198691 1198693 1198697 1198698

119886 = 09 1198685 1198692 11986957334712991198686 1198694 1198696 1198699 119869101198687 1198691 1198693 1198697 1198698

119886 = 1 1198685 1198692 11986957346246701198686 1198694 1198696 1198699 119869101198687 1198691 1198693 1198697 1198698

shown in Table 9 the difference value of IFOA and FOA isshown in Figure 4 and the optimization process of FOA andIFOA is shown in Figure 5 (select 119886 = 05)

From the test results in Table 9 and Figures 4 and 5under the same conditions IFOA results are superior to FOAthe convergence accuracy is more accurate and the optimalresults are better Under the same convergence accuracythe number of valid iterations of IFOA is less than that ofFOA which indicates that IFOA converges faster ThereforeIFOA effectively improves the convergence precision andconvergence speed of FOAThe applicability of IFOA is moreextensive

Scientific Programming 11

Table 9 The results of FOA and IFOA

The value of 119886 IFOA optimal FOA optimal119886 = 0 720856314 720874332119886 = 01 721505085 721515326119886 = 02 721865513 721881176119886 = 03 722802626 72285562119886 = 04 723235140 723309877119886 = 05 725945274 726005691119886 = 06 727560278 727613354119886 = 07 729434504 729495412119886 = 08 732758363 732827122119886 = 09 733471299 733549837119886 = 1 734624670 734714368

18018 10241 15663

52994

7473760417

5307660908

6875978538

89698

000100002000030000400005000060000700008000090000

100000

0 01 02 03 04 05 06 07 08 09 1

The d

iffer

ent v

alue

The value of a

Figure 4 The difference value of IFOA and FOA

0 10 20 30 40 50 60 70 80 90 1007

75

8

85

9

95

Iteration number

Cos

t

IFOAFOA

times106

Figure 5 Optimization process of FOA and IFOA (119886 = 05)

5 Conclusions

The location of distribution centers is a complex optimizationproblem To solve the problem of unreasonable networklayout and poor interpretation of customer demand and highcost of distribution this paper optimizes the location ofdistribution centers minimizes the total cost of distributionand establishes a fast and secure distribution center networksystem The conclusions of this paper are summarized asfollows

In this paper a distribution center model is established toreduce the total cost of the enterpriseThemodel is combinedwith the inherent characteristics of fresh goods e-commercetaking into account the principles of distribution centerselection service levels and freshness constraints Due to theincrease in the number of fresh goods e-commerce enter-prises with more intense competition consumer demand ismore and more uncertain Robust optimization is used tooptimize the distribution center model which makes themodel more robust

An improved fruit fly optimization algorithm (IFOA) isproposed in this paper The search step size is dynamicallyadjusted by introducing a weighting function IFOA willserve to solve the established model However the applica-bility of IFOA is more general In this paper we validatethe uncertain demand model by using an example and weprove that the model of distribution centers is valid and caneffectively handle the uncertainty of demand

This paper considers the influence of uncertain demandon the location of distribution centers for fresh goods Itenriches the fresh goods e-commerce distribution centermodel and provides a theoretical basis for a scientific methodof selecting the locations of fresh e-commerce distributioncenters The applicability of the proposed model is mean-ingful and useful for the selection of fresh e-commercedistribution center locations The shortcomings of this paperis that it only considers the uncertainty of customer demandand does not take into account other factors of uncertaintysuch as uncertain delivery weather conditions and uncertaincorruption rate

It is worth noting that some aspects of the model needto be improved For example we will pay more attentionto a variety of uncertain factors so that the model is moresuitable formore complex situations Because the distributioncenter will be related to the distribution of fresh productscoupled with the international awareness of environmentalprotection strengthened gradually the future will take intoaccount the impacts of low-carbon environmental aspects ofthe distribution center location model

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

This research was sponsored by Project of National SocialScience Foundation of China (15BGL202) project of theplanning subject of ldquothe 12th Five-Year Planrdquo in NationalScience and Technology for the Rural Development inChina Demonstration of Key Technology and Equipment forSafe Distribution of Agricultural Logistics (2015BAD18B01)Project of Beijing Philosophy and Social Science (17GBL013)Project of Beijing Municipal Commission of Education(SM201410011002) Project of Innovation Ability Promotion(PXM2016 014213 000033) 2017 Beijing Technology andBusiness University postgraduate student research abilityenhancing project

12 Scientific Programming

References

[1] RAccorsi AGallo andRManzini ldquoA climate driven decision-support model for the distribution of perishable productsrdquoJournal of Cleaner Production vol 165 pp 917ndash929 2017

[2] E Morganti and J Gonzalez-Feliu ldquoCity logistics for perishableproducts The case of the Parmarsquos Food Hubrdquo Case Studies onTransport Policy vol 3 no 2 pp 120ndash128 2015

[3] J A Orjuela-Castro L A Sanabria-Coronado and Peralta-Lozano A M ldquoCoupling facility location models in the supplychain of perishable fruitsrdquo Research in Transportation Businessamp Management 2017

[4] M Merakli and H Yaman ldquoRobust intermodal hub loca-tion under polyhedral demand uncertaintyrdquo TransportationResearch Part B Methodological vol 86 pp 66ndash85 2016

[5] M a Schuster Puga and J-S Tancrez ldquoA heuristic algorithmfor solving large location-inventory problems with demanduncertaintyrdquo European Journal of Operational Research vol 259no 2 pp 413ndash423 2017

[6] A Hiassat A Diabat and I Rahwan ldquoA genetic algorithmapproach for location-inventory-routing problem with perish-able productsrdquo Journal of Manufacturing Systems vol 42 pp93ndash103 2017

[7] K Govindan A Jafarian R Khodaverdi and K DevikaldquoTwo-echelon multiple-vehicle location-routing problem withtime windows for optimization of sustainable supply chainnetwork of perishable foodrdquo International Journal of ProductionEconomics vol 152 pp 9ndash28 2014

[8] Z Drezner and C H Scott ldquoLocation of a distribution centerfor a perishable productrdquo Mathematical Methods of OperationsResearch vol 78 no 3 pp 301ndash314 2013

[9] S M Seyedhosseini and S M Ghoreyshi ldquoAn integrated modelfor production and distribution planning of perishable prod-ucts with inventory and routing considerationsrdquo MathematicalProblems in Engineering vol 2014 Article ID 475606 10 pages2014

[10] M de Keizer R Akkerman M Grunow J M Bloemhof RHaijema and J G van der Vorst ldquoLogistics network designfor perishable products with heterogeneous quality decayrdquoEuropean Journal of Operational Research vol 262 no 2 pp535ndash549 2017

[11] H Yang L I Hong DUWei et al ldquoResearch on location selec-tion of perishable dairy products distribution center based ontwo-stage distributionrdquoComputer Engineering andApplicationsvol 23 pp 239ndash245 2015

[12] J Zhang and F U Shao-chuan ldquoStudy on location of fresh fooddistribution center with demand influenced by the freshnessrdquoChinese Journal of Management Science vol 19 no 10 pp 473ndash476 2011

[13] T Wu H Shen and C Zhu ldquoA multi-period location modelwith transportation economies-of-scale and perishable inven-toryrdquo International Journal of Production Economics vol 169 pp343ndash349 2015

[14] M Musavi and A Bozorgi-Amiri ldquoA multi-objective sus-tainable hub location-scheduling problem for perishable foodsupply chainrdquo Computers amp Industrial Engineering 2017

[15] M Rezaei-Malek R Tavakkoli-Moghaddam B Zahiri and ABozorgi-Amiri ldquoAn interactive approach for designing a robustdisaster relief logistics network with perishable commoditiesrdquoComputers amp Industrial Engineering vol 94 pp 201ndash215 2016

[16] K Khalili-Damghani A-R Abtahi andA Ghasemi ldquoA new bi-objective location-routing problem for distribution of perish-able products evolutionary computation approachrdquo Journal ofMathematical Modelling and Algorithms in Operations Researchvol 14 no 3 pp 287ndash312 2015

[17] Y Zhang Y Jiang M Zhong N Geng and D Chen ldquoRobustOptimization on Regional WCO-for-Biodiesel Supply Chainunder Supply and Demand Uncertaintiesrdquo Scientific Program-ming vol 2016 Article ID 1087845 15 pages 2016

[18] R Qiu and Y Wang ldquoSupply chain network design underdemand uncertainty and supply disruptions a distributionallyrobust optimization approachrdquo Scientific Programming vol2016 Article ID 3848520 15 pages 2016

[19] A Ben-Tal E Hazan T Koren and S Mannor ldquoOracle-basedrobust optimization via online learningrdquo Operations Researchvol 63 no 3 pp 628ndash638 2015

[20] M Melamed A Ben-Tal and B Golany ldquoOn the averageperformance of the adjustable RO and its use as an offlinetool for multi-period production planning under uncertaintyrdquoComputational Management Science vol 13 no 2 pp 293ndash3152016

[21] A Ghodratnama R Tavakkoli-Moghaddam and A AzaronldquoRobust and fuzzy goal programming optimization approachesfor a novel multi-objective hub location-allocation problem Asupply chain overviewrdquoApplied SoftComputing vol 37 pp 255ndash276 2015

[22] F Habibzadeh Boukani B Farhang Moghaddam and M SPishvaee ldquoRobust optimization approach to capacitated singleand multiple allocation hub location problemsrdquo Computationalamp Applied Mathematics vol 35 no 1 pp 45ndash60 2016

[23] A Jakubovskis ldquoStrategic facility location capacity acquisitionand technology choice decisions under demand uncertaintyrobust vs non-robust optimization approachesrdquo European Jour-nal of Operational Research vol 260 no 3 pp 1095ndash1104 2017

[24] H A Eiselt and V Marianov ldquoA bi-objective model for thelocation of landfills formunicipal solidwasterdquoEuropean Journalof Operational Research vol 235 no 1 pp 187ndash194 2014

[25] M G Bardossy and S Raghavan ldquoRobust Optimization forthe Connected Facility Location Problemrdquo Electronic Notes inDiscrete Mathematics vol 44 pp 149ndash154 2013

[26] V de Rosa E Hartmann M Gebhard and J WollenweberldquoRobust capacitated facility location model for acquisitionsunder uncertaintyrdquoComputers amp Industrial Engineering vol 72pp 206ndash216 2014

[27] M Ehrgott J Ide and A Schoobel ldquoMinmax robustness formulti-objective optimization problemsrdquo European Journal ofOperational Research vol 239 no 1 pp 17ndash31 2014

[28] X-F Xu J Hao Y-R Deng and YWang ldquoDesign optimizationof resource combination for collaborative logistics networkunder uncertaintyrdquo Applied Soft Computing vol 56 pp 684ndash691 2017

[29] E D Majewski M Wirtz M Lampe and etal ldquoRobust multi-objective optimization for sustainable design of distributedenergy supply systemsrdquoComputersampChemical Engineering vol102 pp 26ndash39 2016

[30] M Yunfeng Y Chao M Zhang and H Chunyan ldquoTime-satisfaction-based maximal covering location problemrdquo Chi-nese Journal of Management Science vol 2 pp 45ndash51 2006

[31] W-T Pan ldquoA new fruit fly optimization algorithm takingthe financial distress model as an examplerdquo Knowledge-BasedSystems vol 26 pp 69ndash74 2012

Scientific Programming 13

[32] S Kanarachos J Griffin and M E Fitzpatrick ldquoEfficient trussoptimization using the contrast-based fruit fly optimizationalgorithmrdquo Computers amp Structures vol 182 pp 137ndash148 2017

[33] J Niu W Zhong Y Liang N Luo and F Qian ldquoFruit flyoptimization algorithm based on differential evolution andits application on gasification process operation optimizationrdquoKnowledge-Based Systems vol 88 pp 253ndash263 2015

[34] S-M Lin ldquoAnalysis of service satisfaction in web auctionlogistics service using a combination of Fruit fly optimizationalgorithm and general regression neural networkrdquoNeural Com-puting and Applications vol 22 no 3-4 pp 783ndash791 2013

[35] J Huber A Gossmann andH Stuckenschmidt ldquoCluster-basedhierarchical demand forecasting for perishable goodsrdquo ExpertSystems with Applications vol 76 pp 140ndash151 2017

[36] M Shukla and S Jharkharia ldquoApplicability of ARIMA modelsin wholesale vegetable market An investigationrdquo InternationalJournal of Information Systems and Supply Chain Managementvol 6 no 3 pp 105ndash119 2013

