Research ArticleRoute Optimization of Electric Vehicle considering Soft TimeWindows and Two Ways of Power Replenishment

Ming Meng and Yun Ma

Department of Economics and Management North China Electric Power University Baoding Hebei 071003 China

Correspondence should be addressed to Yun Ma my15131881021163com

Received 30 March 2020 Accepted 4 May 2020 Published 20 May 2020

Academic Editor Demetrio Lagana

Copyright copy 2020 Ming Meng and Yun Ma is is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work isproperly cited

Under the background of severe air pollution and energy shortage electric vehicles (EVs) are promising vehicles to support greensupply chain and clean production In the world the renewal of EVs has become a general trenderefore the concern about EVsis a hot issue at present but EVs have the characteristics of limited driving distance and long charging time When the EVs areused in logistics transportation these characteristics have a significant impact on the vehicle routing problems erefore basedon the research experience of traditional vehicle routing optimization combining with the characteristics of EVs this paperpresents an optimal problem of electric vehicle routes with time windows based on two charging methods and it also designs amathematical model which was caused by early and late arrival as the objective function to minimize the transportation costvehicle use cost power supply cost and penalty cost e model is solved using an ant colony algorithm Finally the ant colonyalgorithm is tested and analysed with an example

1 Introduction

e research on vehicle routing began in the 1950s Dantzigand Ramser firstly proposed the concept of vehicle routingproblem (VRP) which refers to the purpose of distributingor collecting goods between distribution centres and acertain number of customers with different needs throughthe design of vehicle routing and finally reached the goalssuch as the shortest distance the least time and the least cost[1] e importance of transportation in the logistics systemdistribution activities is undeniable but in recent years thelarge use of fossil fuel vehicles has resulted in the rapidconsumption of oil resources and excessive emissions ofgreenhouse gases so considering the balance and optimi-zation of monetary costs and the environmental problems offossil fuel vehicles many vehicle routing problemmodels forfuel or emissions have risen such as the fuel consumptionrate of the VRP was considered by Xiao et al [2] fuelconsumption and carbon emission of the VRP considered byZhang et al [3] a time-dependent VRPmodel of minimizingfuel consumption of Norouzi et al [4] the green vehicle

routing problem (GVRP) model of Poonthalir and Nadar-ajan [5] and the vehicle scheduling problem of minimizingcarbon emission of Wang et al [6]

Because of the environmental protection characteristicsof EVs in recent years with the rapid growth of the marketshare EVs have been introduced into the market as personaland commercial alternative energy vehicles In 2018 thenumber of electric vehicles worldwide exceeded 51 millionan increase of 2 million from 2017 and the growth of newvehicles almost doubled (IEA 2019) In China electricvehicles are growing at the rate of more than 50 per year(IEA 2018) In 2018 the number of electric vehicles in Chinaranked first in the world [7] Compared with traditional fuelvehicles the main advantages of electric vehicles are zerogreenhouse gas emissions high efficiency and low operatingnoise [8] which helps logistics companies get more andmore social and environmental customer support And itgets a green image [9] Fernandez and Casals use sustainableanalysis and practical estimation methods that take intoaccount the life cycle carbon emissions of electric vehicles toanalyse the contribution of electric vehicles to reducing

HindawiAdvances in Operations ResearchVolume 2020 Article ID 5612872 10 pageshttpsdoiorg10115520205612872

greenhouse gas emissions [10 11] Wu et al used the lifecycle assessment method to estimate that the total life cyclegreenhouse gas emission reduction potential of batteryelectric vehicles will gradually reach 134 in 2020 [12] Inaddition to environmental benefits EVs also have economicbenefits Compared with traditional fossil fuel poweredvehicles EVs consume 10 to 15 of the fuel cost of tra-ditional vehicles at the same distance [13] erefore thefocus on EVs has become a hot issue at present Howeverdue to the characteristics of EVs such as low endurancemileage and long charging time it becomes a significant andchallenging task to study its VRP

Electric vehicles refer to cars that use electric engines toprovide energy through their own chemical batteries eelectrical energy used by EVs can be converted into manykinds of clean energy which is the main force of environ-mental protection vehicles in the future with a high energyutilization rate and being clean and pollution-free As adistribution vehicle electric vehicles need to be charged muchtime for long-distance distribution and the power replen-ishment time is longer than the refueling timeerefore it isnecessary to consider the charging problems that may occurin the charging process Based on traditional fuel vehicle routeoptimization the introduction of the charging stations is theprimary issue of electric vehicle upgrading combining withthe characteristics of EVs Electric distribution companiesapply some coordination methods to control the chargingloadat can affect the charging duration Yang et al studiedthe charging scheduling of electric vehicles on the highway[14] Dogan and Alci optimized the charging schedule ofelectric vehicles considering the cost of battery degradation[15] Dogan et al based on a heuristic algorithm for chargeand discharge coordination optimization [16] Aravinthanand Jewell proposed a two-step method for scheduling EVcharging which limits the impact on EV charging on dis-tribution assets [17]

At present fast charging is the most common chargingstrategy Schucking et al proposed five charging strategies andbelieved that DC fast charging is essential [18] In addition tofast charging on the issue of charging strategy batteryswitching is also a relatively popular charging strategy Adlerand Mirchandani used real-time highway data to find theoptimal battery exchange strategy [19] Yang and Sun studiedthe location routing problem of the battery switching stationof EVs with large capacity and optimized the routing plan andthe selection of battery switching stations [20] Dai et alregarded the battery exchange strategy of EVs as the back-ground and it provided reference for the determination ofdecision variables such as the number of backup batteries inAC power station and the charging selection of EVs [21]Margaritis et al analysed the advantages and disadvantages ofbattery exchange strategy to the government users andenterprises based on the EU [22]is study combines the twocharging strategies of fast charging and battery switchingefast charging time is related to the remaining power fixedbattery replacement time and the power replenishmentmethod with less time is selected

In the large-scale application of EVs in modern logisticsin addition to considering the plan to charge or replace

batteries on the way the delivery time is also extremelyimportant for logistics companies so we need to considersome important practical factors such as customer timewindows In the actual distribution activities more andmore logistics enterprises begin to pay attention to thetimeliness of package delivery For customers ldquopunctualityrdquois one of the important factors affecting customer experi-ence so the vehicle routing problem with time windows(VRPTW) has also become an important part of the re-search By adding time windows constraints to the basic VRPmodel and Solomon built VRPTW model in which timewindow is a hard time window that must be observed [23]Qureshi further expanded the concept of the hard timewindow extended the problem to the category of the softtime windows and determined the strictness of time win-dows by setting penalty function [24]e soft time windowsproblem is widely used Goeke considered the problembetween time windows and EVs is pickup and delivery [25]Keskin and Catay studied partial charging strategies forelectric vehicles with time windows [26] Desaulniers et alstudied the effective route optimization of battery electriccommercial vehicle fleets and they considered four variantsof the route problem of electric vehicle with time windows[9] Goeke studied the pickup and delivery of EVs with timewindows (PDPTW-EV) In the PDPTW-EV access locationis limited by time windows [25] Many scholars introducedcharging stations and time windows for discussion [27 28]is study combines the two hot charging strategies of fastcharging and battery switching e fast charging time isrelated to the remaining power fixed the switching time andthe power replenishment method with less time is selectedis paper not only considers the problem of chargingstations but also uses the broken line time windows to limitthe distribution time based on the soft time windows

In summary compared with other similar studies themain contributions of this paper are as follows (1) in orderto calculate the cost of logistics enterprises more accuratelyand save cost this paper considers the cost of transportationas much as possible that is to say fixed cost transportationcost charging cost and time penalty cost And it establishesa mixed-integer linear programming model (MILP) with thegoal of minimizing the total cost (2) in order to savecharging time two commonly used charging methods areconsidered and one with shorter charging time is selectedand (3) considering the customerrsquos time tolerance thebroken line soft time windows is adopted

e rest of this paper is organized as follows Section 2describes the problem and identifications of the main as-sumptions In Section 3 the MILP model is established andthe description of the method of solving the model isprovided In Section 4 the test results of an example aregiven and the sensitivity analysis is carried out Finally thepaper summarizes in Section 5

2 Problem Description

is problem can be abstracted as that an enterprise usesEVs to provide distribution services for n customers withtime windows after the distribution centre is fully charged

2 Advances in Operations Research

Each customerrsquos demand service duration good servicetime windows and customer tolerance level are needed to beknown Finally reasonable planning of the vehicle distri-bution route is necessary so that the total cost of distributionis small

e soft time windows can relax the constraints of timewindows optimize resource allocation and reduce energyconsumption and road congestion so the time windowsstudied in this paper mainly are soft time windows Asshown in Figure 1 in the traditional soft time windowswhether the vehicle arrives before or after l the customer isallowed to serve but they are required to pay the corre-sponding penalty fee which is generally a simple linearrelationship with the degree of time deviation However forthe deviation of the best service time windows customershave the difference between tolerance and intoleranceerefore based on the traditional soft time windowsconsidering the tolerance range of customers this paperproposes a broken line time window

According to the customer tolerance level (z) and serviceduration (tf) the tolerance time window can be obtained onthe basis of the optimal time window [eprime lprime] whereeprime e minus z times tf lprime l + z times tf If the vehicle provides ser-vices in the best time window [e l] there will be no penaltycost to be paid If the vehicle provides services in the interval[eprime e][eprime e] or [l lprime] there will be only less penalty cost to bepaid If the vehicle starts service earlier than eprime or later thanlprime there will be more penalty cost to be paid Compared withthe traditional soft time windows the broken line soft timewindows take the actual feelings of customers into con-sideration which will be conducive to better coordinationbetween enterprises and customers reasonable allocationand optimization of resources

In view of the above considerations the problems andbasic assumptions to be solved are as follows (1) each vehiclecan meet the needs of multiple customer points and eachcustomer point can only be served by one vehicle after thecompletion of the distribution service the vehicle must driveback to the distribution centre (2) all vehicles are the sametype and the total transportation volume shall not exceed thecapacity limit of EVs (3) each customerrsquos location coordi-nates demand quantity and service duration are known andthere are optimal service time windows and tolerance timewindows (4) the time window penalty coefficient of eachcustomer node is the same (5) EVs can only be charged ortheir battery can be replaced in the distribution centre orpower station (6) each customer must be visited and can onlybe visited once (7) the road is smooth without consideringtraffic congestion and other special situations (8) it is as-sumed that the transportation cost generated by the vehicle islinearly related to the route length and the use cost of eachvehicle is fixed and (9) the objective function of this problemis to minimize the total distribution cost

3 Materials and Method

In this part according to the electric vehicle routing problemwith time windows (EVRPTW) we establish a MILP modeland determine the constraints

31 Defining Variables e parameters and decision vari-ables used to describe the MILP model are shown in thefollowing

N set of all nodes n in networksV set of all nodes v in networksC set of all nodes c in networksD network D NcupCcup o consisting of sets of nodesD 0 1 2 |N| + |C| n set of customer nodes where n isin Nv set of EV nodes where v isin Vc set of charging station nodes where c isin Co set of distribution centre nodesC0 fixed cost per vehicleC1 electric vehicle unit distance transportation costEC total electricity supplementary costC2 charging cost per unit timeC3 single battery replacement costi j index of nodes i 0 1 2 ndij distance from the node i to the node j i j isin Dqn demand of the customer node n and n isin NQ rated load capacity of electric vehiclesP battery capacity of electric vehiclesg charge coefficientP1

dv the residual power of EVs when v reaches the nodeDP2

dv residual electricity of the electric vehicle V leavingnode Dp battery capacity of electric vehiclesh power consumption coefficientg charge coefficienttfi if i represents the customer point tfi representsthe service time of electric vehicle at the node i if irepresents the charging stations then tfi represents theelectric vehiclersquos power replenishment time i isin NcupM

tci single battery change time and i isin Ctwi waiting time of electric vehicles at the customernode i

