Expert Systems with Applications 40 (2013) 5730–5739

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Expert Systems with Applications

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A bi-objective optimization of supply chain design and distributionoperations using non-dominated sorting algorithm: A case study

0957-4174/$ - see front matter � 2013 Elsevier Ltd. All rights reserved.http://dx.doi.org/10.1016/j.eswa.2013.03.047

⇑ Corresponding author. Tel.: +1 509 313 3421; fax: +1 509 313 5811.E-mail address: chen@jepson.gonzaga.edu (J.C.H. Chen).

B. Latha Shankar a, S. Basavarajappa b, Rajeshwar S. Kadadevaramath a, Jason C.H. Chen c,⇑a Department of Industrial Engineering & Management, Siddaganga Institute of Technology, Tumkur 572103, Karnataka, Indiab Department of Studies in Mechanical Engineering, University B.D.T. College of Engineering, Davangere 577004, Karnataka, Indiac Graduate School of Business, Gonzaga University, Spokane, WA, USA

a r t i c l e i n f o a b s t r a c t

Keywords:Three-echelonSupply chainParticle swarmSwarm intelligenceNon-dominating sortingBi-objective

This paper considers simultaneous optimization of strategic design and distribution decisions for three-echelon supply chain architecture consisting of following three players; suppliers, production plants, anddistribution centers (DCs). The key design decisions considered are: the number and location of plants inthe system, the flow of raw materials from suppliers to plants, the quantity of products to be shippedfrom plants to distribution centers, so as to minimize the combined facility location, production, inven-tory, and shipment costs and maximize fill rate. To achieve this, three-echelon network model is math-ematically represented and solved using swarm intelligence based Multi-objective Hybrid Particle SwarmOptimization algorithm (MOHPSO). This heuristic incorporates non-dominated sorting (NDS) procedureto achieve bi-objective optimization of two conflicting objectives. The applicability of proposed optimi-zation algorithm was then tested by applying it to standard test problems found in literature. On achiev-ing comparable results, the approach was applied to actual data of a pump manufacturing industry. Theresults show that the proposed solution approach performs efficiently.

� 2013 Elsevier Ltd. All rights reserved.

1. Introduction

In today’s industrial environment, the rapid technologicaladvancements, together with increased economic uncertaintyand the globalization of economic activities have resulted in toughcompetition, and chaotic, demanding customers. There is a need tofocus on revenue growth, asset utilization, cost reduction, shortand reliable delivery time, increased customer satisfaction so asto balance customers’ demands with the need for profitablegrowth. Realizing that supply chain (SC) can be a strategic differen-tiator in this direction, market leaders keep refining their SCs so asto gain competitive advantage (Cohen & Roussel, 2005).

SC is an integrated system of facilities and activities that synchro-nizes inter-related business functions of material procurement,material transformation to intermediates and final products and dis-tribution of these products to customers. Supply chain management(SCM) is a set of approaches utilized to efficiently integrate suppli-ers, manufacturers, warehouses, and stores, so that merchandise isproduced and distributed at the right quantities, to the right loca-tions, and at the right time, in order to minimize system-wide costswhile satisfying service level requirements across the entire SC.(Simchi-Levi, Kaminsky, & Simchi-Levi, 2001). Thus SC consists of

many independent organizations each of which tries to focus onits own inherent objectives in business for better profitability. Manyof the interests of these organizations will be conflicting. Such aproblem which tries to optimize many conflicting objectives simul-taneously is called multi-objective optimization problem and hasmany optimal solutions. In such a situation, analyzing the systemusing traditional optimization techniques such as weighted objec-tive method leads to subjective and sub-optimal results. The idealsituation is that the decision maker should be presented with a vec-tor of optimal solutions. The final decision is made among them bytaking the total balance over all criteria into account. This balancingover criteria is called trade-off. The trade-off level may change overtime due to uncertainty and global competitiveness. Hence the SCperformance needs to be evaluated continuously and SC managersshould make timely and right decisions (Shen, 2007).

Real SCs are to be optimized simultaneously considering morethan one objective. This is because design, planning and schedulingprojects are usually involving trade-offs among different conflict-ing goals such as customer service levels, fill rates, safe inventorylevels, volume flexibility etc. (Chen & Lee, 2004). In this work abi-objective mixed-integer non-linear programming model is for-mulated that accounts for major characteristics of SC, such asmaterial cost, production cost, inventory cost, fill rate etc. Two con-flicting objectives considered are, (1) Minimizing total SC operatingcost of production, inventory, and distribution. (2) Maximizing fill

B. Latha Shankar et al. / Expert Systems with Applications 40 (2013) 5730–5739 5731

rate. The problem is then solved using NDS based MOHPSO algo-rithm. The proposed approach is illustrated through a live casestudy of a pump manufacturing industry. This bi-objective modelwhen solved results in Pareto-optimal curve that reveals thetrade-off between the total SC operating costs and fill rate. Thesolution simultaneously predicts the optimal network design, facil-ity location, SC operating cost, inventory control, and logisticsmanagement decisions. The cost values obtained are comparedwith actual industrial data.

Rest of the paper is organized as follows. Section 2 deals withthe work that is done previously in the related field. Section 3explains modeling and mathematical formulation of design-distribution network considered. Section 4 deals with Hybrid MOP-SO methodology adopted to solve bi-objective design-distributionproblem. A systematic application of the proposed algorithm isdemonstrated in Section 5. Section 6 includes results and discus-sions, which is followed by concluding Section 7 where in futurework is outlined.