[37] C Sun and X Luo ldquoThe influencing factors and countermea-sures of supply uncertainty in supply chainrdquo Economic ResearchGuide vol 11 pp 146-147 2013

[38] S Minner and S Transchel ldquoOrder variability in perish-able product supply chainsrdquo European Journal of OperationalResearch vol 260 no 1 pp 93ndash107 2017

Submit your manuscripts athttpswwwhindawicom

Computer Games Technology

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Distributed Sensor Networks

International Journal of

Advances in

FuzzySystems

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014

International Journal of

ReconfigurableComputing

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 201

Applied Computational Intelligence and Soft Computing

thinspAdvancesthinspinthinsp

Artificial Intelligence

HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014

Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Hindawi Publishing Corporation

httpwwwhindawicom Volume 2014

Advances in

Multimedia

International Journal of

Biomedical Imaging

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 201

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Computational Intelligence and Neuroscience

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

8 Scientific Programming

Table 3 Distance between supplier ℎ and distribution center 119894 (km)

1198681 1198682 1198683 1198684 1198685 1198686 1198687 11986881198671 1431 2912 19945 12093 7738 8814 3214 79831198672 7382 9424 11886 4712 4500 1204 6527 109651198673 13223 11025 10594 3544 9126 6395 7580 6324

0 10 20 30 40 50 60 70 80 90 100minus1

minus0998

minus0996

minus0994

minus0992

minus099

minus0988

minus0986

minus0984

Iteration number

Smel

l

IFOAFOA

0

0002

0004

0006

0008

001

0012

0014

Smel

l

f1(x)

0 10 20 30 40 50 60 70 80 90 100Iteration number

IFOAFOA

f2(x)

Figure 2 Optimization process of FOA and IFOA

position and optimal value of the individual andthe global optimal individual

(4) Find the fruit flies with the best smell concen-tration and allow the flies to fly to the optimalposition

(5) Stop the search if the maximum evaluationnumber is reached otherwise repeat

(6) According to the IFOA optimal location resultsthen find the corresponding best location of thedistribution center and the optimal distributionpath

4 Computational Results

Experiments are proposed in this part to prove the effective-ness and feasibility of the location model Both deterministicand uncertain demand scenarios are considered and then acomparison and analysis of the results of the two situationsis providedThe numerical calculation problem is consideredto occur in a developed city where a fresh goods e-commercefirm chooses to rent a certain number of distribution centerswithin an appropriate area The area of suppliers is 3 and thearea of customers is 10 The firm chooses to rent 3 locationsfrom a set of 8 candidate distribution centers

The distance between the supplier and the candidatedistribution center and the distance between the candidatedistribution center and the demand point are obtained by

using the Euclidean theorem The details are shown inTables 3 and 4 The tables consider the different qualitiesof each candidate distribution center such as the locationtransportation economy and other conditions Fixed costsoperating costs and the largest inventory are also different asshown in Table 5 The maximum supply capacity of supplierℎ is shown in Table 6

The average traveling speed is 45 kmh for the distributionvehicles in the region the average unit freight from thesupplier to the distribution center is 15 yuan(tsdotkm) and thefreight rate from the distribution center to the demand pointis 18 yuan(tsdotkm) To simplify the follow-up calculation thenumerical calculations only consider the distribution of twofresh goods using the corruption coefficients of 015 and008 and the unit prices of 4 yuankg and 6 yuankg Theaverage satisfaction threshold for customer satisfaction is075 and the average satisfaction threshold for freshness is07 If the delivery vehicle arrives late the compensation feeis 50 yuan(hsdott) The demand point time window is shown inTable 7

We consider cases where demand is both deterministicand uncertain The calculation and comparative analysisof two cases can be conducted more directly to verifywhether the model can help the fresh goods e-commerceto suppress the uncertainty interference by demand Themethod used to predict the consumer demand is the multi-variate autoregressive integrated moving average (AMIMA)model in this paper Fresh e-commerce is characterized

Scientific Programming 9

Table 4 Distance between distribution center 119894 and customer 119895 (km)

1198681 1198682 1198683 1198684 1198685 1198686 1198687 11986881198691 14200 4134 24550 16717 8919 11733 7560 144361198692 5420 9642 20535 14220 5903 8628 10072 180711198693 11610 1170 19564 11682 5178 7156 2469 102011198694 6525 18398 13761 12419 12180 11123 16497 214241198695 4827 7716 17279 10536 2282 4850 7000 145791198696 9904 15932 6296 4810 10720 7694 12857 146731198697 22649 13509 20341 14670 16589 15631 12035 48871198698 10718 3383 17310 9420 4161 5215 721 89051198699 12879 19474 3981 7506 14322 11287 16319 1711411986910 15277 14586 7910 3984 12248 9166 11140 8238

Table 5 Fixed costs operating costs and maximum inventory

Candidate distribution centers 1198681 1198682 1198683 1198684 1198685 1198686 1198687 1198688Fixed costs (million) 145 138 123 148 129 123 138 136Operating costs (million) 007 006 006 009 005 006 007 006Maximum inventoryt 1000 900 700 1100 1000 900 1200 800

Table 6 The maximum supply capacity of supplier

Supplier 1198671 1198672 1198673Themaximum supply capacityt 8800 7900 6300

Table 7 Time window and determined demand of customer

Customer (119879119895min 119879119895 119879119895max) Demand (t)1198691 (2 25 3) 2001198692 (3 4 5) 4001198693 (1 15 2) 3501198694 (1 2 25) 2501198695 (2 3 4) 1501198696 (3 35 4) 3501198697 (15 25 3) 3001198698 (2 3 45) 1801198699 (15 25 3) 35011986910 (3 4 5) 300

by consumers ordering through the Internet so fresh e-commerce companies can collect customer information andorder information (eg customersrsquo purchasing frequencypurchasing preferences and position distribution) Thenthe fresh e-commerce company can use this informationto classify consumers and predict consumer demand Theautoregressive part of the multiple ARIMAmodel representsa linear combination of past values while themoving averagepart of the multiple ARIMAmodel is a linear combination ofpast forecasting errorsThe advantage of themultiple ARIMAmodel is that it improves prediction accuracy facilitatesstatistics and reduces the cost of prediction Moreover it cancombine product cost changes with demand uncertainty topredict consumer demand [35] In view of this the multi-variate ARIMA model is suitable to predict the consumerdemand for fresh e-commerce Although the AMIMAmodel

can more accurately predict the uncertainty of demand thesize of fresh e-commercersquos consumers is small and widelydistributed so there is still uncertainty in demand To learnmore about the multivariate ARIMA model studies [35 36]are suggested The deterministic demand for each customeris shown in Table 7

The affected factors of uncertain supply involve envi-ronmental factors (eg the natural environment economicenvironment and political environment) and the abilities ofsuppliers (eg production capacity equipment capacity) [37]First the planting period for fresh foods is the quarter or yearas a unit the period is longer than for other products Fresh e-commerce can be investigated in advance through the Inter-net and then the product cultivation of the fresh food and thefield investigation can be planned accordingly Second thesuppliers of fresh electricity providers are typically farmersand fresh food bases around the region These suppliersare less affected by global economic changes and politicalchanges The selection diversity of suppliers also allows freshe-commerce companies to evaluate and select suppliers inadvance In addition the equipment failure problem has lessof an effect on fresh e-commerce because fresh productscan be delivered to the distribution center though simplepretreatment packaging In summary the supply of fresh e-commerce is uncertain but fresh e-commerce companies areless affected by these uncertain factors due to the specialnature of fresh foods The current delivery mode of freshproducts is from a mono type and large batch distributionto a multitype delivery mode and small batch distributionEach time an order is made the consumer evaluates thefresh electricity service (eg Amazon Fresh and MotionOptimization) For the majority of instances the perishablenature of a product results in the supply process having alower variability than the demand process [38] Thereforethis paper focuses on the location model for distributioncenters under uncertain demand

10 Scientific Programming

0 009 014027033

071093

119

165 175191

0

0005

001

0015

002

0025

0 01 02 03 04 05 06 07 08 09 1

The i

ncre

ase r

atio

The value of a

Figure 3 The increase ratio of the total cost of uncertain demand

For the case of uncertainty we assume that the demandfor each demand point is 119904 = 5 The number of scenariosfor each demand point can be different from each other Thevalue of the demand scenario is determined by the surveyand then the five cases are generated randomly by Matlab 83as the demand scenario of the demand point 119895 The demandscenario of the 10 demandpoints can be obtained by repeatingthe process ten times

The discrete demand probability distribution is 1199010119895119904 119869 =119895 | 119895 = 1 2 119899For 1199010119895119904 in the range (0 1) the simulations are randomly

generated between the 10 numbers normalized and repeatedten times in order to get all the demand points in theuncertain demand scenarioTheprobability demand scenarioof customer 119895 (119901119895119904) meets the uncertainty set Let thedecentralized matrix be 119876 = 119886119868 where 119886 is a nonnegativeparameter and 119868 is an identity matrix

In the experiment let 119886 = 05 and 119886 = 08 respectivelyCalculate 119901119895119904

The specific initialization parameter is set to maxgen =100 sizepop = 20 The program is implemented in Matlab83 and run on a computer with 26GHz Intel i5-4210MCPU 4GB of RAM andWindows 10The distribution centerdecision-making program and the total cost are shown inTable 8

For the deterministic demand situation the optimal deci-sion is to choose distribution center 119868211986851198686 from the candidatelist The total cost is 7208 million For the uncertain demandsituation when 119886 = 01 to 119886 = 04 the optimal decision isto choose distribution centers 119868211986851198686 The distribution rangeis constant but the cost increases When 119886 = 05 to 119886 = 07the optimal decision is to choose distribution centers 119868211986851198686but the distribution range is different from the deterministicdemand situation When 119886 = 08 to 119886 = 1 the optimaldecision is to choose distribution centers 119868511986861198687 The increaseratio of the total cost in the case of uncertainty is comparedto the total cost in the demand determination as shownin Figure 3 Enterprises in the decision-making before theconsumer demand should be the historical data for statisticaland analysis determine the variation range of parameter119886 and make decisions based on cost and self-conditions(Figure 3)

Then using FOA to solve themodel and initial parametersand operating environment equally with IFOA the results are

Table 8 The decision-making program and the total cost ofdistribution center

The value of 119886 Decision-makingprogram and

distribution rangeCost (RMB)

119886 = 0 1198682 1198691 1198693 11986977208563141198685 1198692 1198695 11986981198686 1198694 1198696 1198699 11986910

119886 = 01 1198682 1198691 1198693 11986977215050851198685 1198692 1198695 11986981198686 1198694 1198696 1198699 11986910

119886 = 02 1198682 1198691 1198693 11986977218655131198685 1198692 1198695 11986981198686 1198694 1198696 1198699 11986910

119886 = 03 1198682 1198691 1198693 11986977228026261198685 1198692 1198695 11986981198686 1198694 1198696 1198699 11986910

119886 = 04 1198682 1198691 1198693 11986977232351401198685 1198692 1198695 11986981198686 1198694 1198696 1198699 11986910

119886 = 05 1198682 1198691 1198693 11986977259452741198685 1198692 1198694 1198695 11986981198686 1198696 1198699 11986910

119886 = 06 1198682 1198691 1198693 11986977275602781198685 1198692 1198694 1198695 11986981198686 1198696 1198699 11986910

119886 = 07 1198682 1198691 1198693 11986977294345041198685 1198692 1198694 1198695 11986981198686 1198696 1198699 11986910

119886 = 08 1198685 1198692 11986957327583631198686 1198694 1198696 1198699 119869101198687 1198691 1198693 1198697 1198698

119886 = 09 1198685 1198692 11986957334712991198686 1198694 1198696 1198699 119869101198687 1198691 1198693 1198697 1198698

119886 = 1 1198685 1198692 11986957346246701198686 1198694 1198696 1198699 119869101198687 1198691 1198693 1198697 1198698

shown in Table 9 the difference value of IFOA and FOA isshown in Figure 4 and the optimization process of FOA andIFOA is shown in Figure 5 (select 119886 = 05)

From the test results in Table 9 and Figures 4 and 5under the same conditions IFOA results are superior to FOAthe convergence accuracy is more accurate and the optimalresults are better Under the same convergence accuracythe number of valid iterations of IFOA is less than that ofFOA which indicates that IFOA converges faster ThereforeIFOA effectively improves the convergence precision andconvergence speed of FOAThe applicability of IFOA is moreextensive