0 e l

Cost

Time0 eprime l

Cost

Timee lprime

Figure 1 Penalty cost function under traditional soft time win-dows and polygonal line soft time windows

Advances in Operations Research 3

tvi the time point when the vehicle v arrives at thecustomer node i where tv

0 0tprimevi the start time of the v-car service customer node itij time of electric vehicles from i to jspeed driving speed of electric vehiclesei the lower limit of the best service time windows ofthe customer node ili the upper limit of the best service window of thecustomer node ieiprime the lower limit of tolerance time windows of thecustomer node iliprime upper limits of tolerance time windows of the cus-tomer node iρm unit time penalty cost of vehicles violating the timewindows m (1 2 3 4)xijv if the vehicle v is from i to j then xijv 1 oth-erwise xijv 0xov if the vehicle v returns to the distribution centreafter delivering a customer group then xov 1 oth-erwise xov 0yiv the task of the customer node i is completed by thevehicle v then yiv 1 otherwise yiv 0

32 Model and Method e objective function is to mini-mize the comprehensive cost including transportation costvehicle use cost electricity replenishment cost and timewindow penalty cost e formula of the MILP model is asfollows

Fmin C0 1113944visinV

xov + C1 1113944visinV

1113944iisinD

1113944jisinDinej

xijvdij

+ 1113944visinV

1113944iisinC

ECi tfi( 1113857 + 1113944visinV

1113944iisinN

pui tvi( 1113857

(1)

Among them

ECi tfi( 1113857 C2 times tfi tfi le tci

C3 tfi gt tci1113896 (2)

pui tprimevi1113874 1113875

ρ1 eiprime minus tprimevi1113872 1113873 + ρ2 ei minus ei

prime( 1113857 tprimevi le eiprime

ρ2 ei minus tprimevi1113872 1113873

0

ρ3 tprimevi minus li1113872 1113873

ρ3 liprime minus li( 1113857 + ρ4 tprimevi minus liprime1113872 1113873

eiprime lt tprimevi le ei

ei lt tprimevi le li

li lt tprimevi le liprime

li lt tprimevi

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎩

(3)

subject to

1113944iisinDknei

xikv 1113944jisinDknej

xkjv k isin D(4)

1113944visinV

ynv 1 n isin N (5)

1113944nisinN

ynvqn leQ (6)

1113944visinV

1113944iisinDine0

xoiv le |V| (7)

1113944iisinN

1113944jisinDinej

xijv le |N| (8)

t0Prime 0 (9)

tij dij

speed i j isin D (10)

tfi min tciP minus p1

iv

g1113888 11138891113890 1113891 (11)

tvi tprimevi + tfi + twi i isin N (12)

tprimevi ge t

vi i isin N v isin V (13)

tjprime 1113944

iisinD1113944

jisinDinejxijv tiPrime + tij1113872 1113873 (14)

p1iv p

2iv i isin N (15)

p1ov 100 (16)

p1jv p

2iv minus xijv times

dij

h i j isin D ine j v isin V (17)

p1iv ge 0 i isin D v isin V (18)

xijv xov yiv isin 0 1 i j o isin D v isin V (19)

In the model given above Constraint (4) ensures thatthe vehicle starts from the distribution centre returns tothe distribution centre and focuses on distribution centreConstraint (5) ensures that each customer is served onlyonce by one vehicle Constraint (6) is a restraint on vehicleloading Constraint (7) indicates that the number of EVsserving the customer is less than or equal to the totalnumber of vehicles owned by the distribution centreConstraint (8) requires that the number of customersserved by each vehicle is less than or equal to the totalnumber of customers Constraint (9) requires that whenthe electric vehicle starts from the distribution centre thetime is 0 Constraint (10) indicates that the travel time ofelectric vehicles from the point i to the point j is the ratioof the distance between two points and the travel speedConstraint (11) indicates that when the electric vehiclepasses through the charging stations the charge replen-ishment time is the minimum of the battery replacementtime and fast charging time Constraint (12) indicates thatthe time the electric vehicle leaves the customer node i is

4 Advances in Operations Research

the sum of arriving at the customer node waiting time atthe customer node i and servicing time Constraint (13)shows the relationship between the starting service timeand the arrival time of vehicles at the customer pointConstraint (14) indicates that the time the electric vehiclearrives at the node j is the accumulation of the previoustime Constraint (15) means that neither power con-sumption nor power replenishment occurs at the cus-tomer node i Constraint (16) indicates that when theelectric vehicle starts from the distribution centre thestate of charge is 100 Constraint (17) indicates that theremaining power to node j is equal to the remaining powerto leave node i minus the power consumed on the wayConstraint (18) indicates that the state of charge of electricvehicles is nonnegative at any position Constraint (19)indicates that the decision variable is constrained to 0-1

In this paper the ant colony algorithm is used to solvethe approximate optimal solution of the NP hard probleme ant colony algorithm has the characteristics of dis-tributed computing positive information feedback andheuristic search In essence it is a heuristic global opti-mization algorithm in the evolutionary algorithm ealgorithm imitates the social behaviour of ants in order tofind the shortest route from nest to food source In the antcolony algorithm each ant performs four basic activitiesin the process of route construction (1) select the nextcustomer based on the probable function of the distancefrom the current location to the customer and the routestrength on the arc (2) save the taboo list of the customersin the current route (3) update the residual capacity of thevehicle and (4) update the track intensity on the accessarc and use the method of local search to improve thequality of the solution Finally the taboo lists are deletedand a new iteration is started When the ant colony al-gorithm solves the MILP model the specific steps are asfollows

Step 1 importing data and setting basic parameters

Step 2 calculating the distance between customernodes and the cost and time of distance betweencustomer pointsStep 3 initializing and iterating in order to find the bestroute

Step 4 terminating the algorithm and reporting the bestsolution

Figure 2 shows the traversing process of a single ant inthe iterative search for the best route

e meanings of the mathematical symbols involved inFigure 2 are explained as follows

Current the current location of antsAllowed(k)11138641113865 the collection of client nodes that havenot been accessed initially including all client nodesNext[i]11138641113865 the set of optional customer nodes when theelectric vehicle is in i-nodePnext[i]11138641113865 the collection of optional customer nodes forEV charging closest to i-node

4 Calculation Experiment and Cost Analysis

In order to verify the proposed MILP model the calculationexperiments are carried out based on the known benchmarkinstances and the ant colony algorithm is used to solve themodel

41 Test Examples e experimental data are from Solo-monrsquos VRPTW standard problem set and the data numberis R101 [29] which is characterized by uniform distributionof customer points and narrow time windows In this case avehicle is generally only responsible for the distribution ofseveral customer points and the vehicle route cost is greatlyaffected by the time windows so the data selection of the caseis reasonable In order to draw a clear road map this paperonly selects the first 26 data including 1 distribution centreand 25 customer nodes1 is the distribution centre 2ndash26 isthe customer node 27ndash31 is the charging stations node especific parameters of the example are shown in Table 1 andthe node information is shown in Table 2

In this paper according to the actual situation we madeassumptions about the required data in Table 1 and for thispart of the program design we reserved a data change areawhich is malleable

e MILP model is solved by MATLAB programmingIn order to reduce the influence of random factors as muchas possible this paper repeatedly tests the example 10 timesto get the total cost optimal solution (C) the number ofvehicles (N) route length (L) and penalty cost (P) when theoptimal solution is reached

As can be seen from Table 3 the optimal solution of thisexample is 728308 including the route length when theoptimal solution is reached at 27061 and Table 4 shows thatthe optimal allocation scheme includes 4 routes the routemap is shown in Figure 3

42 Cost Analysis Based on the calculation experiment ofthe Solomon benchmark example the sensitivity analysis ofthe cost affecting the electric vehicle route planning is carriedout

421 Use Cost and Transportation Cost First adjust the usecost from 1000 for each vehicle to 5000 for each vehicle keepthe other parameters unchanged repeat the test for 10 timesand see Table 5 for the results when the optimal solution isreached

It can be seen from Table 5 that after adjusting the usecost of vehicles from 1000 to 5000 after 10 times of oper-ation compared with Table 3 the number of vehicles isreduced from 4 to 2 which is 50 It can be seen that thehigher the use cost of vehicles is the smaller the number ofvehicles used isWhen the use cost of vehicles is much higherthan other costs the vehicle route distribution scheme withthe minimum number of vehicles will be preferred At thesame time the route length is only increased by 3 com-pared with the result in Table 3 while the time windowpenalty is increased by 52 is is understandable because

Advances in Operations Research 5

the proportion of vehicle use cost in the objective functionincreases so the algorithm will tend to find the solution withthe minimum vehicle use

Keep the cost of using vehicles at 5000 per vehicle andadjust the unit transportation cost from 2 to 10 while thepenalty factor of time windows remains unchanged Run theprogram 10 times and see Table 6 for relevant results whenthe optimal solution is reached

It can be seen from Table 6 that after adjusting vehicleuse cost and unit transportation cost at the same time thenumber of vehicles obtained is significantly reduced com-pared with Table 3 It can be seen that when vehicletransportation cost and use cost are much higher than othercosts the route distribution scheme with the least number ofvehicles will be preferred e route length in Table 6 issimilar to that in Table 3 but the penalty cost of timewindows is increased by 53 By increasing the factors ofvehicle use cost and unit freight in the objective function theproportion of time window penalty cost is greatly reducederefore the length of the route and the number of vehiclesare given priority in the result so the time window penalty isgreatly increased is shows the effectiveness of the algo-rithm again in this paper

Ants at current

Whether allowed (k) is

empty

Building Next [Current]

Whether Next [Current]

is empty

Index [] are allgreater than 0

Go to the nearest charging station of current for charging

build Pnext [Current]

Whether Pnext [Current] is

empty

Select j-node according to probability

Current = j

Direct return to distribution center

Current = 0

Return to the distribution center (or return to the distribution center after

charging)Current = 0

Select j-node according to probability

Current = j

Return to the distribution center and

output the total cost

Yes

No

No

Yes

No

No

Yes

Yes

Figure 2 Single ant traversal process to find the best route during iterative search

Table 1 Temperature and wildlife count in the three areas coveredby the test examples

Name ParameterMaximum loading capacity of vehicles 80 piecesUse cost of vehicles 1000 RMBvehicleUnit transportation cost 2 RMBkmSpeed of vehicles 40 kmhFull charge at the charging stations 60 kWhPower consumption per unit distance 1 kWhCost per battery replacement 30 RMBBattery replacement time once 31minService time per customer 10minPenalty coefficient of time windows (1 05 15 2)e customer tolerance level 05Maximum number of iterations 200

6 Advances in Operations Research

422 Time Window Penalty Cost Adjust the penalty co-efficient of the time windows from ρ1 1 ρ2 05 ρ3

15 and ρ4 2 to ρ1 5 ρ2 25 ρ3 75 and ρ4 10keep other parameters unchanged repeat the test 10 timesand see Table 7 for the results when the optimal solution isreached