2. Prior related work

In traditional supply chain management, the focus of the integra-tion of SCN is usually on single objective such as minimizing cost ormaximizing profit (Jayaraman & Pirkul, 2001; Jayaraman & Ross,2003; Syarif, Yun, & Gen, 2002; Yan, Yu, & Cheng, 2003). Since a dec-ade, researchers started incorporating more than one competingobjectives such as each participant’s profit, the average customerservice level, and the average safe inventory level. Different method-ologies found in literature for treating multi-objective optimisationproblems are the weighted-sum method, the -constraint method,goal-programming method, fuzzy method etc. (Azapagic & Clift,1999; Chen & Lee, 2004; Chen, Wang, & Lee, 2003; Zhou, Cheng, &Hua, 2000).

One of the earliest works on multi-objective location problemsis by Ross and Soland (1980). According to them practical problemsinvolving the location of public facilities are multi-criteria prob-lems. They modeled cost and service as general criteria and devel-oped an interactive approach to the resolution of multi-criterialocation problems. Lee, Green, and Kim (1981) presented the appli-cation of integer goal programming to the facility location andproducts allocation problem with multiple, competing objectives.Fernandez and Puerto (2003) presented an exact and an approxi-mate approach to obtain the set of non-dominated solutions fordiscrete multi-objective un-capacitated plant location problem.The two approaches resort to dynamic programming to generatein an efficient way the non-dominated solution sets. Sabri andBeamon (2000) formulated a model that incorporates production,delivery and demand uncertainty and provides a multi-objectiveperformance vector for entire SC network. They adopted multi-objective decision analysis and optimized simultaneously cost, fillrate and flexibility. Nozick and Turnquist (2001) presented an opti-mization model which minimized cost and maximized service.They used a linear function to approximate the safety stockinventory cost function, which was then embedded in a fixed-charge facility location model. They solved the problem heuristi-cally. Shen, Coullard, and Daskin (2003) proposed a jointlocation-inventory problem involving a single supplier and multi-ple retailers with variable demand. They presented computationalresults on several instances of sizes ranging from 33 to 150retailers.

Chen and Lee (2004) proposed a model which simultaneouslyoptimizes conflicting objectives such as each participant’s profit,the average customer service level, and the average safe inventorylevel. Guilléna, Melea, Bagajewiczb, Espuñaa, and Puigjanera(2004) formulated the SCN design problem as multi-objective

stochastic Mixed Integer Linear Programming model for SC design,which was solved by using the standard -constraint method, andbranch and bound techniques. This formulation takes into accountSC profit and customer satisfaction level, considering uncertaintyby means of the concept of financial risk. Shen (2006) addressedprofit-maximizing SC design model where in a company canchoose whether to satisfy a customer’s demand.

Work of Bouzembrak, Allaoui, Goncalves, and Bouchriha (2011)captured a compromise between the total cost and the environmentinfluence. They simultaneously optimized two objective functions;total cost and total CO2 emission in entire SC. Their work helped totake strategic decisions such as warehouses and DCs location, build-ing technology selection and processing/distribution planning. Clas-sical GA was improved by Prakash, Felix, Chan Liao, and Deshmukh(2012) who presented a knowledge based genetic algorithm (KBGA)for the network optimization of SC. Their methodology consideredthree new genetic operators – knowledge based: initialization,selection, crossover, and mutation. The results showed that theirmethodology improved the performance of classical GA by obtain-ing the results in fewer generations. Research by Amin and Zhang(2012) proposed an integrated model for general closed loop supplychain network. Their model considered supplier selection, orderallocation, and closed loop supply chain network configuration,simultaneously. Liu and Papageorgiou (2013) considered threeobjectives; cost, responsiveness and customer service level for inte-grating production, distribution, capacity planning of a global SC.The authors solved their model using e-constraint method. A mul-ti-objective Harmony Search algorithm approach for the efficientdistribution of 24-h emergency units is considered by Landa-Torres,Manjarres, Salcedo-Sanz, Del Ser, and Gil-Lopez (2013). They appliedthis to a realistic case in two regions of Spain and showed that theproposed algorithm is robust and provides a wide range of feasiblesolutions.

Particle swarm optimization (PSO) is one of the evolutionarycomputation techniques and is originally proposed by Kennedyas a simulation of social behavior. It is initially introduced as anoptimization method in 1995 (Kennedy & Eberhart, 1995). Thealgorithm initializes in the beginning of search a population of par-ticles which survive for all generations till end of search. Each par-ticle has memory using which it keeps track of best position it hasacquired so far and best position any other particle acquired so farwithin the neighborhood. The particle will then modify its direc-tion based on components towards its own best position andtowards the overall best position. This kind of systematic acceler-ation finally leads to convergence to the target. PSO can be easilyimplemented and it is computationally in expensive, since itsmemory and CPU speed requirements are low (Eberhart, Simpson,Dobbins, & Dobbins, 1996). Also, it does not require gradientinformation of the objective function, but needs only its values(Kennedy & Eberhart, 1995).

Until 2002 PSO had only been applied to single objective prob-lems, and was giving promising solutions efficiently and effec-tively. In single objective PSO, the swarm population is fixed andare only adjusted by their pbest and the gbest. But, to facilitateMulti-objective approach to PSO a set of non-dominated solutionsmust replace the single global best individual in the standard sin-gle objective PSO. This task of picking suitable global best (gbest)and personal best (pbest) to move the particles through searchspace is much difficult in Multi-objective Particle Swarm Optimiza-tion (MOPSO). According to Coello (1999), a good MOPSO methodmust obtain solutions with a good convergence and diversity alongthe Pareto-optimal front. In 2002, break through studies on incep-tion of multi-objective PSO (MOPSO) were published (Coello &Lechuga, 2002; Fieldsend & Singh, 2002; Hu & Eberhart, 2002;Parsopoulos & Vrahatis, 2002). Each of these studies implementsMOPSO in different ways. Later publications incorporate several

Suppliers Plants DCs

Material flow

Information flow, funds flow

Fig. 1. General three-echelon supply chain model.