Scientific Programming 11

Table 9 The results of FOA and IFOA

The value of 119886 IFOA optimal FOA optimal119886 = 0 720856314 720874332119886 = 01 721505085 721515326119886 = 02 721865513 721881176119886 = 03 722802626 72285562119886 = 04 723235140 723309877119886 = 05 725945274 726005691119886 = 06 727560278 727613354119886 = 07 729434504 729495412119886 = 08 732758363 732827122119886 = 09 733471299 733549837119886 = 1 734624670 734714368

18018 10241 15663

52994

7473760417

5307660908

6875978538

89698

000100002000030000400005000060000700008000090000

100000

0 01 02 03 04 05 06 07 08 09 1

The d

iffer

ent v

alue

The value of a

Figure 4 The difference value of IFOA and FOA

0 10 20 30 40 50 60 70 80 90 1007

75

8

85

9

95

Iteration number

Cos

t

IFOAFOA

times106

Figure 5 Optimization process of FOA and IFOA (119886 = 05)

5 Conclusions

The location of distribution centers is a complex optimizationproblem To solve the problem of unreasonable networklayout and poor interpretation of customer demand and highcost of distribution this paper optimizes the location ofdistribution centers minimizes the total cost of distributionand establishes a fast and secure distribution center networksystem The conclusions of this paper are summarized asfollows

In this paper a distribution center model is established toreduce the total cost of the enterpriseThemodel is combinedwith the inherent characteristics of fresh goods e-commercetaking into account the principles of distribution centerselection service levels and freshness constraints Due to theincrease in the number of fresh goods e-commerce enter-prises with more intense competition consumer demand ismore and more uncertain Robust optimization is used tooptimize the distribution center model which makes themodel more robust

An improved fruit fly optimization algorithm (IFOA) isproposed in this paper The search step size is dynamicallyadjusted by introducing a weighting function IFOA willserve to solve the established model However the applica-bility of IFOA is more general In this paper we validatethe uncertain demand model by using an example and weprove that the model of distribution centers is valid and caneffectively handle the uncertainty of demand

This paper considers the influence of uncertain demandon the location of distribution centers for fresh goods Itenriches the fresh goods e-commerce distribution centermodel and provides a theoretical basis for a scientific methodof selecting the locations of fresh e-commerce distributioncenters The applicability of the proposed model is mean-ingful and useful for the selection of fresh e-commercedistribution center locations The shortcomings of this paperis that it only considers the uncertainty of customer demandand does not take into account other factors of uncertaintysuch as uncertain delivery weather conditions and uncertaincorruption rate

It is worth noting that some aspects of the model needto be improved For example we will pay more attentionto a variety of uncertain factors so that the model is moresuitable formore complex situations Because the distributioncenter will be related to the distribution of fresh productscoupled with the international awareness of environmentalprotection strengthened gradually the future will take intoaccount the impacts of low-carbon environmental aspects ofthe distribution center location model

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

This research was sponsored by Project of National SocialScience Foundation of China (15BGL202) project of theplanning subject of ldquothe 12th Five-Year Planrdquo in NationalScience and Technology for the Rural Development inChina Demonstration of Key Technology and Equipment forSafe Distribution of Agricultural Logistics (2015BAD18B01)Project of Beijing Philosophy and Social Science (17GBL013)Project of Beijing Municipal Commission of Education(SM201410011002) Project of Innovation Ability Promotion(PXM2016 014213 000033) 2017 Beijing Technology andBusiness University postgraduate student research abilityenhancing project

12 Scientific Programming

References

[1] RAccorsi AGallo andRManzini ldquoA climate driven decision-support model for the distribution of perishable productsrdquoJournal of Cleaner Production vol 165 pp 917ndash929 2017

[2] E Morganti and J Gonzalez-Feliu ldquoCity logistics for perishableproducts The case of the Parmarsquos Food Hubrdquo Case Studies onTransport Policy vol 3 no 2 pp 120ndash128 2015

[3] J A Orjuela-Castro L A Sanabria-Coronado and Peralta-Lozano A M ldquoCoupling facility location models in the supplychain of perishable fruitsrdquo Research in Transportation Businessamp Management 2017

[4] M Merakli and H Yaman ldquoRobust intermodal hub loca-tion under polyhedral demand uncertaintyrdquo TransportationResearch Part B Methodological vol 86 pp 66ndash85 2016

[5] M a Schuster Puga and J-S Tancrez ldquoA heuristic algorithmfor solving large location-inventory problems with demanduncertaintyrdquo European Journal of Operational Research vol 259no 2 pp 413ndash423 2017

[6] A Hiassat A Diabat and I Rahwan ldquoA genetic algorithmapproach for location-inventory-routing problem with perish-able productsrdquo Journal of Manufacturing Systems vol 42 pp93ndash103 2017

[7] K Govindan A Jafarian R Khodaverdi and K DevikaldquoTwo-echelon multiple-vehicle location-routing problem withtime windows for optimization of sustainable supply chainnetwork of perishable foodrdquo International Journal of ProductionEconomics vol 152 pp 9ndash28 2014

[8] Z Drezner and C H Scott ldquoLocation of a distribution centerfor a perishable productrdquo Mathematical Methods of OperationsResearch vol 78 no 3 pp 301ndash314 2013

[9] S M Seyedhosseini and S M Ghoreyshi ldquoAn integrated modelfor production and distribution planning of perishable prod-ucts with inventory and routing considerationsrdquo MathematicalProblems in Engineering vol 2014 Article ID 475606 10 pages2014

[10] M de Keizer R Akkerman M Grunow J M Bloemhof RHaijema and J G van der Vorst ldquoLogistics network designfor perishable products with heterogeneous quality decayrdquoEuropean Journal of Operational Research vol 262 no 2 pp535ndash549 2017

[11] H Yang L I Hong DUWei et al ldquoResearch on location selec-tion of perishable dairy products distribution center based ontwo-stage distributionrdquoComputer Engineering andApplicationsvol 23 pp 239ndash245 2015

[12] J Zhang and F U Shao-chuan ldquoStudy on location of fresh fooddistribution center with demand influenced by the freshnessrdquoChinese Journal of Management Science vol 19 no 10 pp 473ndash476 2011

[13] T Wu H Shen and C Zhu ldquoA multi-period location modelwith transportation economies-of-scale and perishable inven-toryrdquo International Journal of Production Economics vol 169 pp343ndash349 2015

[14] M Musavi and A Bozorgi-Amiri ldquoA multi-objective sus-tainable hub location-scheduling problem for perishable foodsupply chainrdquo Computers amp Industrial Engineering 2017

[15] M Rezaei-Malek R Tavakkoli-Moghaddam B Zahiri and ABozorgi-Amiri ldquoAn interactive approach for designing a robustdisaster relief logistics network with perishable commoditiesrdquoComputers amp Industrial Engineering vol 94 pp 201ndash215 2016

[16] K Khalili-Damghani A-R Abtahi andA Ghasemi ldquoA new bi-objective location-routing problem for distribution of perish-able products evolutionary computation approachrdquo Journal ofMathematical Modelling and Algorithms in Operations Researchvol 14 no 3 pp 287ndash312 2015

[17] Y Zhang Y Jiang M Zhong N Geng and D Chen ldquoRobustOptimization on Regional WCO-for-Biodiesel Supply Chainunder Supply and Demand Uncertaintiesrdquo Scientific Program-ming vol 2016 Article ID 1087845 15 pages 2016

[18] R Qiu and Y Wang ldquoSupply chain network design underdemand uncertainty and supply disruptions a distributionallyrobust optimization approachrdquo Scientific Programming vol2016 Article ID 3848520 15 pages 2016

[19] A Ben-Tal E Hazan T Koren and S Mannor ldquoOracle-basedrobust optimization via online learningrdquo Operations Researchvol 63 no 3 pp 628ndash638 2015

[20] M Melamed A Ben-Tal and B Golany ldquoOn the averageperformance of the adjustable RO and its use as an offlinetool for multi-period production planning under uncertaintyrdquoComputational Management Science vol 13 no 2 pp 293ndash3152016

[21] A Ghodratnama R Tavakkoli-Moghaddam and A AzaronldquoRobust and fuzzy goal programming optimization approachesfor a novel multi-objective hub location-allocation problem Asupply chain overviewrdquoApplied SoftComputing vol 37 pp 255ndash276 2015

[22] F Habibzadeh Boukani B Farhang Moghaddam and M SPishvaee ldquoRobust optimization approach to capacitated singleand multiple allocation hub location problemsrdquo Computationalamp Applied Mathematics vol 35 no 1 pp 45ndash60 2016

[23] A Jakubovskis ldquoStrategic facility location capacity acquisitionand technology choice decisions under demand uncertaintyrobust vs non-robust optimization approachesrdquo European Jour-nal of Operational Research vol 260 no 3 pp 1095ndash1104 2017

[24] H A Eiselt and V Marianov ldquoA bi-objective model for thelocation of landfills formunicipal solidwasterdquoEuropean Journalof Operational Research vol 235 no 1 pp 187ndash194 2014

[25] M G Bardossy and S Raghavan ldquoRobust Optimization forthe Connected Facility Location Problemrdquo Electronic Notes inDiscrete Mathematics vol 44 pp 149ndash154 2013

[26] V de Rosa E Hartmann M Gebhard and J WollenweberldquoRobust capacitated facility location model for acquisitionsunder uncertaintyrdquoComputers amp Industrial Engineering vol 72pp 206ndash216 2014

[27] M Ehrgott J Ide and A Schoobel ldquoMinmax robustness formulti-objective optimization problemsrdquo European Journal ofOperational Research vol 239 no 1 pp 17ndash31 2014

[28] X-F Xu J Hao Y-R Deng and YWang ldquoDesign optimizationof resource combination for collaborative logistics networkunder uncertaintyrdquo Applied Soft Computing vol 56 pp 684ndash691 2017

[29] E D Majewski M Wirtz M Lampe and etal ldquoRobust multi-objective optimization for sustainable design of distributedenergy supply systemsrdquoComputersampChemical Engineering vol102 pp 26ndash39 2016

[30] M Yunfeng Y Chao M Zhang and H Chunyan ldquoTime-satisfaction-based maximal covering location problemrdquo Chi-nese Journal of Management Science vol 2 pp 45ndash51 2006

[31] W-T Pan ldquoA new fruit fly optimization algorithm takingthe financial distress model as an examplerdquo Knowledge-BasedSystems vol 26 pp 69ndash74 2012

Scientific Programming 13

[32] S Kanarachos J Griffin and M E Fitzpatrick ldquoEfficient trussoptimization using the contrast-based fruit fly optimizationalgorithmrdquo Computers amp Structures vol 182 pp 137ndash148 2017

[33] J Niu W Zhong Y Liang N Luo and F Qian ldquoFruit flyoptimization algorithm based on differential evolution andits application on gasification process operation optimizationrdquoKnowledge-Based Systems vol 88 pp 253ndash263 2015

[34] S-M Lin ldquoAnalysis of service satisfaction in web auctionlogistics service using a combination of Fruit fly optimizationalgorithm and general regression neural networkrdquoNeural Com-puting and Applications vol 22 no 3-4 pp 783ndash791 2013

[35] J Huber A Gossmann andH Stuckenschmidt ldquoCluster-basedhierarchical demand forecasting for perishable goodsrdquo ExpertSystems with Applications vol 76 pp 140ndash151 2017

[36] M Shukla and S Jharkharia ldquoApplicability of ARIMA modelsin wholesale vegetable market An investigationrdquo InternationalJournal of Information Systems and Supply Chain Managementvol 6 no 3 pp 105ndash119 2013

[37] C Sun and X Luo ldquoThe influencing factors and countermea-sures of supply uncertainty in supply chainrdquo Economic ResearchGuide vol 11 pp 146-147 2013

[38] S Minner and S Transchel ldquoOrder variability in perish-able product supply chainsrdquo European Journal of OperationalResearch vol 260 no 1 pp 93ndash107 2017

Submit your manuscripts athttpswwwhindawicom

Computer Games Technology

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Distributed Sensor Networks

International Journal of

Advances in

FuzzySystems

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014

International Journal of

ReconfigurableComputing

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 201

Applied Computational Intelligence and Soft Computing

thinspAdvancesthinspinthinsp

Artificial Intelligence

HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014

Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Hindawi Publishing Corporation

httpwwwhindawicom Volume 2014

Advances in

Multimedia

International Journal of

Biomedical Imaging

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 201

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Computational Intelligence and Neuroscience