After the penalty cost coefficient increases 5 times thecalculation results are shown in Table 7 e route length isreduced by 03 compared with the result in Table 3 but thenumber of optimal vehicles has increased from 4 to 7

Table 2 Node information

Number X-coordinate

Y-coordinate Demand Ready

timeDuedate

1 35 35 0 0 2302 41 49 10 161 1713 35 17 7 50 604 55 45 13 116 1265 55 20 19 149 1596 15 30 26 34 447 25 30 3 99 1098 20 50 5 81 919 10 43 9 95 10510 55 60 16 97 10711 30 60 16 124 13412 20 65 12 67 7713 50 35 19 63 7314 30 25 23 159 16915 15 10 20 32 4216 30 5 8 16 7117 10 20 19 75 8518 5 30 2 157 16719 20 40 12 87 9720 15 60 17 76 8621 45 65 9 126 13622 45 20 11 62 7223 45 10 18 97 10724 55 5 29 68 7825 65 35 3 153 16326 65 20 6 172 18227 10 32 0 0 23028 27 47 0 0 23029 40 30 0 0 23030 50 50 0 0 23031 60 10 0 0 230

Table 3 Related results of the test examples

Operation times C N L P

1 740418 4 27208 2372112 761371 4 27804 2544153 776436 3 26293 3814294 758694 4 28075 2669485 728308 4 27061 2238966 756774 3 25858 3629467 759047 3 26997 3617058 749176 4 26934 2314079 760367 3 27103 37248810 746696 3 26306 357825Average 753729 35 26964 305027

Table 4 Sequence of routes when the test examples reaches theoptimal solution

Vehicle Route number1 1ndash14ndash22ndash23ndash24ndash27ndash9ndash12 1ndash7ndash6ndash18ndash17ndash15ndash16ndash28ndash19ndash20ndash13 1ndash3ndash5ndash26ndash25ndash4ndash13ndash28ndash8ndash14 1ndash2ndash21ndash10ndash11ndash12ndash1

0 10 20 30 40 50 60 700

10

20

30

40

50

60

70

1

2

3

4

5

6 7

8

9

1011

12

13

14

1516

17

18

19

2021

22

2324

25

26

27

28

29

30

31

Figure 3 Corresponding route trajectory when the examplereaches the optimal solution

Table 5 Impact of adjusting use cost on results

Operation times N L P

1 2 28125 6036132 2 27501 6646813 2 26850 6809434 2 28149 6021615 2 28076 6722076 2 26862 6450827 2 27284 6257538 2 27415 5855419 2 28566 63446310 2 28063 602555Average 2 27689 631700

Table 6 Impact of adjusting use cost and unit transportation coston results

Operation times N L P

1 2 28125 6524182 2 27501 6646813 2 27241 6992544 2 28149 6021615 2 28123 6679206 2 26862 6593437 2 27284 6257538 2 27415 6323099 2 28538 63446310 2 28063 602555Average 2 27730 644086

Advances in Operations Research 7

indicated an increase of 75 and we can see that thenumber of vehicles has increased significantly is isunderstandable for the change of the penalty cost coeffi-cient increases the penalty cost in the objective function sothe algorithm will tend to find more solutions for vehiclesto serve customers e increase in the number of vehicleswill inevitably lead to a decrease in the average drivingroute length which proves the effectiveness of the algo-rithm again erefore the higher the cost of fines is themore vehicles are required is has led logistics companiesto prepare more vehicles under strict time window con-ditions making the customerrsquos total demand unchanged oreven increased

423 Electricity Replenishment Cost e battery capacity is60 kWh the charging time needs 60min and the powerchange time is 31min e shortest power supply mode isselected erefore when the supplementary power is notmore than half quick charging is preferred Otherwisechoose the battery replacement strategy e charging costper unit time is 1 RMBmin and the cost of single batteryreplacement is 30 RMB Now the cost of power supply isincreasing e charging cost per unit time is 50 RMBminand the cost of single battery replacement is 1500 RMB eresults are shown in Table 8 and the vehicle route when theoptimal solution is reached is shown in Figure 4

It can be seen from Table 8 that after the unit charge costis adjusted from 1 to 50 and the single battery change cost isadjusted from 30 to 1500 after ten runs compared withTable 3 the number of vehicles increased from 4 to 5 ve-hicles indicated an increase of 25 At the same time it canbe seen that the number of charging stations passed inFigure 3 is 3 however the number of charging stationspassed in Figure 4 is 2 Increased costs have drived com-panies to choose more vehicles to avoid charging In ad-dition compared with Table 3 the route length is reduced by06 together with the penalty cost is reduced by 103And the increase in the number of vehicles serving cus-tomers leads to a reduction in the possibility of reducingtime penalties and costs is proves the effectiveness of thealgorithm erefore when the charging facilities are notperfect together with the power replenishment cost is highthe logistics companies tend to use more vehicles to avoidcharging as much as possible

5 Conclusions

At present most of the literature studies use a chargingstrategy and the customer tolerance is not considered whilestudying the customer time windows In this paper thecharging strategy of combining two charging ways isadopted the broken line soft time windows is used con-sidering the customer tolerance and the MILP model of theEVRPTW is finally established And through the calculationexperiment of the Solomon benchmark example the cost ofaffecting the route optimization of electric vehicle is ana-lysed the availability as well as effectiveness of data andalgorithm are proved and the management opinions on thepractical application of MILP model are put forward

(1) e higher the use cost and freight of vehicles are theless the number of vehicles used When the use costand freight of vehicles are much higher than othercosts the vehicle route distribution scheme with theleast number of vehicles is preferred

(2) e higher the penalty cost of time windows is thehigher the number of vehicles used for vehicle dis-tribution is In the case of strict time windows lo-gistics companies need to prepare more vehicles thanthe total demand of customers

Table 7 Impact of adjusting time window penalty costs on results

Operation times N L1 8 279772 7 234703 7 291224 7 245155 6 284256 6 271807 8 265798 6 259409 7 2897610 7 26766Average 69 26895

Table 8 Impact of adjusted electricity supplement costs on results

Operation times N L P

1 4 28415 3492102 5 27377 2099193 5 27284 2372204 5 26824 2601645 5 24432 2244606 5 25166 2644777 4 27103 3498758 5 26605 2281859 4 28159 35634810 5 26555 255216Average 47 26792 273507

0 10 20 30 40 50 60 700

10

20

30

40

50

60

70

1

2

3

4

5

6 7

8

9

101112

13

14

1516

17

18

19

2021

22

2324

25

26

27

28

29

30

31

Figure 4 Vehicle route at high electricity replenishment cost

8 Advances in Operations Research

(3) Logistics companies tend to use more EVs to avoidcharging as much as possible when charging facilitiesare not perfect and the cost of power supply is high

e model can help the logistics enterprises providesome suggestions for the route optimization help to pro-mote the application of EVs in the field of logistics andimprove energy efficiency energy conservation and emis-sion reduction e proposed MILP model is helpful toreduce the logistics cost However the traditional short-comings of VRP still exist in the EVRPTW model Forexample it is still a NP-hard and it is difficult to solve large-scale problems e focus of future research may be todeveloping more effective heuristic algorithm to solve large-scale problems consider the real-time changes of trafficconditions and expand the direction of the dynamic vehicleroute

Data Availability

e data used to support the findings of this study are in-cluded within the article

Conflicts of Interest

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

Acknowledgments

is research was funded by the National Natural ScienceFoundation of China grant no 71471061 and the Funda-mental Research Funds for the Central Universities grantno 2017MS171

References

[1] G B Dantzig and J H Ramser ldquoe truck dispatchingproblemrdquoManagement Science vol 6 no 1 pp 80ndash91 1959

[2] Y Xiao Q Zhao I Kaku and Y Xu ldquoDevelopment of a fuelconsumption optimization model for the capacitated vehiclerouting problemrdquo Computers amp Operations Research vol 39no 7 pp 1419ndash1431 2012

[3] J Zhang Y ZhaoW Xue and J Li ldquoVehicle routing problemwith fuel consumption and carbon emissionrdquo InternationalJournal of Production Economics vol 170 pp 234ndash242 2015

[4] N Norouzi M Sadegh-Amalnick and R Tavakkoli-Mog-haddam ldquoModified particle swarm optimization in a time-dependent vehicle routing problem minimizing fuel con-sumptionrdquo Optimization Letters vol 11 no 1 pp 121ndash1342017

[5] G Poonthalir and R Nadarajan ldquoA fuel efficient green vehiclerouting problem with varying speed constraint (F-GVRP)rdquoExpert Systems with Applications vol 100 pp 131ndash144 2018

[6] J Wang S Yao J Sheng and H Yang ldquoMinimizing totalcarbon emissions in an integrated machine scheduling andvehicle routing problemrdquo Journal of Cleaner Productionvol 229 pp 1004ndash1017 2019

[7] S-C Ma Y Fan J-F Guo J-H Xu and J Zhu ldquoAnalysingonline behaviour to determine Chinese consumersrsquo prefer-ences for electric vehiclesrdquo Journal of Cleaner Productionvol 229 pp 244ndash255 2019

[8] B G Pollet I Staffell and J L Shang ldquoCurrent status ofhybrid battery and fuel cell electric vehicles from electro-chemistry to market prospectsrdquo Electrochimica Acta vol 84pp 235ndash249 2012

[9] G Desaulniers F Errico S Irnich and M Schneider ldquoExactalgorithms for electric vehicle-routing problems with win-dowsrdquo Operations Research vol 64 no 6 pp 1177ndash15652016

[10] R A Fernandez ldquoAmore realistic approach to electric vehiclecontribution to greenhouse gas emissions in the cityrdquo Journalof Cleaner Production vol 172 pp 949ndash959 2018

[11] L C Casals E Martinez-Laserna B A Garcia and N NietoldquoSustainability analysis of the electric vehicle use in Europe forCO2 emissions reductionrdquo Journal of Cleaner Productionvol 127 pp 425ndash437 2016

[12] Z Wu M Wang J Zheng X Sun M Zhao and X WangldquoLife cycle greenhouse gas emission reduction potential ofbattery electric vehiclerdquo Journal of Cleaner Productionvol 190 pp 462ndash470 2018

[13] Y Xiao X Zuo I Kaku S Zhou and X Pan ldquoDevelopmentof energy consumption optimization model for the electricvehicle routing problem with time windowsrdquo Journal ofCleaner Production vol 225 pp 647ndash663 2019

[14] S-N YangW-S Cheng Y-C Hsu C-H Gan and Y-B LinldquoCharge scheduling of electric vehicles in highwaysrdquo Math-ematical and Computer Modelling vol 57 no 11-12pp 2873ndash2882 2013

[15] A Dogan andM Alci ldquoHeuristic optimization of EV chargingschedule considering battery degradation costrdquo Elektronika irElektrotechnika vol 24 no 6 pp 15ndash20 2018

[16] A Dogan S Bahceci F Daldaban and M Alci ldquoOptimi-zation of chargedischarge coordination to satisfy networkrequirements using heuristic algorithms in vehicle-to-gridconceptrdquo Advances in Electrical and Computer Engineeringvol 18 no 1 pp 121ndash130 2018