5732 B. Latha Shankar et al. / Expert Systems with Applications 40 (2013) 5730–5739

mechanisms such as elitism, diversity operators, mutation opera-tors, constraint handling and crowding distance etc. into multi-objective optimization algorithms so as to improve convergenceand produce a well distributed Pareto front (Carlo & Naval, 2005;Coello, Pulido, & Lechuga, 2004; Yang, 2008).

Bilgen (2010) addressed the production and distribution plan-ning problem in a SC system, which included the allocation of pro-duction volumes among various production lines in themanufacturing plants, and the delivery of the goods to the distribu-tion centers. This work makes use of fuzzy models, which considersthe fuzziness in the capacity constraints, and the aspiration level ofcosts based on various aggregation operators. Guo and Hou (2010)developed a simulation model to describe the operations of athird-party logistics provider. They developed an MOPSOalgorithm combining with the simulation model to identify non-dominated solutions that constitute the trade-off curve betweenfill rate and total inventory. Tsou, Yang, Chen, and Lee (2011)presented a bi-objective model to represent a fixed order systemunder lost sales. They considered cycle stock investment and ser-vice level to be simultaneously optimized. They utilized a solverbased on MOPSO to find the inventory management policies. Ven-katesan and Kumanan (2012) proposed discrete particle swarmalgorithm (MODPS) to optimize the SC network with the objectivesof minimisation of SC cost, minimisation of demand fulfilment leadtime and maximization of volume flexibility. In the first stage theperformance of two global guide selection techniques are evalu-ated and in the second stage proposed MODPS is compared withnon-dominated sorting genetic algorithm-II. The results indicatethat the proposed approach is effective in producing high-qualityPareto-optimal solutions. Dehbari, Pourrousta, Ebrahim Neghad,Tavakkoli-Moghaddam, and Javanshir (2012) formulated a modelto address SC problem where a whole seller/producer distributesgoods among various retailers. The problem was solved using a hy-brid of particle swarm optimization and simulated annealing andthe results were compared with other hybrid method of Ant colonyand Tabu search.

Multi echelon SC network optimization problems are NP-hardproblems and have conflicting objectives. Above theoretical surveyindicates that very little research has been carried out toimplement Particle Swarm intelligence based algorithm in multi-objective optimization of multi-echelon SC network problems. Inparticular particle swarm algorithm is rarely applied for multi-objective optimization of combined strategic and tactical decisionsfor multi-echelon SC network. Hence in this paper a new applica-tion of meta-heuristic based on swarm intelligence called HybridMOPSO algorithm is demonstrated for bi-objective optimizationof SC network of a pump manufacturing industry.

3. Mathematical formulation of the model

This section deals with formulation of a multi-objective modelthat can be used to explore the trade-off between the total SC costsand the level of service provided to the customers. Total SC costcomponents are fixed plant location costs, transportation costsfrom the suppliers to the plants, total production costs at the plantsand transportation costs from plants to DCs. This model is devel-oped for a general SC network consisting of three different levelenterprises. The first-level enterprise is the DC from which theproducts are sold to customers subject to a given lower bound ofcustomer service. The second level enterprise is the plant or man-ufacturer and third level is the supplier. Revenues come from saleof products and costs arise from facilities, labor, transportation,material and inventories. In order to overcome difficulty in math-ematical formulation and convergence, a minimum target for thedemand satisfaction, which must be attained in all the scenarios,is incorporated as a constraint within the existing formulation.

3.1. Problem description

This work considers three-echelon capacitated plant location–distribution network model as shown in Fig. 1.

The notations used in this network model are listed in Table 1with their meaning.

The model defines decision variables as shown in Table 2.The problem is then formulated as the following integer model:

Objective 1 : Min:Xn

i¼1

fiyi þXn

i¼1

Xl

h¼1

Xp

c¼1

cchixhci þXn

i¼1

Xm

j¼1

cijxij ð1Þ

Objective 2 : Max

Pni¼1

Pmj¼1xijPm

j¼1Djð2Þ

Subject to

Xn

i¼1

xhci 6 Sch For h ¼ 1; . . . l; c ¼ 1; . . . p ð3Þ

Xn

i¼1

xij 6 Dj For j ¼ 1; . . . :m ð4Þ

Xm

j¼1

xij 6 Kiyi For i ¼ 1; . . . n ð5Þ

Xl

h¼1

xhci �Xm

j¼1

xij P 0 For i ¼ 1; . . . n; c ¼ 1; . . . p ð6Þ

0:80 6

Pni¼1

Pmj¼1xijPm

j¼1Dj6 1 ð7Þ

Yi 2 f0;1g for i ¼ 1 . . . n ð8Þ

The objective function (1) minimizes the total cost (fixed cost + var-iable cost) of setting up and operating the network and it has threeterms. The first term represents annual fixed cost of locating plants.The second term captures costs of making and shipping from thesuppliers to the plants. The third term represents the averageannual producing, stocking and shipping cost at the plants and in-cludes processing cost, working inventory cost, stocking cost, thefixed administrative cost of ordering, as well as the fixed shipmentcost from plants to DCs. Ordering cost is based on economic orderquantity. Objective function (2) maximizes fill rate. Fill rate here

Table 1Notations and their meanings used in the mathematical formulation.