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Scientific Programming 9

Table 4 Distance between distribution center 119894 and customer 119895 (km)

1198681 1198682 1198683 1198684 1198685 1198686 1198687 11986881198691 14200 4134 24550 16717 8919 11733 7560 144361198692 5420 9642 20535 14220 5903 8628 10072 180711198693 11610 1170 19564 11682 5178 7156 2469 102011198694 6525 18398 13761 12419 12180 11123 16497 214241198695 4827 7716 17279 10536 2282 4850 7000 145791198696 9904 15932 6296 4810 10720 7694 12857 146731198697 22649 13509 20341 14670 16589 15631 12035 48871198698 10718 3383 17310 9420 4161 5215 721 89051198699 12879 19474 3981 7506 14322 11287 16319 1711411986910 15277 14586 7910 3984 12248 9166 11140 8238

Table 5 Fixed costs operating costs and maximum inventory

Candidate distribution centers 1198681 1198682 1198683 1198684 1198685 1198686 1198687 1198688Fixed costs (million) 145 138 123 148 129 123 138 136Operating costs (million) 007 006 006 009 005 006 007 006Maximum inventoryt 1000 900 700 1100 1000 900 1200 800

Table 6 The maximum supply capacity of supplier

Supplier 1198671 1198672 1198673Themaximum supply capacityt 8800 7900 6300

Table 7 Time window and determined demand of customer

Customer (119879119895min 119879119895 119879119895max) Demand (t)1198691 (2 25 3) 2001198692 (3 4 5) 4001198693 (1 15 2) 3501198694 (1 2 25) 2501198695 (2 3 4) 1501198696 (3 35 4) 3501198697 (15 25 3) 3001198698 (2 3 45) 1801198699 (15 25 3) 35011986910 (3 4 5) 300

by consumers ordering through the Internet so fresh e-commerce companies can collect customer information andorder information (eg customersrsquo purchasing frequencypurchasing preferences and position distribution) Thenthe fresh e-commerce company can use this informationto classify consumers and predict consumer demand Theautoregressive part of the multiple ARIMAmodel representsa linear combination of past values while themoving averagepart of the multiple ARIMAmodel is a linear combination ofpast forecasting errorsThe advantage of themultiple ARIMAmodel is that it improves prediction accuracy facilitatesstatistics and reduces the cost of prediction Moreover it cancombine product cost changes with demand uncertainty topredict consumer demand [35] In view of this the multi-variate ARIMA model is suitable to predict the consumerdemand for fresh e-commerce Although the AMIMAmodel

can more accurately predict the uncertainty of demand thesize of fresh e-commercersquos consumers is small and widelydistributed so there is still uncertainty in demand To learnmore about the multivariate ARIMA model studies [35 36]are suggested The deterministic demand for each customeris shown in Table 7

The affected factors of uncertain supply involve envi-ronmental factors (eg the natural environment economicenvironment and political environment) and the abilities ofsuppliers (eg production capacity equipment capacity) [37]First the planting period for fresh foods is the quarter or yearas a unit the period is longer than for other products Fresh e-commerce can be investigated in advance through the Inter-net and then the product cultivation of the fresh food and thefield investigation can be planned accordingly Second thesuppliers of fresh electricity providers are typically farmersand fresh food bases around the region These suppliersare less affected by global economic changes and politicalchanges The selection diversity of suppliers also allows freshe-commerce companies to evaluate and select suppliers inadvance In addition the equipment failure problem has lessof an effect on fresh e-commerce because fresh productscan be delivered to the distribution center though simplepretreatment packaging In summary the supply of fresh e-commerce is uncertain but fresh e-commerce companies areless affected by these uncertain factors due to the specialnature of fresh foods The current delivery mode of freshproducts is from a mono type and large batch distributionto a multitype delivery mode and small batch distributionEach time an order is made the consumer evaluates thefresh electricity service (eg Amazon Fresh and MotionOptimization) For the majority of instances the perishablenature of a product results in the supply process having alower variability than the demand process [38] Thereforethis paper focuses on the location model for distributioncenters under uncertain demand

10 Scientific Programming

0 009 014027033

071093

119

165 175191

0

0005

001

0015

002

0025

0 01 02 03 04 05 06 07 08 09 1

The i

ncre

ase r

atio

The value of a

Figure 3 The increase ratio of the total cost of uncertain demand

For the case of uncertainty we assume that the demandfor each demand point is 119904 = 5 The number of scenariosfor each demand point can be different from each other Thevalue of the demand scenario is determined by the surveyand then the five cases are generated randomly by Matlab 83as the demand scenario of the demand point 119895 The demandscenario of the 10 demandpoints can be obtained by repeatingthe process ten times

The discrete demand probability distribution is 1199010119895119904 119869 =119895 | 119895 = 1 2 119899For 1199010119895119904 in the range (0 1) the simulations are randomly

generated between the 10 numbers normalized and repeatedten times in order to get all the demand points in theuncertain demand scenarioTheprobability demand scenarioof customer 119895 (119901119895119904) meets the uncertainty set Let thedecentralized matrix be 119876 = 119886119868 where 119886 is a nonnegativeparameter and 119868 is an identity matrix

In the experiment let 119886 = 05 and 119886 = 08 respectivelyCalculate 119901119895119904

The specific initialization parameter is set to maxgen =100 sizepop = 20 The program is implemented in Matlab83 and run on a computer with 26GHz Intel i5-4210MCPU 4GB of RAM andWindows 10The distribution centerdecision-making program and the total cost are shown inTable 8

For the deterministic demand situation the optimal deci-sion is to choose distribution center 119868211986851198686 from the candidatelist The total cost is 7208 million For the uncertain demandsituation when 119886 = 01 to 119886 = 04 the optimal decision isto choose distribution centers 119868211986851198686 The distribution rangeis constant but the cost increases When 119886 = 05 to 119886 = 07the optimal decision is to choose distribution centers 119868211986851198686but the distribution range is different from the deterministicdemand situation When 119886 = 08 to 119886 = 1 the optimaldecision is to choose distribution centers 119868511986861198687 The increaseratio of the total cost in the case of uncertainty is comparedto the total cost in the demand determination as shownin Figure 3 Enterprises in the decision-making before theconsumer demand should be the historical data for statisticaland analysis determine the variation range of parameter119886 and make decisions based on cost and self-conditions(Figure 3)

Then using FOA to solve themodel and initial parametersand operating environment equally with IFOA the results are

Table 8 The decision-making program and the total cost ofdistribution center

The value of 119886 Decision-makingprogram and

distribution rangeCost (RMB)

119886 = 0 1198682 1198691 1198693 11986977208563141198685 1198692 1198695 11986981198686 1198694 1198696 1198699 11986910

119886 = 01 1198682 1198691 1198693 11986977215050851198685 1198692 1198695 11986981198686 1198694 1198696 1198699 11986910

119886 = 02 1198682 1198691 1198693 11986977218655131198685 1198692 1198695 11986981198686 1198694 1198696 1198699 11986910

119886 = 03 1198682 1198691 1198693 11986977228026261198685 1198692 1198695 11986981198686 1198694 1198696 1198699 11986910

119886 = 04 1198682 1198691 1198693 11986977232351401198685 1198692 1198695 11986981198686 1198694 1198696 1198699 11986910

119886 = 05 1198682 1198691 1198693 11986977259452741198685 1198692 1198694 1198695 11986981198686 1198696 1198699 11986910

119886 = 06 1198682 1198691 1198693 11986977275602781198685 1198692 1198694 1198695 11986981198686 1198696 1198699 11986910

119886 = 07 1198682 1198691 1198693 11986977294345041198685 1198692 1198694 1198695 11986981198686 1198696 1198699 11986910

119886 = 08 1198685 1198692 11986957327583631198686 1198694 1198696 1198699 119869101198687 1198691 1198693 1198697 1198698

119886 = 09 1198685 1198692 11986957334712991198686 1198694 1198696 1198699 119869101198687 1198691 1198693 1198697 1198698

119886 = 1 1198685 1198692 11986957346246701198686 1198694 1198696 1198699 119869101198687 1198691 1198693 1198697 1198698

shown in Table 9 the difference value of IFOA and FOA isshown in Figure 4 and the optimization process of FOA andIFOA is shown in Figure 5 (select 119886 = 05)

From the test results in Table 9 and Figures 4 and 5under the same conditions IFOA results are superior to FOAthe convergence accuracy is more accurate and the optimalresults are better Under the same convergence accuracythe number of valid iterations of IFOA is less than that ofFOA which indicates that IFOA converges faster ThereforeIFOA effectively improves the convergence precision andconvergence speed of FOAThe applicability of IFOA is moreextensive

Scientific Programming 11

Table 9 The results of FOA and IFOA

The value of 119886 IFOA optimal FOA optimal119886 = 0 720856314 720874332119886 = 01 721505085 721515326119886 = 02 721865513 721881176119886 = 03 722802626 72285562119886 = 04 723235140 723309877119886 = 05 725945274 726005691119886 = 06 727560278 727613354119886 = 07 729434504 729495412119886 = 08 732758363 732827122119886 = 09 733471299 733549837119886 = 1 734624670 734714368

18018 10241 15663

52994

7473760417

5307660908

6875978538

89698

000100002000030000400005000060000700008000090000

100000

0 01 02 03 04 05 06 07 08 09 1

The d

iffer

ent v

alue

The value of a

Figure 4 The difference value of IFOA and FOA

0 10 20 30 40 50 60 70 80 90 1007

75

8

85

9

95

Iteration number

Cos

t

IFOAFOA

times106

Figure 5 Optimization process of FOA and IFOA (119886 = 05)

5 Conclusions

The location of distribution centers is a complex optimizationproblem To solve the problem of unreasonable networklayout and poor interpretation of customer demand and highcost of distribution this paper optimizes the location ofdistribution centers minimizes the total cost of distributionand establishes a fast and secure distribution center networksystem The conclusions of this paper are summarized asfollows

In this paper a distribution center model is established toreduce the total cost of the enterpriseThemodel is combinedwith the inherent characteristics of fresh goods e-commercetaking into account the principles of distribution centerselection service levels and freshness constraints Due to theincrease in the number of fresh goods e-commerce enter-prises with more intense competition consumer demand ismore and more uncertain Robust optimization is used tooptimize the distribution center model which makes themodel more robust

An improved fruit fly optimization algorithm (IFOA) isproposed in this paper The search step size is dynamicallyadjusted by introducing a weighting function IFOA willserve to solve the established model However the applica-bility of IFOA is more general In this paper we validatethe uncertain demand model by using an example and weprove that the model of distribution centers is valid and caneffectively handle the uncertainty of demand

This paper considers the influence of uncertain demandon the location of distribution centers for fresh goods Itenriches the fresh goods e-commerce distribution centermodel and provides a theoretical basis for a scientific methodof selecting the locations of fresh e-commerce distributioncenters The applicability of the proposed model is mean-ingful and useful for the selection of fresh e-commercedistribution center locations The shortcomings of this paperis that it only considers the uncertainty of customer demandand does not take into account other factors of uncertaintysuch as uncertain delivery weather conditions and uncertaincorruption rate

It is worth noting that some aspects of the model needto be improved For example we will pay more attentionto a variety of uncertain factors so that the model is moresuitable formore complex situations Because the distributioncenter will be related to the distribution of fresh productscoupled with the international awareness of environmentalprotection strengthened gradually the future will take intoaccount the impacts of low-carbon environmental aspects ofthe distribution center location model

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

This research was sponsored by Project of National SocialScience Foundation of China (15BGL202) project of theplanning subject of ldquothe 12th Five-Year Planrdquo in NationalScience and Technology for the Rural Development inChina Demonstration of Key Technology and Equipment forSafe Distribution of Agricultural Logistics (2015BAD18B01)Project of Beijing Philosophy and Social Science (17GBL013)Project of Beijing Municipal Commission of Education(SM201410011002) Project of Innovation Ability Promotion(PXM2016 014213 000033) 2017 Beijing Technology andBusiness University postgraduate student research abilityenhancing project

12 Scientific Programming

References

[1] RAccorsi AGallo andRManzini ldquoA climate driven decision-support model for the distribution of perishable productsrdquoJournal of Cleaner Production vol 165 pp 917ndash929 2017

[2] E Morganti and J Gonzalez-Feliu ldquoCity logistics for perishableproducts The case of the Parmarsquos Food Hubrdquo Case Studies onTransport Policy vol 3 no 2 pp 120ndash128 2015