[17] V Aravinthan and W Jewell ldquoControlled electric vehiclecharging for mitigating impacts on distribution assetsrdquo IEEETransactions on Smart Grid vol 6 no 2 pp 999ndash1009 2015

[18] M Schucking P Jochem W Fichtner O Wollersheim andK Stella ldquoCharging strategies for economic operations ofelectric vehicles in commercial applicationsrdquo TransportationResearch Part D Transport and Environment vol 51pp 173ndash189 2017

[19] J D Adler and P B Mirchandani ldquoOnline routing andbattery reservations for electric vehicles with swappablebatteriesrdquo Transportation Research Part B Methodologicalvol 70 pp 285ndash302 2014

[20] J Yang and H Sun ldquoBattery swap station location-routingproblem with capacitated electric vehiclesrdquo Computers ampOperations Research vol 55 pp 217ndash232 2015

[21] Q Dai T Cai S Duan and F Zhao ldquoStochastic modeling andforecasting of load demand for electric bus battery-swapstationrdquo IEEE Transactions on Power Delivery vol 29 no 4pp 1909ndash1917 2014

[22] D Margaritis A Anagnostopoulou A Tromaras andM Boile ldquoElectric commercial vehicles practical perspectivesand future research directionsrdquo Research in TransportationBusiness amp Management vol 18 pp 4ndash10 2016

[23] MM Solomon and J Desrosiers ldquoSurvey paper-time windowconstrained routing and scheduling problemsrdquo Trans-portation Science vol 22 no 1 pp 1ndash13 1988

[24] A G Qureshi E Taniguchi and T Yamada ldquoAn exact so-lution approach for vehicle routing and scheduling problemswith soft time windowsrdquo Transportation Research Part E

Advances in Operations Research 9

Logistics and Transportation Review vol 45 no 6 pp 960ndash977 2009

[25] D Goeke ldquoGranular tabu search for the pickup and deliveryproblem with time windows and electric vehiclesrdquo EuropeanJournal of Operational Research vol 278 no 3 pp 821ndash8362019

[26] M Keskin and B Ccedilatay ldquoPartial recharge strategies for theelectric vehicle routing problem with time windowsrdquoTransportation Research Part C Emerging Technologiesvol 65 pp 111ndash127 2016

[27] M Schneider A Stenger and D Goeke ldquoe electric vehicle-routing problem with time windows and recharging stationsrdquoTransportation Science vol 48 no 4 pp 500ndash520 2014

[28] G Hiermann J Puchinger S Ropke and R F Hartl ldquoeelectric fleet size and mix vehicle routing problem with timewindows and recharging stationsrdquo European Journal of Op-erational Research vol 252 no 3 pp 995ndash1018 2016

[29] Solomon benchmark problems httpwcbaneuedusimmsolomonr101htm

10 Advances in Operations Research

Each customerrsquos demand service duration good servicetime windows and customer tolerance level are needed to beknown Finally reasonable planning of the vehicle distri-bution route is necessary so that the total cost of distributionis small

e soft time windows can relax the constraints of timewindows optimize resource allocation and reduce energyconsumption and road congestion so the time windowsstudied in this paper mainly are soft time windows Asshown in Figure 1 in the traditional soft time windowswhether the vehicle arrives before or after l the customer isallowed to serve but they are required to pay the corre-sponding penalty fee which is generally a simple linearrelationship with the degree of time deviation However forthe deviation of the best service time windows customershave the difference between tolerance and intoleranceerefore based on the traditional soft time windowsconsidering the tolerance range of customers this paperproposes a broken line time window

According to the customer tolerance level (z) and serviceduration (tf) the tolerance time window can be obtained onthe basis of the optimal time window [eprime lprime] whereeprime e minus z times tf lprime l + z times tf If the vehicle provides ser-vices in the best time window [e l] there will be no penaltycost to be paid If the vehicle provides services in the interval[eprime e][eprime e] or [l lprime] there will be only less penalty cost to bepaid If the vehicle starts service earlier than eprime or later thanlprime there will be more penalty cost to be paid Compared withthe traditional soft time windows the broken line soft timewindows take the actual feelings of customers into con-sideration which will be conducive to better coordinationbetween enterprises and customers reasonable allocationand optimization of resources

In view of the above considerations the problems andbasic assumptions to be solved are as follows (1) each vehiclecan meet the needs of multiple customer points and eachcustomer point can only be served by one vehicle after thecompletion of the distribution service the vehicle must driveback to the distribution centre (2) all vehicles are the sametype and the total transportation volume shall not exceed thecapacity limit of EVs (3) each customerrsquos location coordi-nates demand quantity and service duration are known andthere are optimal service time windows and tolerance timewindows (4) the time window penalty coefficient of eachcustomer node is the same (5) EVs can only be charged ortheir battery can be replaced in the distribution centre orpower station (6) each customer must be visited and can onlybe visited once (7) the road is smooth without consideringtraffic congestion and other special situations (8) it is as-sumed that the transportation cost generated by the vehicle islinearly related to the route length and the use cost of eachvehicle is fixed and (9) the objective function of this problemis to minimize the total distribution cost

3 Materials and Method

In this part according to the electric vehicle routing problemwith time windows (EVRPTW) we establish a MILP modeland determine the constraints

31 Defining Variables e parameters and decision vari-ables used to describe the MILP model are shown in thefollowing

N set of all nodes n in networksV set of all nodes v in networksC set of all nodes c in networksD network D NcupCcup o consisting of sets of nodesD 0 1 2 |N| + |C| n set of customer nodes where n isin Nv set of EV nodes where v isin Vc set of charging station nodes where c isin Co set of distribution centre nodesC0 fixed cost per vehicleC1 electric vehicle unit distance transportation costEC total electricity supplementary costC2 charging cost per unit timeC3 single battery replacement costi j index of nodes i 0 1 2 ndij distance from the node i to the node j i j isin Dqn demand of the customer node n and n isin NQ rated load capacity of electric vehiclesP battery capacity of electric vehiclesg charge coefficientP1

dv the residual power of EVs when v reaches the nodeDP2

dv residual electricity of the electric vehicle V leavingnode Dp battery capacity of electric vehiclesh power consumption coefficientg charge coefficienttfi if i represents the customer point tfi representsthe service time of electric vehicle at the node i if irepresents the charging stations then tfi represents theelectric vehiclersquos power replenishment time i isin NcupM

tci single battery change time and i isin Ctwi waiting time of electric vehicles at the customernode i

0 e l

Cost

Time0 eprime l

Cost

Timee lprime

Figure 1 Penalty cost function under traditional soft time win-dows and polygonal line soft time windows

Advances in Operations Research 3

tvi the time point when the vehicle v arrives at thecustomer node i where tv

0 0tprimevi the start time of the v-car service customer node itij time of electric vehicles from i to jspeed driving speed of electric vehiclesei the lower limit of the best service time windows ofthe customer node ili the upper limit of the best service window of thecustomer node ieiprime the lower limit of tolerance time windows of thecustomer node iliprime upper limits of tolerance time windows of the cus-tomer node iρm unit time penalty cost of vehicles violating the timewindows m (1 2 3 4)xijv if the vehicle v is from i to j then xijv 1 oth-erwise xijv 0xov if the vehicle v returns to the distribution centreafter delivering a customer group then xov 1 oth-erwise xov 0yiv the task of the customer node i is completed by thevehicle v then yiv 1 otherwise yiv 0

32 Model and Method e objective function is to mini-mize the comprehensive cost including transportation costvehicle use cost electricity replenishment cost and timewindow penalty cost e formula of the MILP model is asfollows

Fmin C0 1113944visinV

xov + C1 1113944visinV

1113944iisinD

1113944jisinDinej

xijvdij

+ 1113944visinV

1113944iisinC

ECi tfi( 1113857 + 1113944visinV

1113944iisinN

pui tvi( 1113857

(1)

Among them

ECi tfi( 1113857 C2 times tfi tfi le tci

C3 tfi gt tci1113896 (2)

pui tprimevi1113874 1113875

ρ1 eiprime minus tprimevi1113872 1113873 + ρ2 ei minus ei

prime( 1113857 tprimevi le eiprime

ρ2 ei minus tprimevi1113872 1113873

0

ρ3 tprimevi minus li1113872 1113873

ρ3 liprime minus li( 1113857 + ρ4 tprimevi minus liprime1113872 1113873

eiprime lt tprimevi le ei

ei lt tprimevi le li

li lt tprimevi le liprime

li lt tprimevi

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎩

(3)

subject to

1113944iisinDknei

xikv 1113944jisinDknej

xkjv k isin D(4)

1113944visinV

ynv 1 n isin N (5)

1113944nisinN

ynvqn leQ (6)

1113944visinV

1113944iisinDine0

xoiv le |V| (7)

1113944iisinN

1113944jisinDinej

xijv le |N| (8)

t0Prime 0 (9)

tij dij

speed i j isin D (10)

tfi min tciP minus p1

iv

g1113888 11138891113890 1113891 (11)

tvi tprimevi + tfi + twi i isin N (12)

tprimevi ge t

vi i isin N v isin V (13)

tjprime 1113944

iisinD1113944

jisinDinejxijv tiPrime + tij1113872 1113873 (14)

p1iv p

2iv i isin N (15)

p1ov 100 (16)

p1jv p

2iv minus xijv times

dij

h i j isin D ine j v isin V (17)

p1iv ge 0 i isin D v isin V (18)

xijv xov yiv isin 0 1 i j o isin D v isin V (19)

In the model given above Constraint (4) ensures thatthe vehicle starts from the distribution centre returns tothe distribution centre and focuses on distribution centreConstraint (5) ensures that each customer is served onlyonce by one vehicle Constraint (6) is a restraint on vehicleloading Constraint (7) indicates that the number of EVsserving the customer is less than or equal to the totalnumber of vehicles owned by the distribution centreConstraint (8) requires that the number of customersserved by each vehicle is less than or equal to the totalnumber of customers Constraint (9) requires that whenthe electric vehicle starts from the distribution centre thetime is 0 Constraint (10) indicates that the travel time ofelectric vehicles from the point i to the point j is the ratioof the distance between two points and the travel speedConstraint (11) indicates that when the electric vehiclepasses through the charging stations the charge replen-ishment time is the minimum of the battery replacementtime and fast charging time Constraint (12) indicates thatthe time the electric vehicle leaves the customer node i is

4 Advances in Operations Research

the sum of arriving at the customer node waiting time atthe customer node i and servicing time Constraint (13)shows the relationship between the starting service timeand the arrival time of vehicles at the customer pointConstraint (14) indicates that the time the electric vehiclearrives at the node j is the accumulation of the previoustime Constraint (15) means that neither power con-sumption nor power replenishment occurs at the cus-tomer node i Constraint (16) indicates that when theelectric vehicle starts from the distribution centre thestate of charge is 100 Constraint (17) indicates that theremaining power to node j is equal to the remaining powerto leave node i minus the power consumed on the wayConstraint (18) indicates that the state of charge of electricvehicles is nonnegative at any position Constraint (19)indicates that the decision variable is constrained to 0-1