Notationsused

Meaning

n Number of potential plant locations. ði ¼ 1;2 . . . nÞm Number of markets or demand points. ðj ¼ 1;2 . . . mÞl Number of suppliers ðh ¼ 1;2; . . . lÞp Number of components ðc ¼ 1;2; . . . pÞDj Demand from market j,/period.Ki Potential capacity of plant iSch Supply capacity of supplier h for component cfi Fixed cost of keeping plant i open,/periodcchi Cost of making and shipping one component c from supply

source h to plant icij Cost of producing, stocking and shipping one unit from plant i

to market jci Manufacturing cost at plant i,/unitHi Inventory carrying cost at plant i,/unit/periodPTCij Plant transportation cost from plant i to market j,/unitQi Production batch size at plant i, unitsOi Production set up cost at plant i,/set upti Total production lead time at plant i, period.si Unit processing cost at plant i.Xi Work-in-process holding cost at plant i,/period/unitdi Demand rate, units/daypri Production rate, units/day

Table 2Decision variables used in the mathematical formulation.

Notationsused

Meaning

yi 1, If plant i is open, 0 otherwise.xhci Quantity of component c shipped from supplier h to plant i/

periodxij Quantity shipped from plant i to market j/period

B. Latha Shankar et al. / Expert Systems with Applications 40 (2013) 5730–5739 5733

is measured by fraction of demand satisfied from availableinventory.

The constraint in (3) specifies that the total quantity shippedfrom a supplier cannot exceed the supplier’s capacity. The con-straint in (4) requires that the demand at each regional marketbe satisfied to the maximum extent. The constraint in (5) statesthat no plant can supply more than its capacity. Capacity is 0 ifthe plant is closed and Ki if it is open. The constraint in (6) ensuresthat the quantity shipped out of a plant cannot exceed the quantityof raw material received. The constraint in (7) states that fill ratecan vary from 80% to 100%. The constraint in (8) enforces that eachplant is either open (yi = 1) or closed (yi = 0).

cij used in (1) is given by, cij = ci + PTCij where ci is obtained fromproduction echelon model as given below. The total cost of produc-tion, which consists of setup costs, processing costs, work-in-pro-cess carrying costs and finished product carrying costs at plant iper period is given by (9) and ci by (10),

TCi ¼ Oi

Pjxij

Q iþ si

Xj

xij þXi

Xj

xijti þ HiQ i

2

� �ð9Þ

where

Q i ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2� Oi �

Pjxij

Xi 1� dipri

� �vuut ; then ci ¼

TCiPjxij

ð10Þ

This model is a non-linear integer programming model. The solu-tion has the decision variables which characterize the network con-figuration. They include binary variables that represent the

existence of the different plants of the SC and the integer ones thatrepresent the flow of materials from various suppliers to variousplants and the allocation of regional demand to these plants.

4. A particle swarm approach for generating trade-off betweencost and service

4.1. Introduction to particle swarm optimization

PSO is a kind of evolutionary computing technology based onswarm intelligence and widely applied as powerful optimizationtool in research in different engineering domains and real-worldengineering fields. In PSO algorithm, each individual (particle) rep-resents a solution in n-dimensional space. Each particle also hasknowledge of its previous best experience and knows the globalbest experience (solution) found by the entire swarm. Each particleupdates its direction based on information shearing mechanismusing the Eqs. (11) and (12).

Vij ¼ w� v ij þ c1 � r1 � ðpij � xijÞ þ c2 � r2 � ðpgj � xijÞ ð11Þ

Xij ¼ xij þ v ij ð12Þ

where w is the inertia factor influencing the local and global abili-ties of the algorithm, vij is the velocity of the particle i in the jthdimension, c1 and c2 are weights affecting the cognitive and socialfactors, respectively. In any situation, whether individual learning(pbest) is stronger or social- influence (gbest) is stronger isunknown, both will be weighed by uniform random numbers r1

and r2 between 0 and 1, and two random values are generated inde-pendently, so that sometimes the effect of one and sometimes theother will be stronger. pij stands for the best value found by particlei (pbest) and pg denotes the global best found by the entire swarm(gbest). After the velocity is updated, the new position i in its jthdimension is calculated. This process is repeated for every dimen-sion and for all the particles in the swarm. Eventually the swarmas a whole, like a flock of birds collectively foraging for food, is likelyto move close to an optimum of the fitness function (Kennedy &Eberhart, 1995).

4.2. Binary PSO

Kennedy and Eberhart (1997) developed a discrete binary ver-sion of PSO for binary problems. Their model proposes that theprobability of an individual making binary decision is a functionof personal and social factors and is given by (13),

PðxijðtÞ ¼ 1Þ ¼ f ðxijðt � 1Þ;v ijðt � 1Þ; pij; pgjÞ ð13Þ

where� PðxijðtÞ ¼ 1Þ is the probability that individual i will choose 1.

The parameter v ijðtÞ, will determine the probability threshold. Ifv ijðtÞ is higher, the individual is more likely to choose 1, and lowervalues favor the 0 choice. Such a threshold stays in the range [0.0,1.0]. The sigmoid function given in (14) is used to determine theprobability threshold.

Sðv ijÞ ¼1

1þ expðv ijÞð14Þ

Thus the formulae for binary decision are given in (11) and (15).

If qid < sðv idðtÞÞ then xidðtÞ ¼ 1; else xidðtÞ ¼ 0 ð15Þ

Then qid is a vector of random numbers, drawn from a uniform dis-tribution between 0.0 and 1.0. The constant parameter Vmax is oftenset at ±4.0, so that there is always at least a chance of s(Vmax) -ffi 0.0180 that a bit will change state.

Suppliers Plants DCs

Material flow

Information flow, funds flow

Fig. 3. Supply chain model of pump manufacturing company.

5734 B. Latha Shankar et al. / Expert Systems with Applications 40 (2013) 5730–5739

4.3. Hybrid PSO

A hybrid swarm optimizer combines both binary and real val-ued parameters in one search. It simply operates on binary inputswith binary particle swarm algorithm and treats the continuousvariables with real valued particle swarm. Binary PSO algorithmis used to take the location decisions (whether or not to locate afacility at a given candidate site), while the allocation of customersto suppliers decisions are obtained by continuous PSO algorithm(Kennedy & Eberhart, 2001).