[3] J A Orjuela-Castro L A Sanabria-Coronado and Peralta-Lozano A M ldquoCoupling facility location models in the supplychain of perishable fruitsrdquo Research in Transportation Businessamp Management 2017

[4] M Merakli and H Yaman ldquoRobust intermodal hub loca-tion under polyhedral demand uncertaintyrdquo TransportationResearch Part B Methodological vol 86 pp 66ndash85 2016

[5] M a Schuster Puga and J-S Tancrez ldquoA heuristic algorithmfor solving large location-inventory problems with demanduncertaintyrdquo European Journal of Operational Research vol 259no 2 pp 413ndash423 2017

[6] A Hiassat A Diabat and I Rahwan ldquoA genetic algorithmapproach for location-inventory-routing problem with perish-able productsrdquo Journal of Manufacturing Systems vol 42 pp93ndash103 2017

[7] K Govindan A Jafarian R Khodaverdi and K DevikaldquoTwo-echelon multiple-vehicle location-routing problem withtime windows for optimization of sustainable supply chainnetwork of perishable foodrdquo International Journal of ProductionEconomics vol 152 pp 9ndash28 2014

[8] Z Drezner and C H Scott ldquoLocation of a distribution centerfor a perishable productrdquo Mathematical Methods of OperationsResearch vol 78 no 3 pp 301ndash314 2013

[9] S M Seyedhosseini and S M Ghoreyshi ldquoAn integrated modelfor production and distribution planning of perishable prod-ucts with inventory and routing considerationsrdquo MathematicalProblems in Engineering vol 2014 Article ID 475606 10 pages2014

[10] M de Keizer R Akkerman M Grunow J M Bloemhof RHaijema and J G van der Vorst ldquoLogistics network designfor perishable products with heterogeneous quality decayrdquoEuropean Journal of Operational Research vol 262 no 2 pp535ndash549 2017

[11] H Yang L I Hong DUWei et al ldquoResearch on location selec-tion of perishable dairy products distribution center based ontwo-stage distributionrdquoComputer Engineering andApplicationsvol 23 pp 239ndash245 2015

[12] J Zhang and F U Shao-chuan ldquoStudy on location of fresh fooddistribution center with demand influenced by the freshnessrdquoChinese Journal of Management Science vol 19 no 10 pp 473ndash476 2011

[13] T Wu H Shen and C Zhu ldquoA multi-period location modelwith transportation economies-of-scale and perishable inven-toryrdquo International Journal of Production Economics vol 169 pp343ndash349 2015

[14] M Musavi and A Bozorgi-Amiri ldquoA multi-objective sus-tainable hub location-scheduling problem for perishable foodsupply chainrdquo Computers amp Industrial Engineering 2017

[15] M Rezaei-Malek R Tavakkoli-Moghaddam B Zahiri and ABozorgi-Amiri ldquoAn interactive approach for designing a robustdisaster relief logistics network with perishable commoditiesrdquoComputers amp Industrial Engineering vol 94 pp 201ndash215 2016

[16] K Khalili-Damghani A-R Abtahi andA Ghasemi ldquoA new bi-objective location-routing problem for distribution of perish-able products evolutionary computation approachrdquo Journal ofMathematical Modelling and Algorithms in Operations Researchvol 14 no 3 pp 287ndash312 2015

[17] Y Zhang Y Jiang M Zhong N Geng and D Chen ldquoRobustOptimization on Regional WCO-for-Biodiesel Supply Chainunder Supply and Demand Uncertaintiesrdquo Scientific Program-ming vol 2016 Article ID 1087845 15 pages 2016

[18] R Qiu and Y Wang ldquoSupply chain network design underdemand uncertainty and supply disruptions a distributionallyrobust optimization approachrdquo Scientific Programming vol2016 Article ID 3848520 15 pages 2016

[19] A Ben-Tal E Hazan T Koren and S Mannor ldquoOracle-basedrobust optimization via online learningrdquo Operations Researchvol 63 no 3 pp 628ndash638 2015

[20] M Melamed A Ben-Tal and B Golany ldquoOn the averageperformance of the adjustable RO and its use as an offlinetool for multi-period production planning under uncertaintyrdquoComputational Management Science vol 13 no 2 pp 293ndash3152016

[21] A Ghodratnama R Tavakkoli-Moghaddam and A AzaronldquoRobust and fuzzy goal programming optimization approachesfor a novel multi-objective hub location-allocation problem Asupply chain overviewrdquoApplied SoftComputing vol 37 pp 255ndash276 2015

[22] F Habibzadeh Boukani B Farhang Moghaddam and M SPishvaee ldquoRobust optimization approach to capacitated singleand multiple allocation hub location problemsrdquo Computationalamp Applied Mathematics vol 35 no 1 pp 45ndash60 2016

[23] A Jakubovskis ldquoStrategic facility location capacity acquisitionand technology choice decisions under demand uncertaintyrobust vs non-robust optimization approachesrdquo European Jour-nal of Operational Research vol 260 no 3 pp 1095ndash1104 2017

[24] H A Eiselt and V Marianov ldquoA bi-objective model for thelocation of landfills formunicipal solidwasterdquoEuropean Journalof Operational Research vol 235 no 1 pp 187ndash194 2014

[25] M G Bardossy and S Raghavan ldquoRobust Optimization forthe Connected Facility Location Problemrdquo Electronic Notes inDiscrete Mathematics vol 44 pp 149ndash154 2013

[26] V de Rosa E Hartmann M Gebhard and J WollenweberldquoRobust capacitated facility location model for acquisitionsunder uncertaintyrdquoComputers amp Industrial Engineering vol 72pp 206ndash216 2014

[27] M Ehrgott J Ide and A Schoobel ldquoMinmax robustness formulti-objective optimization problemsrdquo European Journal ofOperational Research vol 239 no 1 pp 17ndash31 2014

[28] X-F Xu J Hao Y-R Deng and YWang ldquoDesign optimizationof resource combination for collaborative logistics networkunder uncertaintyrdquo Applied Soft Computing vol 56 pp 684ndash691 2017

[29] E D Majewski M Wirtz M Lampe and etal ldquoRobust multi-objective optimization for sustainable design of distributedenergy supply systemsrdquoComputersampChemical Engineering vol102 pp 26ndash39 2016

[30] M Yunfeng Y Chao M Zhang and H Chunyan ldquoTime-satisfaction-based maximal covering location problemrdquo Chi-nese Journal of Management Science vol 2 pp 45ndash51 2006

[31] W-T Pan ldquoA new fruit fly optimization algorithm takingthe financial distress model as an examplerdquo Knowledge-BasedSystems vol 26 pp 69ndash74 2012

Scientific Programming 13

[32] S Kanarachos J Griffin and M E Fitzpatrick ldquoEfficient trussoptimization using the contrast-based fruit fly optimizationalgorithmrdquo Computers amp Structures vol 182 pp 137ndash148 2017

[33] J Niu W Zhong Y Liang N Luo and F Qian ldquoFruit flyoptimization algorithm based on differential evolution andits application on gasification process operation optimizationrdquoKnowledge-Based Systems vol 88 pp 253ndash263 2015

[34] S-M Lin ldquoAnalysis of service satisfaction in web auctionlogistics service using a combination of Fruit fly optimizationalgorithm and general regression neural networkrdquoNeural Com-puting and Applications vol 22 no 3-4 pp 783ndash791 2013

[35] J Huber A Gossmann andH Stuckenschmidt ldquoCluster-basedhierarchical demand forecasting for perishable goodsrdquo ExpertSystems with Applications vol 76 pp 140ndash151 2017

[36] M Shukla and S Jharkharia ldquoApplicability of ARIMA modelsin wholesale vegetable market An investigationrdquo InternationalJournal of Information Systems and Supply Chain Managementvol 6 no 3 pp 105ndash119 2013

[37] C Sun and X Luo ldquoThe influencing factors and countermea-sures of supply uncertainty in supply chainrdquo Economic ResearchGuide vol 11 pp 146-147 2013

[38] S Minner and S Transchel ldquoOrder variability in perish-able product supply chainsrdquo European Journal of OperationalResearch vol 260 no 1 pp 93ndash107 2017

Submit your manuscripts athttpswwwhindawicom

Computer Games Technology

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Distributed Sensor Networks

International Journal of

Advances in

FuzzySystems

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014

International Journal of

ReconfigurableComputing

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 201

Applied Computational Intelligence and Soft Computing

thinspAdvancesthinspinthinsp

Artificial Intelligence

HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014

Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Hindawi Publishing Corporation

httpwwwhindawicom Volume 2014

Advances in

Multimedia

International Journal of

Biomedical Imaging

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 201

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Computational Intelligence and Neuroscience

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

10 Scientific Programming

0 009 014027033

071093

119

165 175191

0

0005

001

0015

002

0025

0 01 02 03 04 05 06 07 08 09 1

The i

ncre

ase r

atio

The value of a

Figure 3 The increase ratio of the total cost of uncertain demand

For the case of uncertainty we assume that the demandfor each demand point is 119904 = 5 The number of scenariosfor each demand point can be different from each other Thevalue of the demand scenario is determined by the surveyand then the five cases are generated randomly by Matlab 83as the demand scenario of the demand point 119895 The demandscenario of the 10 demandpoints can be obtained by repeatingthe process ten times

The discrete demand probability distribution is 1199010119895119904 119869 =119895 | 119895 = 1 2 119899For 1199010119895119904 in the range (0 1) the simulations are randomly

generated between the 10 numbers normalized and repeatedten times in order to get all the demand points in theuncertain demand scenarioTheprobability demand scenarioof customer 119895 (119901119895119904) meets the uncertainty set Let thedecentralized matrix be 119876 = 119886119868 where 119886 is a nonnegativeparameter and 119868 is an identity matrix

In the experiment let 119886 = 05 and 119886 = 08 respectivelyCalculate 119901119895119904

The specific initialization parameter is set to maxgen =100 sizepop = 20 The program is implemented in Matlab83 and run on a computer with 26GHz Intel i5-4210MCPU 4GB of RAM andWindows 10The distribution centerdecision-making program and the total cost are shown inTable 8

For the deterministic demand situation the optimal deci-sion is to choose distribution center 119868211986851198686 from the candidatelist The total cost is 7208 million For the uncertain demandsituation when 119886 = 01 to 119886 = 04 the optimal decision isto choose distribution centers 119868211986851198686 The distribution rangeis constant but the cost increases When 119886 = 05 to 119886 = 07the optimal decision is to choose distribution centers 119868211986851198686but the distribution range is different from the deterministicdemand situation When 119886 = 08 to 119886 = 1 the optimaldecision is to choose distribution centers 119868511986861198687 The increaseratio of the total cost in the case of uncertainty is comparedto the total cost in the demand determination as shownin Figure 3 Enterprises in the decision-making before theconsumer demand should be the historical data for statisticaland analysis determine the variation range of parameter119886 and make decisions based on cost and self-conditions(Figure 3)

Then using FOA to solve themodel and initial parametersand operating environment equally with IFOA the results are

Table 8 The decision-making program and the total cost ofdistribution center

The value of 119886 Decision-makingprogram and

distribution rangeCost (RMB)

119886 = 0 1198682 1198691 1198693 11986977208563141198685 1198692 1198695 11986981198686 1198694 1198696 1198699 11986910

119886 = 01 1198682 1198691 1198693 11986977215050851198685 1198692 1198695 11986981198686 1198694 1198696 1198699 11986910

119886 = 02 1198682 1198691 1198693 11986977218655131198685 1198692 1198695 11986981198686 1198694 1198696 1198699 11986910

119886 = 03 1198682 1198691 1198693 11986977228026261198685 1198692 1198695 11986981198686 1198694 1198696 1198699 11986910

119886 = 04 1198682 1198691 1198693 11986977232351401198685 1198692 1198695 11986981198686 1198694 1198696 1198699 11986910

119886 = 05 1198682 1198691 1198693 11986977259452741198685 1198692 1198694 1198695 11986981198686 1198696 1198699 11986910

119886 = 06 1198682 1198691 1198693 11986977275602781198685 1198692 1198694 1198695 11986981198686 1198696 1198699 11986910

119886 = 07 1198682 1198691 1198693 11986977294345041198685 1198692 1198694 1198695 11986981198686 1198696 1198699 11986910

119886 = 08 1198685 1198692 11986957327583631198686 1198694 1198696 1198699 119869101198687 1198691 1198693 1198697 1198698