In this paper the ant colony algorithm is used to solvethe approximate optimal solution of the NP hard probleme ant colony algorithm has the characteristics of dis-tributed computing positive information feedback andheuristic search In essence it is a heuristic global opti-mization algorithm in the evolutionary algorithm ealgorithm imitates the social behaviour of ants in order tofind the shortest route from nest to food source In the antcolony algorithm each ant performs four basic activitiesin the process of route construction (1) select the nextcustomer based on the probable function of the distancefrom the current location to the customer and the routestrength on the arc (2) save the taboo list of the customersin the current route (3) update the residual capacity of thevehicle and (4) update the track intensity on the accessarc and use the method of local search to improve thequality of the solution Finally the taboo lists are deletedand a new iteration is started When the ant colony al-gorithm solves the MILP model the specific steps are asfollows

Step 1 importing data and setting basic parameters

Step 2 calculating the distance between customernodes and the cost and time of distance betweencustomer pointsStep 3 initializing and iterating in order to find the bestroute

Step 4 terminating the algorithm and reporting the bestsolution

Figure 2 shows the traversing process of a single ant inthe iterative search for the best route

e meanings of the mathematical symbols involved inFigure 2 are explained as follows

Current the current location of antsAllowed(k)11138641113865 the collection of client nodes that havenot been accessed initially including all client nodesNext[i]11138641113865 the set of optional customer nodes when theelectric vehicle is in i-nodePnext[i]11138641113865 the collection of optional customer nodes forEV charging closest to i-node

4 Calculation Experiment and Cost Analysis

In order to verify the proposed MILP model the calculationexperiments are carried out based on the known benchmarkinstances and the ant colony algorithm is used to solve themodel

41 Test Examples e experimental data are from Solo-monrsquos VRPTW standard problem set and the data numberis R101 [29] which is characterized by uniform distributionof customer points and narrow time windows In this case avehicle is generally only responsible for the distribution ofseveral customer points and the vehicle route cost is greatlyaffected by the time windows so the data selection of the caseis reasonable In order to draw a clear road map this paperonly selects the first 26 data including 1 distribution centreand 25 customer nodes1 is the distribution centre 2ndash26 isthe customer node 27ndash31 is the charging stations node especific parameters of the example are shown in Table 1 andthe node information is shown in Table 2

In this paper according to the actual situation we madeassumptions about the required data in Table 1 and for thispart of the program design we reserved a data change areawhich is malleable

e MILP model is solved by MATLAB programmingIn order to reduce the influence of random factors as muchas possible this paper repeatedly tests the example 10 timesto get the total cost optimal solution (C) the number ofvehicles (N) route length (L) and penalty cost (P) when theoptimal solution is reached

As can be seen from Table 3 the optimal solution of thisexample is 728308 including the route length when theoptimal solution is reached at 27061 and Table 4 shows thatthe optimal allocation scheme includes 4 routes the routemap is shown in Figure 3

42 Cost Analysis Based on the calculation experiment ofthe Solomon benchmark example the sensitivity analysis ofthe cost affecting the electric vehicle route planning is carriedout

421 Use Cost and Transportation Cost First adjust the usecost from 1000 for each vehicle to 5000 for each vehicle keepthe other parameters unchanged repeat the test for 10 timesand see Table 5 for the results when the optimal solution isreached

It can be seen from Table 5 that after adjusting the usecost of vehicles from 1000 to 5000 after 10 times of oper-ation compared with Table 3 the number of vehicles isreduced from 4 to 2 which is 50 It can be seen that thehigher the use cost of vehicles is the smaller the number ofvehicles used isWhen the use cost of vehicles is much higherthan other costs the vehicle route distribution scheme withthe minimum number of vehicles will be preferred At thesame time the route length is only increased by 3 com-pared with the result in Table 3 while the time windowpenalty is increased by 52 is is understandable because

Advances in Operations Research 5

the proportion of vehicle use cost in the objective functionincreases so the algorithm will tend to find the solution withthe minimum vehicle use

Keep the cost of using vehicles at 5000 per vehicle andadjust the unit transportation cost from 2 to 10 while thepenalty factor of time windows remains unchanged Run theprogram 10 times and see Table 6 for relevant results whenthe optimal solution is reached

It can be seen from Table 6 that after adjusting vehicleuse cost and unit transportation cost at the same time thenumber of vehicles obtained is significantly reduced com-pared with Table 3 It can be seen that when vehicletransportation cost and use cost are much higher than othercosts the route distribution scheme with the least number ofvehicles will be preferred e route length in Table 6 issimilar to that in Table 3 but the penalty cost of timewindows is increased by 53 By increasing the factors ofvehicle use cost and unit freight in the objective function theproportion of time window penalty cost is greatly reducederefore the length of the route and the number of vehiclesare given priority in the result so the time window penalty isgreatly increased is shows the effectiveness of the algo-rithm again in this paper

Ants at current

Whether allowed (k) is

empty

Building Next [Current]

Whether Next [Current]

is empty

Index [] are allgreater than 0

Go to the nearest charging station of current for charging

build Pnext [Current]

Whether Pnext [Current] is

empty

Select j-node according to probability

Current = j

Direct return to distribution center

Current = 0

Return to the distribution center (or return to the distribution center after

charging)Current = 0

Select j-node according to probability

Current = j

Return to the distribution center and

output the total cost

Yes

No

No

Yes

No

No

Yes

Yes

Figure 2 Single ant traversal process to find the best route during iterative search

Table 1 Temperature and wildlife count in the three areas coveredby the test examples

Name ParameterMaximum loading capacity of vehicles 80 piecesUse cost of vehicles 1000 RMBvehicleUnit transportation cost 2 RMBkmSpeed of vehicles 40 kmhFull charge at the charging stations 60 kWhPower consumption per unit distance 1 kWhCost per battery replacement 30 RMBBattery replacement time once 31minService time per customer 10minPenalty coefficient of time windows (1 05 15 2)e customer tolerance level 05Maximum number of iterations 200

6 Advances in Operations Research

422 Time Window Penalty Cost Adjust the penalty co-efficient of the time windows from ρ1 1 ρ2 05 ρ3

15 and ρ4 2 to ρ1 5 ρ2 25 ρ3 75 and ρ4 10keep other parameters unchanged repeat the test 10 timesand see Table 7 for the results when the optimal solution isreached

After the penalty cost coefficient increases 5 times thecalculation results are shown in Table 7 e route length isreduced by 03 compared with the result in Table 3 but thenumber of optimal vehicles has increased from 4 to 7

Table 2 Node information

Number X-coordinate

Y-coordinate Demand Ready

timeDuedate

1 35 35 0 0 2302 41 49 10 161 1713 35 17 7 50 604 55 45 13 116 1265 55 20 19 149 1596 15 30 26 34 447 25 30 3 99 1098 20 50 5 81 919 10 43 9 95 10510 55 60 16 97 10711 30 60 16 124 13412 20 65 12 67 7713 50 35 19 63 7314 30 25 23 159 16915 15 10 20 32 4216 30 5 8 16 7117 10 20 19 75 8518 5 30 2 157 16719 20 40 12 87 9720 15 60 17 76 8621 45 65 9 126 13622 45 20 11 62 7223 45 10 18 97 10724 55 5 29 68 7825 65 35 3 153 16326 65 20 6 172 18227 10 32 0 0 23028 27 47 0 0 23029 40 30 0 0 23030 50 50 0 0 23031 60 10 0 0 230

Table 3 Related results of the test examples

Operation times C N L P

1 740418 4 27208 2372112 761371 4 27804 2544153 776436 3 26293 3814294 758694 4 28075 2669485 728308 4 27061 2238966 756774 3 25858 3629467 759047 3 26997 3617058 749176 4 26934 2314079 760367 3 27103 37248810 746696 3 26306 357825Average 753729 35 26964 305027

Table 4 Sequence of routes when the test examples reaches theoptimal solution

Vehicle Route number1 1ndash14ndash22ndash23ndash24ndash27ndash9ndash12 1ndash7ndash6ndash18ndash17ndash15ndash16ndash28ndash19ndash20ndash13 1ndash3ndash5ndash26ndash25ndash4ndash13ndash28ndash8ndash14 1ndash2ndash21ndash10ndash11ndash12ndash1

0 10 20 30 40 50 60 700

10

20

30

40

50

60

70

1

2

3

4

5

6 7

8

9

1011

12

13

14

1516

17

18

19

2021

22

2324

25

26

27

28

29

30

31

Figure 3 Corresponding route trajectory when the examplereaches the optimal solution

Table 5 Impact of adjusting use cost on results

Operation times N L P

1 2 28125 6036132 2 27501 6646813 2 26850 6809434 2 28149 6021615 2 28076 6722076 2 26862 6450827 2 27284 6257538 2 27415 5855419 2 28566 63446310 2 28063 602555Average 2 27689 631700

Table 6 Impact of adjusting use cost and unit transportation coston results

Operation times N L P

1 2 28125 6524182 2 27501 6646813 2 27241 6992544 2 28149 6021615 2 28123 6679206 2 26862 6593437 2 27284 6257538 2 27415 6323099 2 28538 63446310 2 28063 602555Average 2 27730 644086

Advances in Operations Research 7

indicated an increase of 75 and we can see that thenumber of vehicles has increased significantly is isunderstandable for the change of the penalty cost coeffi-cient increases the penalty cost in the objective function sothe algorithm will tend to find more solutions for vehiclesto serve customers e increase in the number of vehicleswill inevitably lead to a decrease in the average drivingroute length which proves the effectiveness of the algo-rithm again erefore the higher the cost of fines is themore vehicles are required is has led logistics companiesto prepare more vehicles under strict time window con-ditions making the customerrsquos total demand unchanged oreven increased

423 Electricity Replenishment Cost e battery capacity is60 kWh the charging time needs 60min and the powerchange time is 31min e shortest power supply mode isselected erefore when the supplementary power is notmore than half quick charging is preferred Otherwisechoose the battery replacement strategy e charging costper unit time is 1 RMBmin and the cost of single batteryreplacement is 30 RMB Now the cost of power supply isincreasing e charging cost per unit time is 50 RMBminand the cost of single battery replacement is 1500 RMB eresults are shown in Table 8 and the vehicle route when theoptimal solution is reached is shown in Figure 4

It can be seen from Table 8 that after the unit charge costis adjusted from 1 to 50 and the single battery change cost isadjusted from 30 to 1500 after ten runs compared withTable 3 the number of vehicles increased from 4 to 5 ve-hicles indicated an increase of 25 At the same time it canbe seen that the number of charging stations passed inFigure 3 is 3 however the number of charging stationspassed in Figure 4 is 2 Increased costs have drived com-panies to choose more vehicles to avoid charging In ad-dition compared with Table 3 the route length is reduced by06 together with the penalty cost is reduced by 103And the increase in the number of vehicles serving cus-tomers leads to a reduction in the possibility of reducingtime penalties and costs is proves the effectiveness of thealgorithm erefore when the charging facilities are notperfect together with the power replenishment cost is highthe logistics companies tend to use more vehicles to avoidcharging as much as possible

5 Conclusions

At present most of the literature studies use a chargingstrategy and the customer tolerance is not considered whilestudying the customer time windows In this paper thecharging strategy of combining two charging ways isadopted the broken line soft time windows is used con-sidering the customer tolerance and the MILP model of theEVRPTW is finally established And through the calculationexperiment of the Solomon benchmark example the cost ofaffecting the route optimization of electric vehicle is ana-lysed the availability as well as effectiveness of data andalgorithm are proved and the management opinions on thepractical application of MILP model are put forward

(1) e higher the use cost and freight of vehicles are theless the number of vehicles used When the use costand freight of vehicles are much higher than othercosts the vehicle route distribution scheme with theleast number of vehicles is preferred