4.4. Multi-objective PSO

Every multi-objective optimization algorithm aims at findingPareto-optimal set or Pareto front consisting of several trade-offsolutions balancing conflicting objectives. The concept of Paretooptimality was proposed by the Italian economist, Vilfredo Pareto,in his work, in 1906 (Eberhart et al., 1996). A general formulationfor a multi-objective optimization problem is given by (16),

Minimize f ðxÞ ¼ ff1ðxÞ; f2ðxÞ; . . . ; fmðxÞg; x�D ð16Þ

where f(x) represents the vector of m objectives and x is a vector of ndecision variables given by x ¼ ðx1; x2; . . . xnÞ. The n-dimensionalvariable x is constrained to lie in a feasible region D which is con-strained by J-inequality and K-equality constraints, given by (17),

D ¼ fx : gjðxÞ 6 0; hkðxÞ ¼ 0; j ¼ 1;2; . . . ; J; k ¼ 1;2; . . . ;Kg: ð17Þ

Thus a multi-objective optimization problem deals with simulta-neous optimization of many objectives which are conflicting orcompeting in nature. They are conflicting because improvement inany objective is not possible without degradation in other objec-tives. Hence there cannot be a single optimum solution whichsimultaneously optimizes all objectives. The resulting outcome isa set of optimal solutions with a varying degree of objective values.This set of solutions is called non-dominated set or Pareto-OptimalSet. Because minimization of total SC cost and maximization of fillrate cannot be achieved at the same time as they are conflictingin nature, there exists a trade-off between them. This type of system

t= t+1

Generate an initial population,

Calculate fitness values, using two objecnonDomList of non-dominated solutions in

Calculate new velocity. U

Calculate the crowding distain nonDomList and choos

Is conconditio

Consider Gbest of non

Calculate the new fitn

No

If new fitness value is better

Identify non-dominated solutionnonDomList. If the number of non-do

then delete solutions that are non

Fig. 2. Flow chart of p

clearly represents a multi-objective optimization situation which isa procedure looking for a compromise policy, based on number ofoptions. Hence the Pareto set solutions and their correspondingdecision variables should be provided, from which the decision-ma-ker can select a solution to satisfy the industrial need.

4.5. Selecting the global best and personal best

The main difficulty in MOPSO is to pick suitable global best(gbest) and personal best (pbest) to move the particles throughsearch space to attain a good convergence and diversity alongthe Pareto-optimal front. In this study, method of selection of pbestand gbest is inspired by NSGA-II. For selecting pbest a method

yes

initial valocity, maximum velocity

tives, initialize Pbest and external repository current iteration. Set the iteration counter to t.

pdate position for each particle

nce for niching. Sort all particles e Gbest with least niche count.

vergence n reached?

-dominated solutions as final

ess value for each particle

than current one update Pbest

s in current iteration and add them to minated solutions exceeds the desired size -dominating with the current solution.

roposed MOHPSO.

B. Latha Shankar et al. / Expert Systems with Applications 40 (2013) 5730–5739 5735

called Prandom is employed, according to which a single pbest ismaintained. Pbest is replaced if new value is less than Pbest forminimization problem, otherwise, if new value is found to bemutually non-dominating with Pbest, one of the two is randomlyselected to be the new Pbest (Everson, Fieldsend, & Singh, 2002).To select gbest from archive, this work makes use of crowding dis-tance measure and niche count (Deb, 2001). The non-dominatedsolutions from the last generations are kept in the archive. Suchan archive will allow the entrance of a solution only if it is non-dominated with respect to the contents of the archive or it domi-nates any of the solutions within the archive (Coello & Lechuga,2002). Finding a relatively large set of Pareto-optimal trade-offsolutions is possible by running the MOPSO for many generations.Niche count nci for ith solution is calculated using sharing functionsh(dij) given in (18) and (19)

nci ¼XN

j¼shðdijÞ ð18Þ

ShðdÞ ¼ 1� drshare

� �a; if d 6 rshare

0; otherwise

8<: ð19Þ

Table 3Production details of both the plants.

Sl.no.

Parameters Plant 1 Plant 2

1 Job overheads in Rs. 67.90 /pump

71.00 /pump

2 Employee cost in Rs. 29.00 /pump

29.80 /pump

3 Power cost in Rs. 2.01/pump 2.01/pump4 Factory overheads including

testing in Rs.39.00/pump

40.27/pump

5 Other overheads including repair andmaintenance in Rs.

18.58/pump

19.10/pump

6 Production capacity/month 3500pumps 2000pumps

Table 4Transportation costs to all distribution centers from plants P1, P2 (Rs/kg).

DC 1 DC 2 DC 3 DC 4 DC 5 DC 6 DC 7

Plant 1 6.86 1.00 6.20 2.57 3.15 0.15 5.00Plant 2 5.97 0.15 5.46 1.69 2.47 0.90 4.36

Table 5Supplier details showing capacity, making cost and transportation cost of each item from

Suppliers Notation used Product Capacit

Raja magnetic, Chennai V1 Stator stamping 1500Aluminum body 2000Rotor stampings 1500

Raja magnetic, Bangalore V2 Stator stamping 1500Aluminum body 2000Rotor stampings 1500

Raiker, Bangalore V3 Stator stamping 4000Rotor stampings 2000

Adivinayaga wires, Chennai V4 Copper wire 2000Precision wires – Daman V5 Copper wire 1000Ganga engg. – Chennai V6 Aluminum body 2000SKF bearings V7 Bearings 5000HCH bearings V8 Bearings 6000Solid state – Bangalore V9 Capacitor 2000imported capacitors V10 Capacitor 3000Apex bright bars – Channai V11 Shaft 3000Sunil Lal Prabhudas Mumbai V12 Shaft 2000Veesaa foundries – Channai V13 Castings 20000C R tools – Coimbatore V14 Impeller 5000

It provides an estimate of extent of crowding near a solution. Heredij is the distance between the ith and jth solutions. Its value isalways greater than or equal to one because sh(dii) = 1. After calcu-lating nc for each solution in the archive the gbest is selected fromthe archive whose nc is the smallest. This ensures diversity beingmaintained as one which is comparatively less crowded is selected(Deb, 2001). The flow chart of MOPSO algorithm used in this work isas shown in Fig. 2.