119886 = 09 1198685 1198692 11986957334712991198686 1198694 1198696 1198699 119869101198687 1198691 1198693 1198697 1198698

119886 = 1 1198685 1198692 11986957346246701198686 1198694 1198696 1198699 119869101198687 1198691 1198693 1198697 1198698

shown in Table 9 the difference value of IFOA and FOA isshown in Figure 4 and the optimization process of FOA andIFOA is shown in Figure 5 (select 119886 = 05)

From the test results in Table 9 and Figures 4 and 5under the same conditions IFOA results are superior to FOAthe convergence accuracy is more accurate and the optimalresults are better Under the same convergence accuracythe number of valid iterations of IFOA is less than that ofFOA which indicates that IFOA converges faster ThereforeIFOA effectively improves the convergence precision andconvergence speed of FOAThe applicability of IFOA is moreextensive

Scientific Programming 11

Table 9 The results of FOA and IFOA

The value of 119886 IFOA optimal FOA optimal119886 = 0 720856314 720874332119886 = 01 721505085 721515326119886 = 02 721865513 721881176119886 = 03 722802626 72285562119886 = 04 723235140 723309877119886 = 05 725945274 726005691119886 = 06 727560278 727613354119886 = 07 729434504 729495412119886 = 08 732758363 732827122119886 = 09 733471299 733549837119886 = 1 734624670 734714368

18018 10241 15663

52994

7473760417

5307660908

6875978538

89698

000100002000030000400005000060000700008000090000

100000

0 01 02 03 04 05 06 07 08 09 1

The d

iffer

ent v

alue

The value of a

Figure 4 The difference value of IFOA and FOA

0 10 20 30 40 50 60 70 80 90 1007

75

8

85

9

95

Iteration number

Cos

t

IFOAFOA

times106

Figure 5 Optimization process of FOA and IFOA (119886 = 05)

5 Conclusions

The location of distribution centers is a complex optimizationproblem To solve the problem of unreasonable networklayout and poor interpretation of customer demand and highcost of distribution this paper optimizes the location ofdistribution centers minimizes the total cost of distributionand establishes a fast and secure distribution center networksystem The conclusions of this paper are summarized asfollows

In this paper a distribution center model is established toreduce the total cost of the enterpriseThemodel is combinedwith the inherent characteristics of fresh goods e-commercetaking into account the principles of distribution centerselection service levels and freshness constraints Due to theincrease in the number of fresh goods e-commerce enter-prises with more intense competition consumer demand ismore and more uncertain Robust optimization is used tooptimize the distribution center model which makes themodel more robust

An improved fruit fly optimization algorithm (IFOA) isproposed in this paper The search step size is dynamicallyadjusted by introducing a weighting function IFOA willserve to solve the established model However the applica-bility of IFOA is more general In this paper we validatethe uncertain demand model by using an example and weprove that the model of distribution centers is valid and caneffectively handle the uncertainty of demand

This paper considers the influence of uncertain demandon the location of distribution centers for fresh goods Itenriches the fresh goods e-commerce distribution centermodel and provides a theoretical basis for a scientific methodof selecting the locations of fresh e-commerce distributioncenters The applicability of the proposed model is mean-ingful and useful for the selection of fresh e-commercedistribution center locations The shortcomings of this paperis that it only considers the uncertainty of customer demandand does not take into account other factors of uncertaintysuch as uncertain delivery weather conditions and uncertaincorruption rate

It is worth noting that some aspects of the model needto be improved For example we will pay more attentionto a variety of uncertain factors so that the model is moresuitable formore complex situations Because the distributioncenter will be related to the distribution of fresh productscoupled with the international awareness of environmentalprotection strengthened gradually the future will take intoaccount the impacts of low-carbon environmental aspects ofthe distribution center location model

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

This research was sponsored by Project of National SocialScience Foundation of China (15BGL202) project of theplanning subject of ldquothe 12th Five-Year Planrdquo in NationalScience and Technology for the Rural Development inChina Demonstration of Key Technology and Equipment forSafe Distribution of Agricultural Logistics (2015BAD18B01)Project of Beijing Philosophy and Social Science (17GBL013)Project of Beijing Municipal Commission of Education(SM201410011002) Project of Innovation Ability Promotion(PXM2016 014213 000033) 2017 Beijing Technology andBusiness University postgraduate student research abilityenhancing project

12 Scientific Programming

References

[1] RAccorsi AGallo andRManzini ldquoA climate driven decision-support model for the distribution of perishable productsrdquoJournal of Cleaner Production vol 165 pp 917ndash929 2017

[2] E Morganti and J Gonzalez-Feliu ldquoCity logistics for perishableproducts The case of the Parmarsquos Food Hubrdquo Case Studies onTransport Policy vol 3 no 2 pp 120ndash128 2015

[3] J A Orjuela-Castro L A Sanabria-Coronado and Peralta-Lozano A M ldquoCoupling facility location models in the supplychain of perishable fruitsrdquo Research in Transportation Businessamp Management 2017

[4] M Merakli and H Yaman ldquoRobust intermodal hub loca-tion under polyhedral demand uncertaintyrdquo TransportationResearch Part B Methodological vol 86 pp 66ndash85 2016

[5] M a Schuster Puga and J-S Tancrez ldquoA heuristic algorithmfor solving large location-inventory problems with demanduncertaintyrdquo European Journal of Operational Research vol 259no 2 pp 413ndash423 2017

[6] A Hiassat A Diabat and I Rahwan ldquoA genetic algorithmapproach for location-inventory-routing problem with perish-able productsrdquo Journal of Manufacturing Systems vol 42 pp93ndash103 2017

[7] K Govindan A Jafarian R Khodaverdi and K DevikaldquoTwo-echelon multiple-vehicle location-routing problem withtime windows for optimization of sustainable supply chainnetwork of perishable foodrdquo International Journal of ProductionEconomics vol 152 pp 9ndash28 2014

[8] Z Drezner and C H Scott ldquoLocation of a distribution centerfor a perishable productrdquo Mathematical Methods of OperationsResearch vol 78 no 3 pp 301ndash314 2013

[9] S M Seyedhosseini and S M Ghoreyshi ldquoAn integrated modelfor production and distribution planning of perishable prod-ucts with inventory and routing considerationsrdquo MathematicalProblems in Engineering vol 2014 Article ID 475606 10 pages2014

[10] M de Keizer R Akkerman M Grunow J M Bloemhof RHaijema and J G van der Vorst ldquoLogistics network designfor perishable products with heterogeneous quality decayrdquoEuropean Journal of Operational Research vol 262 no 2 pp535ndash549 2017

[11] H Yang L I Hong DUWei et al ldquoResearch on location selec-tion of perishable dairy products distribution center based ontwo-stage distributionrdquoComputer Engineering andApplicationsvol 23 pp 239ndash245 2015

[12] J Zhang and F U Shao-chuan ldquoStudy on location of fresh fooddistribution center with demand influenced by the freshnessrdquoChinese Journal of Management Science vol 19 no 10 pp 473ndash476 2011

[13] T Wu H Shen and C Zhu ldquoA multi-period location modelwith transportation economies-of-scale and perishable inven-toryrdquo International Journal of Production Economics vol 169 pp343ndash349 2015

[14] M Musavi and A Bozorgi-Amiri ldquoA multi-objective sus-tainable hub location-scheduling problem for perishable foodsupply chainrdquo Computers amp Industrial Engineering 2017

[15] M Rezaei-Malek R Tavakkoli-Moghaddam B Zahiri and ABozorgi-Amiri ldquoAn interactive approach for designing a robustdisaster relief logistics network with perishable commoditiesrdquoComputers amp Industrial Engineering vol 94 pp 201ndash215 2016

[16] K Khalili-Damghani A-R Abtahi andA Ghasemi ldquoA new bi-objective location-routing problem for distribution of perish-able products evolutionary computation approachrdquo Journal ofMathematical Modelling and Algorithms in Operations Researchvol 14 no 3 pp 287ndash312 2015

[17] Y Zhang Y Jiang M Zhong N Geng and D Chen ldquoRobustOptimization on Regional WCO-for-Biodiesel Supply Chainunder Supply and Demand Uncertaintiesrdquo Scientific Program-ming vol 2016 Article ID 1087845 15 pages 2016

[18] R Qiu and Y Wang ldquoSupply chain network design underdemand uncertainty and supply disruptions a distributionallyrobust optimization approachrdquo Scientific Programming vol2016 Article ID 3848520 15 pages 2016

[19] A Ben-Tal E Hazan T Koren and S Mannor ldquoOracle-basedrobust optimization via online learningrdquo Operations Researchvol 63 no 3 pp 628ndash638 2015

[20] M Melamed A Ben-Tal and B Golany ldquoOn the averageperformance of the adjustable RO and its use as an offlinetool for multi-period production planning under uncertaintyrdquoComputational Management Science vol 13 no 2 pp 293ndash3152016

[21] A Ghodratnama R Tavakkoli-Moghaddam and A AzaronldquoRobust and fuzzy goal programming optimization approachesfor a novel multi-objective hub location-allocation problem Asupply chain overviewrdquoApplied SoftComputing vol 37 pp 255ndash276 2015

[22] F Habibzadeh Boukani B Farhang Moghaddam and M SPishvaee ldquoRobust optimization approach to capacitated singleand multiple allocation hub location problemsrdquo Computationalamp Applied Mathematics vol 35 no 1 pp 45ndash60 2016

[23] A Jakubovskis ldquoStrategic facility location capacity acquisitionand technology choice decisions under demand uncertaintyrobust vs non-robust optimization approachesrdquo European Jour-nal of Operational Research vol 260 no 3 pp 1095ndash1104 2017

[24] H A Eiselt and V Marianov ldquoA bi-objective model for thelocation of landfills formunicipal solidwasterdquoEuropean Journalof Operational Research vol 235 no 1 pp 187ndash194 2014

[25] M G Bardossy and S Raghavan ldquoRobust Optimization forthe Connected Facility Location Problemrdquo Electronic Notes inDiscrete Mathematics vol 44 pp 149ndash154 2013

[26] V de Rosa E Hartmann M Gebhard and J WollenweberldquoRobust capacitated facility location model for acquisitionsunder uncertaintyrdquoComputers amp Industrial Engineering vol 72pp 206ndash216 2014

[27] M Ehrgott J Ide and A Schoobel ldquoMinmax robustness formulti-objective optimization problemsrdquo European Journal ofOperational Research vol 239 no 1 pp 17ndash31 2014

[28] X-F Xu J Hao Y-R Deng and YWang ldquoDesign optimizationof resource combination for collaborative logistics networkunder uncertaintyrdquo Applied Soft Computing vol 56 pp 684ndash691 2017

[29] E D Majewski M Wirtz M Lampe and etal ldquoRobust multi-objective optimization for sustainable design of distributedenergy supply systemsrdquoComputersampChemical Engineering vol102 pp 26ndash39 2016

[30] M Yunfeng Y Chao M Zhang and H Chunyan ldquoTime-satisfaction-based maximal covering location problemrdquo Chi-nese Journal of Management Science vol 2 pp 45ndash51 2006

[31] W-T Pan ldquoA new fruit fly optimization algorithm takingthe financial distress model as an examplerdquo Knowledge-BasedSystems vol 26 pp 69ndash74 2012

Scientific Programming 13

[32] S Kanarachos J Griffin and M E Fitzpatrick ldquoEfficient trussoptimization using the contrast-based fruit fly optimizationalgorithmrdquo Computers amp Structures vol 182 pp 137ndash148 2017

[33] J Niu W Zhong Y Liang N Luo and F Qian ldquoFruit flyoptimization algorithm based on differential evolution andits application on gasification process operation optimizationrdquoKnowledge-Based Systems vol 88 pp 253ndash263 2015

[34] S-M Lin ldquoAnalysis of service satisfaction in web auctionlogistics service using a combination of Fruit fly optimizationalgorithm and general regression neural networkrdquoNeural Com-puting and Applications vol 22 no 3-4 pp 783ndash791 2013

[35] J Huber A Gossmann andH Stuckenschmidt ldquoCluster-basedhierarchical demand forecasting for perishable goodsrdquo ExpertSystems with Applications vol 76 pp 140ndash151 2017

[36] M Shukla and S Jharkharia ldquoApplicability of ARIMA modelsin wholesale vegetable market An investigationrdquo InternationalJournal of Information Systems and Supply Chain Managementvol 6 no 3 pp 105ndash119 2013

[37] C Sun and X Luo ldquoThe influencing factors and countermea-sures of supply uncertainty in supply chainrdquo Economic ResearchGuide vol 11 pp 146-147 2013