(2) e higher the penalty cost of time windows is thehigher the number of vehicles used for vehicle dis-tribution is In the case of strict time windows lo-gistics companies need to prepare more vehicles thanthe total demand of customers

Table 7 Impact of adjusting time window penalty costs on results

Operation times N L1 8 279772 7 234703 7 291224 7 245155 6 284256 6 271807 8 265798 6 259409 7 2897610 7 26766Average 69 26895

Table 8 Impact of adjusted electricity supplement costs on results

Operation times N L P

1 4 28415 3492102 5 27377 2099193 5 27284 2372204 5 26824 2601645 5 24432 2244606 5 25166 2644777 4 27103 3498758 5 26605 2281859 4 28159 35634810 5 26555 255216Average 47 26792 273507

0 10 20 30 40 50 60 700

10

20

30

40

50

60

70

1

2

3

4

5

6 7

8

9

101112

13

14

1516

17

18

19

2021

22

2324

25

26

27

28

29

30

31

Figure 4 Vehicle route at high electricity replenishment cost

8 Advances in Operations Research

(3) Logistics companies tend to use more EVs to avoidcharging as much as possible when charging facilitiesare not perfect and the cost of power supply is high

e model can help the logistics enterprises providesome suggestions for the route optimization help to pro-mote the application of EVs in the field of logistics andimprove energy efficiency energy conservation and emis-sion reduction e proposed MILP model is helpful toreduce the logistics cost However the traditional short-comings of VRP still exist in the EVRPTW model Forexample it is still a NP-hard and it is difficult to solve large-scale problems e focus of future research may be todeveloping more effective heuristic algorithm to solve large-scale problems consider the real-time changes of trafficconditions and expand the direction of the dynamic vehicleroute

Data Availability

e data used to support the findings of this study are in-cluded within the article

Conflicts of Interest

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

Acknowledgments

is research was funded by the National Natural ScienceFoundation of China grant no 71471061 and the Funda-mental Research Funds for the Central Universities grantno 2017MS171

References

[1] G B Dantzig and J H Ramser ldquoe truck dispatchingproblemrdquoManagement Science vol 6 no 1 pp 80ndash91 1959

[2] Y Xiao Q Zhao I Kaku and Y Xu ldquoDevelopment of a fuelconsumption optimization model for the capacitated vehiclerouting problemrdquo Computers amp Operations Research vol 39no 7 pp 1419ndash1431 2012

[3] J Zhang Y ZhaoW Xue and J Li ldquoVehicle routing problemwith fuel consumption and carbon emissionrdquo InternationalJournal of Production Economics vol 170 pp 234ndash242 2015

[4] N Norouzi M Sadegh-Amalnick and R Tavakkoli-Mog-haddam ldquoModified particle swarm optimization in a time-dependent vehicle routing problem minimizing fuel con-sumptionrdquo Optimization Letters vol 11 no 1 pp 121ndash1342017

[5] G Poonthalir and R Nadarajan ldquoA fuel efficient green vehiclerouting problem with varying speed constraint (F-GVRP)rdquoExpert Systems with Applications vol 100 pp 131ndash144 2018

[6] J Wang S Yao J Sheng and H Yang ldquoMinimizing totalcarbon emissions in an integrated machine scheduling andvehicle routing problemrdquo Journal of Cleaner Productionvol 229 pp 1004ndash1017 2019

[7] S-C Ma Y Fan J-F Guo J-H Xu and J Zhu ldquoAnalysingonline behaviour to determine Chinese consumersrsquo prefer-ences for electric vehiclesrdquo Journal of Cleaner Productionvol 229 pp 244ndash255 2019

[8] B G Pollet I Staffell and J L Shang ldquoCurrent status ofhybrid battery and fuel cell electric vehicles from electro-chemistry to market prospectsrdquo Electrochimica Acta vol 84pp 235ndash249 2012

[9] G Desaulniers F Errico S Irnich and M Schneider ldquoExactalgorithms for electric vehicle-routing problems with win-dowsrdquo Operations Research vol 64 no 6 pp 1177ndash15652016

[10] R A Fernandez ldquoAmore realistic approach to electric vehiclecontribution to greenhouse gas emissions in the cityrdquo Journalof Cleaner Production vol 172 pp 949ndash959 2018

[11] L C Casals E Martinez-Laserna B A Garcia and N NietoldquoSustainability analysis of the electric vehicle use in Europe forCO2 emissions reductionrdquo Journal of Cleaner Productionvol 127 pp 425ndash437 2016

[12] Z Wu M Wang J Zheng X Sun M Zhao and X WangldquoLife cycle greenhouse gas emission reduction potential ofbattery electric vehiclerdquo Journal of Cleaner Productionvol 190 pp 462ndash470 2018

[13] Y Xiao X Zuo I Kaku S Zhou and X Pan ldquoDevelopmentof energy consumption optimization model for the electricvehicle routing problem with time windowsrdquo Journal ofCleaner Production vol 225 pp 647ndash663 2019

[14] S-N YangW-S Cheng Y-C Hsu C-H Gan and Y-B LinldquoCharge scheduling of electric vehicles in highwaysrdquo Math-ematical and Computer Modelling vol 57 no 11-12pp 2873ndash2882 2013

[15] A Dogan andM Alci ldquoHeuristic optimization of EV chargingschedule considering battery degradation costrdquo Elektronika irElektrotechnika vol 24 no 6 pp 15ndash20 2018

[16] A Dogan S Bahceci F Daldaban and M Alci ldquoOptimi-zation of chargedischarge coordination to satisfy networkrequirements using heuristic algorithms in vehicle-to-gridconceptrdquo Advances in Electrical and Computer Engineeringvol 18 no 1 pp 121ndash130 2018

[17] V Aravinthan and W Jewell ldquoControlled electric vehiclecharging for mitigating impacts on distribution assetsrdquo IEEETransactions on Smart Grid vol 6 no 2 pp 999ndash1009 2015

[18] M Schucking P Jochem W Fichtner O Wollersheim andK Stella ldquoCharging strategies for economic operations ofelectric vehicles in commercial applicationsrdquo TransportationResearch Part D Transport and Environment vol 51pp 173ndash189 2017

[19] J D Adler and P B Mirchandani ldquoOnline routing andbattery reservations for electric vehicles with swappablebatteriesrdquo Transportation Research Part B Methodologicalvol 70 pp 285ndash302 2014

[20] J Yang and H Sun ldquoBattery swap station location-routingproblem with capacitated electric vehiclesrdquo Computers ampOperations Research vol 55 pp 217ndash232 2015

[21] Q Dai T Cai S Duan and F Zhao ldquoStochastic modeling andforecasting of load demand for electric bus battery-swapstationrdquo IEEE Transactions on Power Delivery vol 29 no 4pp 1909ndash1917 2014

[22] D Margaritis A Anagnostopoulou A Tromaras andM Boile ldquoElectric commercial vehicles practical perspectivesand future research directionsrdquo Research in TransportationBusiness amp Management vol 18 pp 4ndash10 2016

[23] MM Solomon and J Desrosiers ldquoSurvey paper-time windowconstrained routing and scheduling problemsrdquo Trans-portation Science vol 22 no 1 pp 1ndash13 1988

[24] A G Qureshi E Taniguchi and T Yamada ldquoAn exact so-lution approach for vehicle routing and scheduling problemswith soft time windowsrdquo Transportation Research Part E

Advances in Operations Research 9

Logistics and Transportation Review vol 45 no 6 pp 960ndash977 2009

[25] D Goeke ldquoGranular tabu search for the pickup and deliveryproblem with time windows and electric vehiclesrdquo EuropeanJournal of Operational Research vol 278 no 3 pp 821ndash8362019

[26] M Keskin and B Ccedilatay ldquoPartial recharge strategies for theelectric vehicle routing problem with time windowsrdquoTransportation Research Part C Emerging Technologiesvol 65 pp 111ndash127 2016

[27] M Schneider A Stenger and D Goeke ldquoe electric vehicle-routing problem with time windows and recharging stationsrdquoTransportation Science vol 48 no 4 pp 500ndash520 2014

[28] G Hiermann J Puchinger S Ropke and R F Hartl ldquoeelectric fleet size and mix vehicle routing problem with timewindows and recharging stationsrdquo European Journal of Op-erational Research vol 252 no 3 pp 995ndash1018 2016

[29] Solomon benchmark problems httpwcbaneuedusimmsolomonr101htm

10 Advances in Operations Research

tvi the time point when the vehicle v arrives at thecustomer node i where tv

0 0tprimevi the start time of the v-car service customer node itij time of electric vehicles from i to jspeed driving speed of electric vehiclesei the lower limit of the best service time windows ofthe customer node ili the upper limit of the best service window of thecustomer node ieiprime the lower limit of tolerance time windows of thecustomer node iliprime upper limits of tolerance time windows of the cus-tomer node iρm unit time penalty cost of vehicles violating the timewindows m (1 2 3 4)xijv if the vehicle v is from i to j then xijv 1 oth-erwise xijv 0xov if the vehicle v returns to the distribution centreafter delivering a customer group then xov 1 oth-erwise xov 0yiv the task of the customer node i is completed by thevehicle v then yiv 1 otherwise yiv 0

32 Model and Method e objective function is to mini-mize the comprehensive cost including transportation costvehicle use cost electricity replenishment cost and timewindow penalty cost e formula of the MILP model is asfollows

Fmin C0 1113944visinV

xov + C1 1113944visinV

1113944iisinD

1113944jisinDinej

xijvdij

+ 1113944visinV

1113944iisinC

ECi tfi( 1113857 + 1113944visinV

1113944iisinN

pui tvi( 1113857

(1)

Among them

ECi tfi( 1113857 C2 times tfi tfi le tci

C3 tfi gt tci1113896 (2)

pui tprimevi1113874 1113875

ρ1 eiprime minus tprimevi1113872 1113873 + ρ2 ei minus ei

prime( 1113857 tprimevi le eiprime

ρ2 ei minus tprimevi1113872 1113873

0

ρ3 tprimevi minus li1113872 1113873

ρ3 liprime minus li( 1113857 + ρ4 tprimevi minus liprime1113872 1113873

eiprime lt tprimevi le ei

ei lt tprimevi le li

li lt tprimevi le liprime

li lt tprimevi

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎩

(3)

subject to

1113944iisinDknei

xikv 1113944jisinDknej

xkjv k isin D(4)

1113944visinV

ynv 1 n isin N (5)

1113944nisinN

ynvqn leQ (6)

1113944visinV

1113944iisinDine0

xoiv le |V| (7)

1113944iisinN

1113944jisinDinej

xijv le |N| (8)

t0Prime 0 (9)

tij dij

speed i j isin D (10)

tfi min tciP minus p1

iv

g1113888 11138891113890 1113891 (11)

tvi tprimevi + tfi + twi i isin N (12)

tprimevi ge t

vi i isin N v isin V (13)

tjprime 1113944

iisinD1113944

jisinDinejxijv tiPrime + tij1113872 1113873 (14)

p1iv p

2iv i isin N (15)

p1ov 100 (16)

p1jv p

2iv minus xijv times

dij

h i j isin D ine j v isin V (17)

p1iv ge 0 i isin D v isin V (18)

xijv xov yiv isin 0 1 i j o isin D v isin V (19)