5. Case study

An industrial live case study of Mono block pumps is consideredto evaluate and validate the performance of the proposed MOHPSO.The SC for pump manufacturing is as shown in Fig. 3. This industryhas a product range of 26 varieties of standard and non-standardpumps with a turnover of Rs. 14 Crores/annum. It has 14 supplierssupplying 9 components that make up the product. There are twoplants one in Coimbatore (P1) and another in Hosur (P2).

5.1. Input data for the SC model

The details of plant 1 and plant 2 are indicated in Table 3.The products from these two plants are distributed to the

customers through 7 distribution centers located at various majorcities namely Delhi (DC1), Bangalore (DC2), Calcutta (DC3), Secun-drabad (DC4), Pune (DC5), Coimbatore (DC6) and Ahmadabad(DC7). The transportation costs incurred by the plants in the eventof transferring the finished products to various distribution centersare given below in Table 4.

5.1.1. Product detailsAmong the different types of Mono-block pumps manufactured

by the industry, the SC activities for ‘Regenerative Mono-set pump(ENR-9)’ are analyzed for the period from April 2011 to March2012. They have 14 different suppliers for supplying 9 major rawmaterials considered. Also they have 7 distribution centers for dis-tributing their products. Among the various raw materials requiredfor manufacturing a pump 11 major raw materials are considered.They are listed below with their respective notations used to indi-cate them.

� Stator stampings (C1)� Copper wire (C2)

suppliers to different plants.

y (Kgs) Making Cost (Rs/kg) Supplier Transportation Cost (Rs/kg)

Plant1 Plant 2

84.00 0.15 0.85212.0067.0084.00 1.00 0.25212.0067.0088.00 1.00 0.2576.00400.00 0.15 0.90390.00 2.80 2.00208.00 0.15 0.8519.00 0.05 0.087.00 0.05 0.0823.50 0.25 0.0517.50 0.25 0.0544.00 0.10 0.9042.50 3.00 2.1554.00 0.20 0.85176.00 0.10 0.85

Table 6Demands generated at DCs.

Plant Delhi(DC1)

Bangalore(DC2)

Calcutta(DC3)

Secundrabad(DC4)

Pune(DC5)

Coimbatore(DC6)

Ahmedabad(DC7)

Demands at DCs from April 2011 to March2012

180 178 506 641 588 410 402

Table 7Weights or number of units of the component in a pump.

Component Weights or no of units (kg or no of units)

C1 1.270C2 0.535C3 0.500C4 2.000C5 1.000C6 0.900C7 0.400C8 3.345C9 0.250

Table 8Indices used in the mathematical model.

Index Meaning Total number used

C Raw material 9V Supplier 14P Plant 2D Customer zone 7

5736 B. Latha Shankar et al. / Expert Systems with Applications 40 (2013) 5730–5739

� Aluminum body (C3)� Bearings (C4)� Capacitor (C5)� Rotor stampings (C6)� Shaft (C7)� Casting (C8)� Impeller (C9)

5.1.2. Supplier detailsIn order to meet the demand, the organization is buying the re-

quired sand, mild steel and sodium silicate oil from different sup-pliers. The capacity and the selling price of each supplier, thetransportation cost of each item from supplier to different plantsare given in Table 5 and the demand information at different cus-tomer zones is given in Table 6.

The list of weights or no of units of each raw material used in apump are given in Table 7.

5.2. Mathematical modeling

5.2.1. Indices and notations descriptionQuantity of raw materials supplied from suppliers to the plants

and quantity of finished products moved from plants to DCs arerepresented as per the indices given below in the Tables 8 and 9.

5.2.2. Derived equations from the mathematical modelTotal SC cost is the sum of total supplier cost (TSC), total plant cost

(TPC) and total distribution center cost (TDC) and given by (20).

TSCC ¼ TSCþ TPCþ TDC ð20Þ

Total supplier cost (TSC) is the sum of supplier raw material cost(SRC) and supplier transportation cost (STC) and given by (21).

TSC ¼ SRCþ STC ð21Þ

Here supplier raw material cost (SRC) is given by (22), Suppliertransportation cost (STC) is given by (23), and Total Plant cost(TPC) is given by (24).