[38] S Minner and S Transchel ldquoOrder variability in perish-able product supply chainsrdquo European Journal of OperationalResearch vol 260 no 1 pp 93ndash107 2017

Submit your manuscripts athttpswwwhindawicom

Computer Games Technology

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Distributed Sensor Networks

International Journal of

Advances in

FuzzySystems

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014

International Journal of

ReconfigurableComputing

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 201

Applied Computational Intelligence and Soft Computing

thinspAdvancesthinspinthinsp

Artificial Intelligence

HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014

Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Hindawi Publishing Corporation

httpwwwhindawicom Volume 2014

Advances in

Multimedia

International Journal of

Biomedical Imaging

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 201

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Computational Intelligence and Neuroscience

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Scientific Programming 11

Table 9 The results of FOA and IFOA

The value of 119886 IFOA optimal FOA optimal119886 = 0 720856314 720874332119886 = 01 721505085 721515326119886 = 02 721865513 721881176119886 = 03 722802626 72285562119886 = 04 723235140 723309877119886 = 05 725945274 726005691119886 = 06 727560278 727613354119886 = 07 729434504 729495412119886 = 08 732758363 732827122119886 = 09 733471299 733549837119886 = 1 734624670 734714368

18018 10241 15663

52994

7473760417

5307660908

6875978538

89698

000100002000030000400005000060000700008000090000

100000

0 01 02 03 04 05 06 07 08 09 1

The d

iffer

ent v

alue

The value of a

Figure 4 The difference value of IFOA and FOA

0 10 20 30 40 50 60 70 80 90 1007

75

8

85

9

95

Iteration number

Cos

t

IFOAFOA

times106

Figure 5 Optimization process of FOA and IFOA (119886 = 05)

5 Conclusions

The location of distribution centers is a complex optimizationproblem To solve the problem of unreasonable networklayout and poor interpretation of customer demand and highcost of distribution this paper optimizes the location ofdistribution centers minimizes the total cost of distributionand establishes a fast and secure distribution center networksystem The conclusions of this paper are summarized asfollows

In this paper a distribution center model is established toreduce the total cost of the enterpriseThemodel is combinedwith the inherent characteristics of fresh goods e-commercetaking into account the principles of distribution centerselection service levels and freshness constraints Due to theincrease in the number of fresh goods e-commerce enter-prises with more intense competition consumer demand ismore and more uncertain Robust optimization is used tooptimize the distribution center model which makes themodel more robust

An improved fruit fly optimization algorithm (IFOA) isproposed in this paper The search step size is dynamicallyadjusted by introducing a weighting function IFOA willserve to solve the established model However the applica-bility of IFOA is more general In this paper we validatethe uncertain demand model by using an example and weprove that the model of distribution centers is valid and caneffectively handle the uncertainty of demand

This paper considers the influence of uncertain demandon the location of distribution centers for fresh goods Itenriches the fresh goods e-commerce distribution centermodel and provides a theoretical basis for a scientific methodof selecting the locations of fresh e-commerce distributioncenters The applicability of the proposed model is mean-ingful and useful for the selection of fresh e-commercedistribution center locations The shortcomings of this paperis that it only considers the uncertainty of customer demandand does not take into account other factors of uncertaintysuch as uncertain delivery weather conditions and uncertaincorruption rate

It is worth noting that some aspects of the model needto be improved For example we will pay more attentionto a variety of uncertain factors so that the model is moresuitable formore complex situations Because the distributioncenter will be related to the distribution of fresh productscoupled with the international awareness of environmentalprotection strengthened gradually the future will take intoaccount the impacts of low-carbon environmental aspects ofthe distribution center location model

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

This research was sponsored by Project of National SocialScience Foundation of China (15BGL202) project of theplanning subject of ldquothe 12th Five-Year Planrdquo in NationalScience and Technology for the Rural Development inChina Demonstration of Key Technology and Equipment forSafe Distribution of Agricultural Logistics (2015BAD18B01)Project of Beijing Philosophy and Social Science (17GBL013)Project of Beijing Municipal Commission of Education(SM201410011002) Project of Innovation Ability Promotion(PXM2016 014213 000033) 2017 Beijing Technology andBusiness University postgraduate student research abilityenhancing project

12 Scientific Programming

References

[1] RAccorsi AGallo andRManzini ldquoA climate driven decision-support model for the distribution of perishable productsrdquoJournal of Cleaner Production vol 165 pp 917ndash929 2017

[2] E Morganti and J Gonzalez-Feliu ldquoCity logistics for perishableproducts The case of the Parmarsquos Food Hubrdquo Case Studies onTransport Policy vol 3 no 2 pp 120ndash128 2015

[3] J A Orjuela-Castro L A Sanabria-Coronado and Peralta-Lozano A M ldquoCoupling facility location models in the supplychain of perishable fruitsrdquo Research in Transportation Businessamp Management 2017

[4] M Merakli and H Yaman ldquoRobust intermodal hub loca-tion under polyhedral demand uncertaintyrdquo TransportationResearch Part B Methodological vol 86 pp 66ndash85 2016

[5] M a Schuster Puga and J-S Tancrez ldquoA heuristic algorithmfor solving large location-inventory problems with demanduncertaintyrdquo European Journal of Operational Research vol 259no 2 pp 413ndash423 2017

[6] A Hiassat A Diabat and I Rahwan ldquoA genetic algorithmapproach for location-inventory-routing problem with perish-able productsrdquo Journal of Manufacturing Systems vol 42 pp93ndash103 2017

[7] K Govindan A Jafarian R Khodaverdi and K DevikaldquoTwo-echelon multiple-vehicle location-routing problem withtime windows for optimization of sustainable supply chainnetwork of perishable foodrdquo International Journal of ProductionEconomics vol 152 pp 9ndash28 2014

[8] Z Drezner and C H Scott ldquoLocation of a distribution centerfor a perishable productrdquo Mathematical Methods of OperationsResearch vol 78 no 3 pp 301ndash314 2013

[9] S M Seyedhosseini and S M Ghoreyshi ldquoAn integrated modelfor production and distribution planning of perishable prod-ucts with inventory and routing considerationsrdquo MathematicalProblems in Engineering vol 2014 Article ID 475606 10 pages2014

[10] M de Keizer R Akkerman M Grunow J M Bloemhof RHaijema and J G van der Vorst ldquoLogistics network designfor perishable products with heterogeneous quality decayrdquoEuropean Journal of Operational Research vol 262 no 2 pp535ndash549 2017

[11] H Yang L I Hong DUWei et al ldquoResearch on location selec-tion of perishable dairy products distribution center based ontwo-stage distributionrdquoComputer Engineering andApplicationsvol 23 pp 239ndash245 2015

[12] J Zhang and F U Shao-chuan ldquoStudy on location of fresh fooddistribution center with demand influenced by the freshnessrdquoChinese Journal of Management Science vol 19 no 10 pp 473ndash476 2011

[13] T Wu H Shen and C Zhu ldquoA multi-period location modelwith transportation economies-of-scale and perishable inven-toryrdquo International Journal of Production Economics vol 169 pp343ndash349 2015

[14] M Musavi and A Bozorgi-Amiri ldquoA multi-objective sus-tainable hub location-scheduling problem for perishable foodsupply chainrdquo Computers amp Industrial Engineering 2017

[15] M Rezaei-Malek R Tavakkoli-Moghaddam B Zahiri and ABozorgi-Amiri ldquoAn interactive approach for designing a robustdisaster relief logistics network with perishable commoditiesrdquoComputers amp Industrial Engineering vol 94 pp 201ndash215 2016

[16] K Khalili-Damghani A-R Abtahi andA Ghasemi ldquoA new bi-objective location-routing problem for distribution of perish-able products evolutionary computation approachrdquo Journal ofMathematical Modelling and Algorithms in Operations Researchvol 14 no 3 pp 287ndash312 2015

[17] Y Zhang Y Jiang M Zhong N Geng and D Chen ldquoRobustOptimization on Regional WCO-for-Biodiesel Supply Chainunder Supply and Demand Uncertaintiesrdquo Scientific Program-ming vol 2016 Article ID 1087845 15 pages 2016

[18] R Qiu and Y Wang ldquoSupply chain network design underdemand uncertainty and supply disruptions a distributionallyrobust optimization approachrdquo Scientific Programming vol2016 Article ID 3848520 15 pages 2016

[19] A Ben-Tal E Hazan T Koren and S Mannor ldquoOracle-basedrobust optimization via online learningrdquo Operations Researchvol 63 no 3 pp 628ndash638 2015

[20] M Melamed A Ben-Tal and B Golany ldquoOn the averageperformance of the adjustable RO and its use as an offlinetool for multi-period production planning under uncertaintyrdquoComputational Management Science vol 13 no 2 pp 293ndash3152016

[21] A Ghodratnama R Tavakkoli-Moghaddam and A AzaronldquoRobust and fuzzy goal programming optimization approachesfor a novel multi-objective hub location-allocation problem Asupply chain overviewrdquoApplied SoftComputing vol 37 pp 255ndash276 2015

[22] F Habibzadeh Boukani B Farhang Moghaddam and M SPishvaee ldquoRobust optimization approach to capacitated singleand multiple allocation hub location problemsrdquo Computationalamp Applied Mathematics vol 35 no 1 pp 45ndash60 2016

[23] A Jakubovskis ldquoStrategic facility location capacity acquisitionand technology choice decisions under demand uncertaintyrobust vs non-robust optimization approachesrdquo European Jour-nal of Operational Research vol 260 no 3 pp 1095ndash1104 2017

[24] H A Eiselt and V Marianov ldquoA bi-objective model for thelocation of landfills formunicipal solidwasterdquoEuropean Journalof Operational Research vol 235 no 1 pp 187ndash194 2014

[25] M G Bardossy and S Raghavan ldquoRobust Optimization forthe Connected Facility Location Problemrdquo Electronic Notes inDiscrete Mathematics vol 44 pp 149ndash154 2013

[26] V de Rosa E Hartmann M Gebhard and J WollenweberldquoRobust capacitated facility location model for acquisitionsunder uncertaintyrdquoComputers amp Industrial Engineering vol 72pp 206ndash216 2014

[27] M Ehrgott J Ide and A Schoobel ldquoMinmax robustness formulti-objective optimization problemsrdquo European Journal ofOperational Research vol 239 no 1 pp 17ndash31 2014

[28] X-F Xu J Hao Y-R Deng and YWang ldquoDesign optimizationof resource combination for collaborative logistics networkunder uncertaintyrdquo Applied Soft Computing vol 56 pp 684ndash691 2017

[29] E D Majewski M Wirtz M Lampe and etal ldquoRobust multi-objective optimization for sustainable design of distributedenergy supply systemsrdquoComputersampChemical Engineering vol102 pp 26ndash39 2016

[30] M Yunfeng Y Chao M Zhang and H Chunyan ldquoTime-satisfaction-based maximal covering location problemrdquo Chi-nese Journal of Management Science vol 2 pp 45ndash51 2006

[31] W-T Pan ldquoA new fruit fly optimization algorithm takingthe financial distress model as an examplerdquo Knowledge-BasedSystems vol 26 pp 69ndash74 2012

Scientific Programming 13

[32] S Kanarachos J Griffin and M E Fitzpatrick ldquoEfficient trussoptimization using the contrast-based fruit fly optimizationalgorithmrdquo Computers amp Structures vol 182 pp 137ndash148 2017

[33] J Niu W Zhong Y Liang N Luo and F Qian ldquoFruit flyoptimization algorithm based on differential evolution andits application on gasification process operation optimizationrdquoKnowledge-Based Systems vol 88 pp 253ndash263 2015

[34] S-M Lin ldquoAnalysis of service satisfaction in web auctionlogistics service using a combination of Fruit fly optimizationalgorithm and general regression neural networkrdquoNeural Com-puting and Applications vol 22 no 3-4 pp 783ndash791 2013

[35] J Huber A Gossmann andH Stuckenschmidt ldquoCluster-basedhierarchical demand forecasting for perishable goodsrdquo ExpertSystems with Applications vol 76 pp 140ndash151 2017

[36] M Shukla and S Jharkharia ldquoApplicability of ARIMA modelsin wholesale vegetable market An investigationrdquo InternationalJournal of Information Systems and Supply Chain Managementvol 6 no 3 pp 105ndash119 2013