In the model given above Constraint (4) ensures thatthe vehicle starts from the distribution centre returns tothe distribution centre and focuses on distribution centreConstraint (5) ensures that each customer is served onlyonce by one vehicle Constraint (6) is a restraint on vehicleloading Constraint (7) indicates that the number of EVsserving the customer is less than or equal to the totalnumber of vehicles owned by the distribution centreConstraint (8) requires that the number of customersserved by each vehicle is less than or equal to the totalnumber of customers Constraint (9) requires that whenthe electric vehicle starts from the distribution centre thetime is 0 Constraint (10) indicates that the travel time ofelectric vehicles from the point i to the point j is the ratioof the distance between two points and the travel speedConstraint (11) indicates that when the electric vehiclepasses through the charging stations the charge replen-ishment time is the minimum of the battery replacementtime and fast charging time Constraint (12) indicates thatthe time the electric vehicle leaves the customer node i is

4 Advances in Operations Research

the sum of arriving at the customer node waiting time atthe customer node i and servicing time Constraint (13)shows the relationship between the starting service timeand the arrival time of vehicles at the customer pointConstraint (14) indicates that the time the electric vehiclearrives at the node j is the accumulation of the previoustime Constraint (15) means that neither power con-sumption nor power replenishment occurs at the cus-tomer node i Constraint (16) indicates that when theelectric vehicle starts from the distribution centre thestate of charge is 100 Constraint (17) indicates that theremaining power to node j is equal to the remaining powerto leave node i minus the power consumed on the wayConstraint (18) indicates that the state of charge of electricvehicles is nonnegative at any position Constraint (19)indicates that the decision variable is constrained to 0-1

In this paper the ant colony algorithm is used to solvethe approximate optimal solution of the NP hard probleme ant colony algorithm has the characteristics of dis-tributed computing positive information feedback andheuristic search In essence it is a heuristic global opti-mization algorithm in the evolutionary algorithm ealgorithm imitates the social behaviour of ants in order tofind the shortest route from nest to food source In the antcolony algorithm each ant performs four basic activitiesin the process of route construction (1) select the nextcustomer based on the probable function of the distancefrom the current location to the customer and the routestrength on the arc (2) save the taboo list of the customersin the current route (3) update the residual capacity of thevehicle and (4) update the track intensity on the accessarc and use the method of local search to improve thequality of the solution Finally the taboo lists are deletedand a new iteration is started When the ant colony al-gorithm solves the MILP model the specific steps are asfollows

Step 1 importing data and setting basic parameters

Step 2 calculating the distance between customernodes and the cost and time of distance betweencustomer pointsStep 3 initializing and iterating in order to find the bestroute

Step 4 terminating the algorithm and reporting the bestsolution

Figure 2 shows the traversing process of a single ant inthe iterative search for the best route

e meanings of the mathematical symbols involved inFigure 2 are explained as follows

Current the current location of antsAllowed(k)11138641113865 the collection of client nodes that havenot been accessed initially including all client nodesNext[i]11138641113865 the set of optional customer nodes when theelectric vehicle is in i-nodePnext[i]11138641113865 the collection of optional customer nodes forEV charging closest to i-node

4 Calculation Experiment and Cost Analysis

In order to verify the proposed MILP model the calculationexperiments are carried out based on the known benchmarkinstances and the ant colony algorithm is used to solve themodel

41 Test Examples e experimental data are from Solo-monrsquos VRPTW standard problem set and the data numberis R101 [29] which is characterized by uniform distributionof customer points and narrow time windows In this case avehicle is generally only responsible for the distribution ofseveral customer points and the vehicle route cost is greatlyaffected by the time windows so the data selection of the caseis reasonable In order to draw a clear road map this paperonly selects the first 26 data including 1 distribution centreand 25 customer nodes1 is the distribution centre 2ndash26 isthe customer node 27ndash31 is the charging stations node especific parameters of the example are shown in Table 1 andthe node information is shown in Table 2

In this paper according to the actual situation we madeassumptions about the required data in Table 1 and for thispart of the program design we reserved a data change areawhich is malleable

e MILP model is solved by MATLAB programmingIn order to reduce the influence of random factors as muchas possible this paper repeatedly tests the example 10 timesto get the total cost optimal solution (C) the number ofvehicles (N) route length (L) and penalty cost (P) when theoptimal solution is reached

As can be seen from Table 3 the optimal solution of thisexample is 728308 including the route length when theoptimal solution is reached at 27061 and Table 4 shows thatthe optimal allocation scheme includes 4 routes the routemap is shown in Figure 3

42 Cost Analysis Based on the calculation experiment ofthe Solomon benchmark example the sensitivity analysis ofthe cost affecting the electric vehicle route planning is carriedout

421 Use Cost and Transportation Cost First adjust the usecost from 1000 for each vehicle to 5000 for each vehicle keepthe other parameters unchanged repeat the test for 10 timesand see Table 5 for the results when the optimal solution isreached

It can be seen from Table 5 that after adjusting the usecost of vehicles from 1000 to 5000 after 10 times of oper-ation compared with Table 3 the number of vehicles isreduced from 4 to 2 which is 50 It can be seen that thehigher the use cost of vehicles is the smaller the number ofvehicles used isWhen the use cost of vehicles is much higherthan other costs the vehicle route distribution scheme withthe minimum number of vehicles will be preferred At thesame time the route length is only increased by 3 com-pared with the result in Table 3 while the time windowpenalty is increased by 52 is is understandable because

Advances in Operations Research 5

the proportion of vehicle use cost in the objective functionincreases so the algorithm will tend to find the solution withthe minimum vehicle use

Keep the cost of using vehicles at 5000 per vehicle andadjust the unit transportation cost from 2 to 10 while thepenalty factor of time windows remains unchanged Run theprogram 10 times and see Table 6 for relevant results whenthe optimal solution is reached

It can be seen from Table 6 that after adjusting vehicleuse cost and unit transportation cost at the same time thenumber of vehicles obtained is significantly reduced com-pared with Table 3 It can be seen that when vehicletransportation cost and use cost are much higher than othercosts the route distribution scheme with the least number ofvehicles will be preferred e route length in Table 6 issimilar to that in Table 3 but the penalty cost of timewindows is increased by 53 By increasing the factors ofvehicle use cost and unit freight in the objective function theproportion of time window penalty cost is greatly reducederefore the length of the route and the number of vehiclesare given priority in the result so the time window penalty isgreatly increased is shows the effectiveness of the algo-rithm again in this paper

Ants at current

Whether allowed (k) is

empty

Building Next [Current]

Whether Next [Current]

is empty

Index [] are allgreater than 0

Go to the nearest charging station of current for charging

build Pnext [Current]

Whether Pnext [Current] is

empty

Select j-node according to probability

Current = j

Direct return to distribution center

Current = 0

Return to the distribution center (or return to the distribution center after

charging)Current = 0

Select j-node according to probability

Current = j

Return to the distribution center and

output the total cost

Yes

No

No

Yes

No

No

Yes

Yes

Figure 2 Single ant traversal process to find the best route during iterative search

Table 1 Temperature and wildlife count in the three areas coveredby the test examples

Name ParameterMaximum loading capacity of vehicles 80 piecesUse cost of vehicles 1000 RMBvehicleUnit transportation cost 2 RMBkmSpeed of vehicles 40 kmhFull charge at the charging stations 60 kWhPower consumption per unit distance 1 kWhCost per battery replacement 30 RMBBattery replacement time once 31minService time per customer 10minPenalty coefficient of time windows (1 05 15 2)e customer tolerance level 05Maximum number of iterations 200

6 Advances in Operations Research

422 Time Window Penalty Cost Adjust the penalty co-efficient of the time windows from ρ1 1 ρ2 05 ρ3

15 and ρ4 2 to ρ1 5 ρ2 25 ρ3 75 and ρ4 10keep other parameters unchanged repeat the test 10 timesand see Table 7 for the results when the optimal solution isreached

After the penalty cost coefficient increases 5 times thecalculation results are shown in Table 7 e route length isreduced by 03 compared with the result in Table 3 but thenumber of optimal vehicles has increased from 4 to 7

Table 2 Node information

Number X-coordinate

Y-coordinate Demand Ready

timeDuedate

1 35 35 0 0 2302 41 49 10 161 1713 35 17 7 50 604 55 45 13 116 1265 55 20 19 149 1596 15 30 26 34 447 25 30 3 99 1098 20 50 5 81 919 10 43 9 95 10510 55 60 16 97 10711 30 60 16 124 13412 20 65 12 67 7713 50 35 19 63 7314 30 25 23 159 16915 15 10 20 32 4216 30 5 8 16 7117 10 20 19 75 8518 5 30 2 157 16719 20 40 12 87 9720 15 60 17 76 8621 45 65 9 126 13622 45 20 11 62 7223 45 10 18 97 10724 55 5 29 68 7825 65 35 3 153 16326 65 20 6 172 18227 10 32 0 0 23028 27 47 0 0 23029 40 30 0 0 23030 50 50 0 0 23031 60 10 0 0 230

Table 3 Related results of the test examples

Operation times C N L P

1 740418 4 27208 2372112 761371 4 27804 2544153 776436 3 26293 3814294 758694 4 28075 2669485 728308 4 27061 2238966 756774 3 25858 3629467 759047 3 26997 3617058 749176 4 26934 2314079 760367 3 27103 37248810 746696 3 26306 357825Average 753729 35 26964 305027

Table 4 Sequence of routes when the test examples reaches theoptimal solution

Vehicle Route number1 1ndash14ndash22ndash23ndash24ndash27ndash9ndash12 1ndash7ndash6ndash18ndash17ndash15ndash16ndash28ndash19ndash20ndash13 1ndash3ndash5ndash26ndash25ndash4ndash13ndash28ndash8ndash14 1ndash2ndash21ndash10ndash11ndash12ndash1

0 10 20 30 40 50 60 700

10

20

30

40

50

60

70

1

2

3

4

5

6 7

8

9

1011

12

13

14

1516

17

18

19

2021

22

2324

25

26

27

28

29

30

31

Figure 3 Corresponding route trajectory when the examplereaches the optimal solution

Table 5 Impact of adjusting use cost on results

Operation times N L P

1 2 28125 6036132 2 27501 6646813 2 26850 6809434 2 28149 6021615 2 28076 6722076 2 26862 6450827 2 27284 6257538 2 27415 5855419 2 28566 63446310 2 28063 602555Average 2 27689 631700

Table 6 Impact of adjusting use cost and unit transportation coston results

Operation times N L P

1 2 28125 6524182 2 27501 6646813 2 27241 6992544 2 28149 6021615 2 28123 6679206 2 26862 6593437 2 27284 6257538 2 27415 6323099 2 28538 63446310 2 28063 602555Average 2 27730 644086

Advances in Operations Research 7

indicated an increase of 75 and we can see that thenumber of vehicles has increased significantly is isunderstandable for the change of the penalty cost coeffi-cient increases the penalty cost in the objective function sothe algorithm will tend to find more solutions for vehiclesto serve customers e increase in the number of vehicleswill inevitably lead to a decrease in the average drivingroute length which proves the effectiveness of the algo-rithm again erefore the higher the cost of fines is themore vehicles are required is has led logistics companiesto prepare more vehicles under strict time window con-ditions making the customerrsquos total demand unchanged oreven increased