SRC ¼ ½X1;1;1 � 84þ X1;2;1 � 84þ X1;3;1 � 88� þ ½X2;4;1 � 400

þ X2;5;1 � 390� þ ½X3;1;1 � 212þ X3;2;1 � 212þ X3;6;1

� 208� þ ½X4;7;1 � 19þ X4;8;1 � 7� þ ½X5;9;1 � 23:5

þ X5;10;1 � 17:50� þ ½X6;1;1 � 67þ X6;2;1 � 67þ X6;3;1

� 76� þ ½X7;11;1 � 44þ X7;12;1 � 42:5� þ ½X8;13;1 � 54�þ ½X9;14;1 � 176� þ ½X1;1;2 � 84þ X1;2;2 � 84þ X1;3;2

� 88� þ ½X2;4;2 � 400þ X2;5;2 � 390� þ ½X3;1;2 � 212

þ X3;2;2 � 212þ X3;6;2 � 208� þ ½X4;7;2 � 19þ X4;8;2

� 7� þ ½X5;9;2 � 23:5þ X5;10;2 � 17:50� þ ½X6;1;2 � 67

þ X6;2;2 � 67þ X6;3;2 � 76� þ ½X7;11;2 � 44þ X7;12;2

� 42:5� þ ½X8;13;2 � 54� þ ½X9;14;2 � 176� ð22Þ

STC ¼ ½X1;1;1 � 0:15þ X1;2;1 � 1þ X1;3;1 � 1� þ ½X2;4;1 � 0:15

þ X2;5;1 � 2:8� þ ½X3;1;1 � 0:15þ X3;2;1 � 1þ X3;6;1

� 0:15� þ ½X4;7;1 � 0:05þ X4;8;1 � 0:05� þ ½X5;9;1 � 0:25

þ X5;10;1 � 0:03� þ ½X6;1;1 � 0:15þ X6;2;1 � 1þ X6;3;1

� 1� þ ½X7;11;1 � 0:1þ X7;12;1 � 3� þ ½X8;13;1 � 0:2�þ ½X9;14;1 � 0:1� þ ½X1;1;2 � 0:85þ X1;2;2 � 0:25þ X1;3;2

� 0:25� þ ½X2;4;2 � 0:9þ X2;5;2 � 2� þ ½X3;1;2 � 0:85

þ X3;2;2 � 0:25þ X3;6;2 � 0:85� þ ½X4;7;2 � 0:08þ X4;8;2

� 0:08� þ ½X5;9;2 � 0:05þ X5;10;2 � 0:05� þ ½X6;1;2

� 0:85þ X6;2;2 � 0:25þ X6;3;2 � 0:25� þ ½X7;11;2 � 0:9

þ X7;12;2 � 2:15� þ ½X8;13;2 � 0:85� þ ½X9;14;2 � 0:85� ð23Þ

TPC ¼ ½Y1;1 þ Y1;2 þ Y1;3 þ Y1;4 þ Y1;5 þ Y1;6 þ Y1;7� � 156:49

þ ½Y1;1 þ Y1;2 þ Y1;3 þ Y1;4 þ Y1;5 þ Y1;6 þ Y1;7�� 162:18 ð24Þ

Total distribution cost (TDC) is the cost incurred in transporting theproducts from the plants to the different DCs. It is given by (25).

TDC ¼ ½Y1;1 � 6:86þ Y1;2 � 1þ Y1;3 � 6:2þ Y1;4 � 2:57

þ Y1;5 � 3:15þ Y1;6 � 0:15þ Y1;7 � 5þ Y2;1 � 5:97

þ Y2;2 � 0:15þ Y2;3 � 5:46þ Y2;4 � 1:69þ Y2;5

� 2:47þ Y2;6 � 0:9þ Y2;7 � 4:36� � 7:5 ð25Þ

5.2.3. ConstraintsThe constraints considered while optimizing the objective func-

tion are demand constraints, plant capacity constraints, suppliercapacity constraints and raw material constraints.

B. Latha Shankar et al. / Expert Systems with Applications 40 (2013) 5730–5739 5737

5.3. Experimental design

The applicability and effectiveness of proposed hybrid MOPSOalgorithm was checked in two stages. Hybrid PSO was first devel-oped and applied to the problem solved in the book by Chopraand Meindl (2005, pp. 137). This problem is of single objective typeand solved using excel solver. While comparing results relateddata, it was found that results were same but computational timetaken was little bit more using new Hybrid PSO algorithm. Thenmulti-objective module was developed and applied for standardtest problem given in a book by Deb (2001, pp. 290). This problemis a simple two-variable, two-objective constraint optimizationproblem. After getting the comparable results both the modulesare combined to arrive at complete algorithm for location-allocation decisions considering multiple objectives. It is thenapplied to the case study explained above. Since this problem con-sidered is a constrained problem it is converted into unconstrainedby exterior Penalty parameter approach. Accordingly objectivefunctions are penalized each time if and only if a constraint is vio-lated, not otherwise. In each iteration, all constraint violations areadded together to get overall constraint violation which is thenmultiplied by penalty parameter and then added to each of theobjective function values.

Sensitivity analysis of proposed hybrid MOPSO model was firstcarried out to arrive at the best parametric values. The randomseeds were generated by a random number generator incorporatedin the program. After running many trial runs with different com-binations of values for each parameter, following parametric val-ues are found to yield best results; number of particles = 20,decrement constant = 0.8, constant personal parameter c1 = 1.05,social parameter c2 = 0.05. Sensitivity analysis has also showedthat higher the penalty parameter value, greater is the explorationand lesser is the exploitation capability of the swarm. After many

Table 9Decision variables used in the mathematical model.

Variable Meaning Number ofdecision

variables

Xc,v,p Quantity of raw material ‘c’ supplied from supplier‘v’ for plant ‘p’

38

Yp,d Quantity of product ‘p’ dispatched from plant ‘p’ tocustomer zone ‘d’

14

Fig. 4. Optimum solutions showing trade-off between total SC cost and totaldemand satisfied.

runs, following condition is found to be ideal that if Penalty valueis greater than 347 then Penalty parameter for next iteration istaken as 1.02 else 1.002. Maximum velocity for location decisionsis taken as 3 and for allocation decisions 50% of the correspondingcapacities.