[37] C Sun and X Luo ldquoThe influencing factors and countermea-sures of supply uncertainty in supply chainrdquo Economic ResearchGuide vol 11 pp 146-147 2013

[38] S Minner and S Transchel ldquoOrder variability in perish-able product supply chainsrdquo European Journal of OperationalResearch vol 260 no 1 pp 93ndash107 2017

Submit your manuscripts athttpswwwhindawicom

Computer Games Technology

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Distributed Sensor Networks

International Journal of

Advances in

FuzzySystems

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014

International Journal of

ReconfigurableComputing

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 201

Applied Computational Intelligence and Soft Computing

thinspAdvancesthinspinthinsp

Artificial Intelligence

HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014

Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Hindawi Publishing Corporation

httpwwwhindawicom Volume 2014

Advances in

Multimedia

International Journal of

Biomedical Imaging

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 201

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Computational Intelligence and Neuroscience

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

12 Scientific Programming

References

[1] RAccorsi AGallo andRManzini ldquoA climate driven decision-support model for the distribution of perishable productsrdquoJournal of Cleaner Production vol 165 pp 917ndash929 2017

[2] E Morganti and J Gonzalez-Feliu ldquoCity logistics for perishableproducts The case of the Parmarsquos Food Hubrdquo Case Studies onTransport Policy vol 3 no 2 pp 120ndash128 2015

[3] J A Orjuela-Castro L A Sanabria-Coronado and Peralta-Lozano A M ldquoCoupling facility location models in the supplychain of perishable fruitsrdquo Research in Transportation Businessamp Management 2017

[4] M Merakli and H Yaman ldquoRobust intermodal hub loca-tion under polyhedral demand uncertaintyrdquo TransportationResearch Part B Methodological vol 86 pp 66ndash85 2016

[5] M a Schuster Puga and J-S Tancrez ldquoA heuristic algorithmfor solving large location-inventory problems with demanduncertaintyrdquo European Journal of Operational Research vol 259no 2 pp 413ndash423 2017

[6] A Hiassat A Diabat and I Rahwan ldquoA genetic algorithmapproach for location-inventory-routing problem with perish-able productsrdquo Journal of Manufacturing Systems vol 42 pp93ndash103 2017

[7] K Govindan A Jafarian R Khodaverdi and K DevikaldquoTwo-echelon multiple-vehicle location-routing problem withtime windows for optimization of sustainable supply chainnetwork of perishable foodrdquo International Journal of ProductionEconomics vol 152 pp 9ndash28 2014

[8] Z Drezner and C H Scott ldquoLocation of a distribution centerfor a perishable productrdquo Mathematical Methods of OperationsResearch vol 78 no 3 pp 301ndash314 2013

[9] S M Seyedhosseini and S M Ghoreyshi ldquoAn integrated modelfor production and distribution planning of perishable prod-ucts with inventory and routing considerationsrdquo MathematicalProblems in Engineering vol 2014 Article ID 475606 10 pages2014

[10] M de Keizer R Akkerman M Grunow J M Bloemhof RHaijema and J G van der Vorst ldquoLogistics network designfor perishable products with heterogeneous quality decayrdquoEuropean Journal of Operational Research vol 262 no 2 pp535ndash549 2017

[11] H Yang L I Hong DUWei et al ldquoResearch on location selec-tion of perishable dairy products distribution center based ontwo-stage distributionrdquoComputer Engineering andApplicationsvol 23 pp 239ndash245 2015

[12] J Zhang and F U Shao-chuan ldquoStudy on location of fresh fooddistribution center with demand influenced by the freshnessrdquoChinese Journal of Management Science vol 19 no 10 pp 473ndash476 2011

[13] T Wu H Shen and C Zhu ldquoA multi-period location modelwith transportation economies-of-scale and perishable inven-toryrdquo International Journal of Production Economics vol 169 pp343ndash349 2015

[14] M Musavi and A Bozorgi-Amiri ldquoA multi-objective sus-tainable hub location-scheduling problem for perishable foodsupply chainrdquo Computers amp Industrial Engineering 2017

[15] M Rezaei-Malek R Tavakkoli-Moghaddam B Zahiri and ABozorgi-Amiri ldquoAn interactive approach for designing a robustdisaster relief logistics network with perishable commoditiesrdquoComputers amp Industrial Engineering vol 94 pp 201ndash215 2016

[16] K Khalili-Damghani A-R Abtahi andA Ghasemi ldquoA new bi-objective location-routing problem for distribution of perish-able products evolutionary computation approachrdquo Journal ofMathematical Modelling and Algorithms in Operations Researchvol 14 no 3 pp 287ndash312 2015

[17] Y Zhang Y Jiang M Zhong N Geng and D Chen ldquoRobustOptimization on Regional WCO-for-Biodiesel Supply Chainunder Supply and Demand Uncertaintiesrdquo Scientific Program-ming vol 2016 Article ID 1087845 15 pages 2016

[18] R Qiu and Y Wang ldquoSupply chain network design underdemand uncertainty and supply disruptions a distributionallyrobust optimization approachrdquo Scientific Programming vol2016 Article ID 3848520 15 pages 2016

[19] A Ben-Tal E Hazan T Koren and S Mannor ldquoOracle-basedrobust optimization via online learningrdquo Operations Researchvol 63 no 3 pp 628ndash638 2015

[20] M Melamed A Ben-Tal and B Golany ldquoOn the averageperformance of the adjustable RO and its use as an offlinetool for multi-period production planning under uncertaintyrdquoComputational Management Science vol 13 no 2 pp 293ndash3152016

[21] A Ghodratnama R Tavakkoli-Moghaddam and A AzaronldquoRobust and fuzzy goal programming optimization approachesfor a novel multi-objective hub location-allocation problem Asupply chain overviewrdquoApplied SoftComputing vol 37 pp 255ndash276 2015

[22] F Habibzadeh Boukani B Farhang Moghaddam and M SPishvaee ldquoRobust optimization approach to capacitated singleand multiple allocation hub location problemsrdquo Computationalamp Applied Mathematics vol 35 no 1 pp 45ndash60 2016

[23] A Jakubovskis ldquoStrategic facility location capacity acquisitionand technology choice decisions under demand uncertaintyrobust vs non-robust optimization approachesrdquo European Jour-nal of Operational Research vol 260 no 3 pp 1095ndash1104 2017

[24] H A Eiselt and V Marianov ldquoA bi-objective model for thelocation of landfills formunicipal solidwasterdquoEuropean Journalof Operational Research vol 235 no 1 pp 187ndash194 2014

[25] M G Bardossy and S Raghavan ldquoRobust Optimization forthe Connected Facility Location Problemrdquo Electronic Notes inDiscrete Mathematics vol 44 pp 149ndash154 2013

[26] V de Rosa E Hartmann M Gebhard and J WollenweberldquoRobust capacitated facility location model for acquisitionsunder uncertaintyrdquoComputers amp Industrial Engineering vol 72pp 206ndash216 2014

[27] M Ehrgott J Ide and A Schoobel ldquoMinmax robustness formulti-objective optimization problemsrdquo European Journal ofOperational Research vol 239 no 1 pp 17ndash31 2014

[28] X-F Xu J Hao Y-R Deng and YWang ldquoDesign optimizationof resource combination for collaborative logistics networkunder uncertaintyrdquo Applied Soft Computing vol 56 pp 684ndash691 2017

[29] E D Majewski M Wirtz M Lampe and etal ldquoRobust multi-objective optimization for sustainable design of distributedenergy supply systemsrdquoComputersampChemical Engineering vol102 pp 26ndash39 2016

[30] M Yunfeng Y Chao M Zhang and H Chunyan ldquoTime-satisfaction-based maximal covering location problemrdquo Chi-nese Journal of Management Science vol 2 pp 45ndash51 2006

[31] W-T Pan ldquoA new fruit fly optimization algorithm takingthe financial distress model as an examplerdquo Knowledge-BasedSystems vol 26 pp 69ndash74 2012

Scientific Programming 13

[32] S Kanarachos J Griffin and M E Fitzpatrick ldquoEfficient trussoptimization using the contrast-based fruit fly optimizationalgorithmrdquo Computers amp Structures vol 182 pp 137ndash148 2017

[33] J Niu W Zhong Y Liang N Luo and F Qian ldquoFruit flyoptimization algorithm based on differential evolution andits application on gasification process operation optimizationrdquoKnowledge-Based Systems vol 88 pp 253ndash263 2015

[34] S-M Lin ldquoAnalysis of service satisfaction in web auctionlogistics service using a combination of Fruit fly optimizationalgorithm and general regression neural networkrdquoNeural Com-puting and Applications vol 22 no 3-4 pp 783ndash791 2013

[35] J Huber A Gossmann andH Stuckenschmidt ldquoCluster-basedhierarchical demand forecasting for perishable goodsrdquo ExpertSystems with Applications vol 76 pp 140ndash151 2017

[36] M Shukla and S Jharkharia ldquoApplicability of ARIMA modelsin wholesale vegetable market An investigationrdquo InternationalJournal of Information Systems and Supply Chain Managementvol 6 no 3 pp 105ndash119 2013

[37] C Sun and X Luo ldquoThe influencing factors and countermea-sures of supply uncertainty in supply chainrdquo Economic ResearchGuide vol 11 pp 146-147 2013

[38] S Minner and S Transchel ldquoOrder variability in perish-able product supply chainsrdquo European Journal of OperationalResearch vol 260 no 1 pp 93ndash107 2017

Submit your manuscripts athttpswwwhindawicom

Computer Games Technology

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Distributed Sensor Networks

International Journal of

Advances in

FuzzySystems

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014

International Journal of

ReconfigurableComputing

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 201

Applied Computational Intelligence and Soft Computing

thinspAdvancesthinspinthinsp

Artificial Intelligence

HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014

Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Hindawi Publishing Corporation

httpwwwhindawicom Volume 2014

Advances in

Multimedia

International Journal of

Biomedical Imaging

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 201

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Computational Intelligence and Neuroscience

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Scientific Programming 13

[32] S Kanarachos J Griffin and M E Fitzpatrick ldquoEfficient trussoptimization using the contrast-based fruit fly optimizationalgorithmrdquo Computers amp Structures vol 182 pp 137ndash148 2017

[33] J Niu W Zhong Y Liang N Luo and F Qian ldquoFruit flyoptimization algorithm based on differential evolution andits application on gasification process operation optimizationrdquoKnowledge-Based Systems vol 88 pp 253ndash263 2015

[34] S-M Lin ldquoAnalysis of service satisfaction in web auctionlogistics service using a combination of Fruit fly optimizationalgorithm and general regression neural networkrdquoNeural Com-puting and Applications vol 22 no 3-4 pp 783ndash791 2013

[35] J Huber A Gossmann andH Stuckenschmidt ldquoCluster-basedhierarchical demand forecasting for perishable goodsrdquo ExpertSystems with Applications vol 76 pp 140ndash151 2017

[36] M Shukla and S Jharkharia ldquoApplicability of ARIMA modelsin wholesale vegetable market An investigationrdquo InternationalJournal of Information Systems and Supply Chain Managementvol 6 no 3 pp 105ndash119 2013

[37] C Sun and X Luo ldquoThe influencing factors and countermea-sures of supply uncertainty in supply chainrdquo Economic ResearchGuide vol 11 pp 146-147 2013

[38] S Minner and S Transchel ldquoOrder variability in perish-able product supply chainsrdquo European Journal of OperationalResearch vol 260 no 1 pp 93ndash107 2017

Submit your manuscripts athttpswwwhindawicom

Computer Games Technology

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Distributed Sensor Networks

International Journal of

Advances in

FuzzySystems

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014

International Journal of

ReconfigurableComputing

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 201

Applied Computational Intelligence and Soft Computing

thinspAdvancesthinspinthinsp

Artificial Intelligence

HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014

Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Hindawi Publishing Corporation

httpwwwhindawicom Volume 2014

Advances in

Multimedia

International Journal of

Biomedical Imaging

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 201

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Computational Intelligence and Neuroscience

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Submit your manuscripts athttpswwwhindawicom

Computer Games Technology

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Distributed Sensor Networks

International Journal of

Advances in

FuzzySystems

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014

International Journal of

ReconfigurableComputing

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 201

Applied Computational Intelligence and Soft Computing

thinspAdvancesthinspinthinsp

Artificial Intelligence

HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014

Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Hindawi Publishing Corporation

httpwwwhindawicom Volume 2014

Advances in

Multimedia

International Journal of

Biomedical Imaging

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 201

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Computational Intelligence and Neuroscience

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014