6. Results and discussions

All the supplier shipment variables and the plant shipment vari-ables are optimized for minimizing the total cost and maximizingdemand satisfied. After running the model for many iterations(maximum number of iterations is set to 25,000), all the feasiblesolutions obtained are graphically shown in Fig. 4 by taking twoobjectives along two axes. In this graph, Pareto front solutions aswell as inferior points are shown. There are five non-dominatedoptimum decision points, whose corresponding objective valuesare given in Table 10 and corresponding decision variables repre-senting optimum location and distribution of goods from suppliersto plants and from plants to DCs for first scenario are tabulated inTables 11 and 12. In ‘‘optimal location of plants’’ column, value of‘‘0’’ represents closing of plants and ‘‘1’’ operating of plants. It canbe observed from Table 11 that for scenario 1, it is optimal for thecompany to keep both the plants open and to supply the entiredemand by operating through both the plants. In general, theremay be many Pareto solutions. The final decision is made amongthem taking the total balance over all criteria into account. Thisis a problem of value judgment of decision maker. Also these deci-sions should be revisited every year as demand and costs change.

When the optimized values are used there will be changes invarious costs involved in the SC. The comparison of those costchanges due to the usage of optimized values with actual valuesavailable in industry are given in Table 13.

Table 10Optimum values of objective functions.

Scenario Total SC cost (Rs.) Fill rate % Actual demand

1 2838569.76 100 29052 2835302.77 99.93 29053 2822434.73 99.90 29054 2818883.61 99.86 29055 2810841.91 99.83 2905

Table 11The optimal plan for material flows from suppliers to plants corresponding to Paretofront points for scenario 1.

Sl. no. Components Suppliers Plants

P1 P2

1 C1 V1 108 1142 V2 306 2513 V3 1276 16384 C2 V4 511 6045 V5 204 2396 C3 V1 14 907 V2 389 2198 V6 262 4799 C4 V7 2102 88010 V8 556 228711 C5 V9 220 25012 V10 1108 133413 C6 V1 773 11614 V2 173 45215 V3 261 85216 C7 V11 510 34917 V12 81 35518 C8 V13 4564 527519 C9 V14 336 457

Table 12The optimal location of plants and optimal flow of goods from plants to DCscorresponding to Pareto front points for scenario 1.

DCs Locationof plants

Plants D1 D2 D3 D4 D5 D6 D7P1 83 128 87 424 441 65 102 1P2 97 50 419 217 147 345 300 1Total qty. supplied 180 178 506 641 588 410 402

Table 13Comparison of costs of the SC when demand satisfied is 100%.

Sl.no.

Various costs involved inthe SC in Rs.

Optimizedvalues

Actualvalues

1 Raw material cost of plant1 1058726.44 13849862 Raw material cost of plant2 1243680 934894.53 Total supplier cost of both the plants 2302406 2319880.54 Number of pumps produced in plant1 1330 17405 Number of pumps produced in plant2 1575 11606 Total manufacturing cost of plant1 237379.7 303492.607 Total manufacturing cost of plant2 289325.9 206608.808 Distribution cost of plant1 4235.36 48795.009 Distribution cost of plant2 5222.65 19183.5010 Total distribution cost of both the

plants536163.61 646058.4

11 Total SC cost of the organization 2838569.76 2949959.86

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7. Conclusions

Since nowadays, the competition is not between the companies,but between the SCs that consist of many such companies, the basicpriority for supply chain management should be designing the SCnetwork properly, to gain competitive advantage. Many real worldissues in SCN architecture are optimization problems and are com-binatorial in nature. There are often a large number of decision vari-ables, many of which can only take on discrete values. Owing tohigh complexity and large search space traditional operations re-search techniques fail to find solutions to such supply chain net-work optimization problems. Hence in this paper a newapplication of meta-heuristic based on swarm intelligence is dem-onstrated for simultaneous optimization of two conflicting objec-tives. For this, an analytical model is formulated for three-echelonSC network for the optimal facility location and capacity allocationdecisions. Fixed location and variable material cost, production,inventory and transportation costs are considered while makingstrategic decisions. Two objective functions of Minimizing totalSC cost and maximizing fill rate are considered as it is importantfor a company to find the right trade-off between supply chain costand customer service in real life situations. An intelligent MOHPSOis used as optimizer. Testing an algorithm’s performance on appli-cation problems is necessary to demonstrate the use of algorithmin practice. Hence the applicability and effectiveness of this algo-rithm is checked by applying it to a pump manufacturing company.The supplier variables to both the plants and plant distribution vari-ables of the organization have been optimized for total SC costreduction and fill rate maximization. The results indicate that thetotal SC cost of the industrial SC network could be reduced by3.8% when demand satisfied is 100%. Similar cost reductions arepossible for different fill rate values. Also, the optimization suggestshow many pumps each plant must manufacture so as to achieve themaximum reduction in SC cost against the existing method of prac-tice. These results clearly indicate that this optimizer can act asdecision support system for location of facilities and distributiondecisions in real three stage SC optimization with many players ineach stage. Location decisions help to decide whether a facilityneeds to be located at a given site or if a facility is already located

whether a facility needs to be operated or not when a demand sce-nario arises. Distribution decisions help to decide flow of productsfrom sources to destination facilities. The model developed hereaids in the design of efficient and effective supply chains, and inthe evaluation of competing SC networks. Whenever demandchanges optimizer can be fine tuned by changing very few param-eters which will make the logistics manager’s task easier. Furtherwhat-if analysis of changing different key parameters will help togain significant managerial insights about different trade-off situa-tions with respect to total cost involved and fraction of demand sat-isfied. This will help to reduce the total cost incurred in producingthe product especially when demand is less by closing few of thefacilities which will increase the savings in monetary terms. Thisstudy could be further extended by considering other types ofpumps and provide a holistic solution to the industry and also ac-count more features like uncertainty, stock planning, lead timeand credit days of the suppliers. By incorporating these details,the theoretical model could move closer to the actual model ofthe organization.

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