423 Electricity Replenishment Cost e battery capacity is60 kWh the charging time needs 60min and the powerchange time is 31min e shortest power supply mode isselected erefore when the supplementary power is notmore than half quick charging is preferred Otherwisechoose the battery replacement strategy e charging costper unit time is 1 RMBmin and the cost of single batteryreplacement is 30 RMB Now the cost of power supply isincreasing e charging cost per unit time is 50 RMBminand the cost of single battery replacement is 1500 RMB eresults are shown in Table 8 and the vehicle route when theoptimal solution is reached is shown in Figure 4

It can be seen from Table 8 that after the unit charge costis adjusted from 1 to 50 and the single battery change cost isadjusted from 30 to 1500 after ten runs compared withTable 3 the number of vehicles increased from 4 to 5 ve-hicles indicated an increase of 25 At the same time it canbe seen that the number of charging stations passed inFigure 3 is 3 however the number of charging stationspassed in Figure 4 is 2 Increased costs have drived com-panies to choose more vehicles to avoid charging In ad-dition compared with Table 3 the route length is reduced by06 together with the penalty cost is reduced by 103And the increase in the number of vehicles serving cus-tomers leads to a reduction in the possibility of reducingtime penalties and costs is proves the effectiveness of thealgorithm erefore when the charging facilities are notperfect together with the power replenishment cost is highthe logistics companies tend to use more vehicles to avoidcharging as much as possible

5 Conclusions

At present most of the literature studies use a chargingstrategy and the customer tolerance is not considered whilestudying the customer time windows In this paper thecharging strategy of combining two charging ways isadopted the broken line soft time windows is used con-sidering the customer tolerance and the MILP model of theEVRPTW is finally established And through the calculationexperiment of the Solomon benchmark example the cost ofaffecting the route optimization of electric vehicle is ana-lysed the availability as well as effectiveness of data andalgorithm are proved and the management opinions on thepractical application of MILP model are put forward

(1) e higher the use cost and freight of vehicles are theless the number of vehicles used When the use costand freight of vehicles are much higher than othercosts the vehicle route distribution scheme with theleast number of vehicles is preferred

(2) e higher the penalty cost of time windows is thehigher the number of vehicles used for vehicle dis-tribution is In the case of strict time windows lo-gistics companies need to prepare more vehicles thanthe total demand of customers

Table 7 Impact of adjusting time window penalty costs on results

Operation times N L1 8 279772 7 234703 7 291224 7 245155 6 284256 6 271807 8 265798 6 259409 7 2897610 7 26766Average 69 26895

Table 8 Impact of adjusted electricity supplement costs on results

Operation times N L P

1 4 28415 3492102 5 27377 2099193 5 27284 2372204 5 26824 2601645 5 24432 2244606 5 25166 2644777 4 27103 3498758 5 26605 2281859 4 28159 35634810 5 26555 255216Average 47 26792 273507

0 10 20 30 40 50 60 700

10

20

30

40

50

60

70

1

2

3

4

5

6 7

8

9

101112

13

14

1516

17

18

19

2021

22

2324

25

26

27

28

29

30

31

Figure 4 Vehicle route at high electricity replenishment cost

8 Advances in Operations Research

(3) Logistics companies tend to use more EVs to avoidcharging as much as possible when charging facilitiesare not perfect and the cost of power supply is high

e model can help the logistics enterprises providesome suggestions for the route optimization help to pro-mote the application of EVs in the field of logistics andimprove energy efficiency energy conservation and emis-sion reduction e proposed MILP model is helpful toreduce the logistics cost However the traditional short-comings of VRP still exist in the EVRPTW model Forexample it is still a NP-hard and it is difficult to solve large-scale problems e focus of future research may be todeveloping more effective heuristic algorithm to solve large-scale problems consider the real-time changes of trafficconditions and expand the direction of the dynamic vehicleroute

Data Availability

e data used to support the findings of this study are in-cluded within the article

Conflicts of Interest

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

Acknowledgments

is research was funded by the National Natural ScienceFoundation of China grant no 71471061 and the Funda-mental Research Funds for the Central Universities grantno 2017MS171

References

[1] G B Dantzig and J H Ramser ldquoe truck dispatchingproblemrdquoManagement Science vol 6 no 1 pp 80ndash91 1959

[2] Y Xiao Q Zhao I Kaku and Y Xu ldquoDevelopment of a fuelconsumption optimization model for the capacitated vehiclerouting problemrdquo Computers amp Operations Research vol 39no 7 pp 1419ndash1431 2012

[3] J Zhang Y ZhaoW Xue and J Li ldquoVehicle routing problemwith fuel consumption and carbon emissionrdquo InternationalJournal of Production Economics vol 170 pp 234ndash242 2015

[4] N Norouzi M Sadegh-Amalnick and R Tavakkoli-Mog-haddam ldquoModified particle swarm optimization in a time-dependent vehicle routing problem minimizing fuel con-sumptionrdquo Optimization Letters vol 11 no 1 pp 121ndash1342017

[5] G Poonthalir and R Nadarajan ldquoA fuel efficient green vehiclerouting problem with varying speed constraint (F-GVRP)rdquoExpert Systems with Applications vol 100 pp 131ndash144 2018

[6] J Wang S Yao J Sheng and H Yang ldquoMinimizing totalcarbon emissions in an integrated machine scheduling andvehicle routing problemrdquo Journal of Cleaner Productionvol 229 pp 1004ndash1017 2019

[7] S-C Ma Y Fan J-F Guo J-H Xu and J Zhu ldquoAnalysingonline behaviour to determine Chinese consumersrsquo prefer-ences for electric vehiclesrdquo Journal of Cleaner Productionvol 229 pp 244ndash255 2019

[8] B G Pollet I Staffell and J L Shang ldquoCurrent status ofhybrid battery and fuel cell electric vehicles from electro-chemistry to market prospectsrdquo Electrochimica Acta vol 84pp 235ndash249 2012

[9] G Desaulniers F Errico S Irnich and M Schneider ldquoExactalgorithms for electric vehicle-routing problems with win-dowsrdquo Operations Research vol 64 no 6 pp 1177ndash15652016

[10] R A Fernandez ldquoAmore realistic approach to electric vehiclecontribution to greenhouse gas emissions in the cityrdquo Journalof Cleaner Production vol 172 pp 949ndash959 2018

[11] L C Casals E Martinez-Laserna B A Garcia and N NietoldquoSustainability analysis of the electric vehicle use in Europe forCO2 emissions reductionrdquo Journal of Cleaner Productionvol 127 pp 425ndash437 2016

[12] Z Wu M Wang J Zheng X Sun M Zhao and X WangldquoLife cycle greenhouse gas emission reduction potential ofbattery electric vehiclerdquo Journal of Cleaner Productionvol 190 pp 462ndash470 2018

[13] Y Xiao X Zuo I Kaku S Zhou and X Pan ldquoDevelopmentof energy consumption optimization model for the electricvehicle routing problem with time windowsrdquo Journal ofCleaner Production vol 225 pp 647ndash663 2019

[14] S-N YangW-S Cheng Y-C Hsu C-H Gan and Y-B LinldquoCharge scheduling of electric vehicles in highwaysrdquo Math-ematical and Computer Modelling vol 57 no 11-12pp 2873ndash2882 2013

[15] A Dogan andM Alci ldquoHeuristic optimization of EV chargingschedule considering battery degradation costrdquo Elektronika irElektrotechnika vol 24 no 6 pp 15ndash20 2018

[16] A Dogan S Bahceci F Daldaban and M Alci ldquoOptimi-zation of chargedischarge coordination to satisfy networkrequirements using heuristic algorithms in vehicle-to-gridconceptrdquo Advances in Electrical and Computer Engineeringvol 18 no 1 pp 121ndash130 2018

[17] V Aravinthan and W Jewell ldquoControlled electric vehiclecharging for mitigating impacts on distribution assetsrdquo IEEETransactions on Smart Grid vol 6 no 2 pp 999ndash1009 2015

[18] M Schucking P Jochem W Fichtner O Wollersheim andK Stella ldquoCharging strategies for economic operations ofelectric vehicles in commercial applicationsrdquo TransportationResearch Part D Transport and Environment vol 51pp 173ndash189 2017

[19] J D Adler and P B Mirchandani ldquoOnline routing andbattery reservations for electric vehicles with swappablebatteriesrdquo Transportation Research Part B Methodologicalvol 70 pp 285ndash302 2014

[20] J Yang and H Sun ldquoBattery swap station location-routingproblem with capacitated electric vehiclesrdquo Computers ampOperations Research vol 55 pp 217ndash232 2015

[21] Q Dai T Cai S Duan and F Zhao ldquoStochastic modeling andforecasting of load demand for electric bus battery-swapstationrdquo IEEE Transactions on Power Delivery vol 29 no 4pp 1909ndash1917 2014

[22] D Margaritis A Anagnostopoulou A Tromaras andM Boile ldquoElectric commercial vehicles practical perspectivesand future research directionsrdquo Research in TransportationBusiness amp Management vol 18 pp 4ndash10 2016

[23] MM Solomon and J Desrosiers ldquoSurvey paper-time windowconstrained routing and scheduling problemsrdquo Trans-portation Science vol 22 no 1 pp 1ndash13 1988

[24] A G Qureshi E Taniguchi and T Yamada ldquoAn exact so-lution approach for vehicle routing and scheduling problemswith soft time windowsrdquo Transportation Research Part E

Advances in Operations Research 9

Logistics and Transportation Review vol 45 no 6 pp 960ndash977 2009

[25] D Goeke ldquoGranular tabu search for the pickup and deliveryproblem with time windows and electric vehiclesrdquo EuropeanJournal of Operational Research vol 278 no 3 pp 821ndash8362019

[26] M Keskin and B Ccedilatay ldquoPartial recharge strategies for theelectric vehicle routing problem with time windowsrdquoTransportation Research Part C Emerging Technologiesvol 65 pp 111ndash127 2016

[27] M Schneider A Stenger and D Goeke ldquoe electric vehicle-routing problem with time windows and recharging stationsrdquoTransportation Science vol 48 no 4 pp 500ndash520 2014

[28] G Hiermann J Puchinger S Ropke and R F Hartl ldquoeelectric fleet size and mix vehicle routing problem with timewindows and recharging stationsrdquo European Journal of Op-erational Research vol 252 no 3 pp 995ndash1018 2016

[29] Solomon benchmark problems httpwcbaneuedusimmsolomonr101htm

10 Advances in Operations Research

the sum of arriving at the customer node waiting time atthe customer node i and servicing time Constraint (13)shows the relationship between the starting service timeand the arrival time of vehicles at the customer pointConstraint (14) indicates that the time the electric vehiclearrives at the node j is the accumulation of the previoustime Constraint (15) means that neither power con-sumption nor power replenishment occurs at the cus-tomer node i Constraint (16) indicates that when theelectric vehicle starts from the distribution centre thestate of charge is 100 Constraint (17) indicates that theremaining power to node j is equal to the remaining powerto leave node i minus the power consumed on the wayConstraint (18) indicates that the state of charge of electricvehicles is nonnegative at any position Constraint (19)indicates that the decision variable is constrained to 0-1

In this paper the ant colony algorithm is used to solvethe approximate optimal solution of the NP hard probleme ant colony algorithm has the characteristics of dis-tributed computing positive information feedback andheuristic search In essence it is a heuristic global opti-mization algorithm in the evolutionary algorithm ealgorithm imitates the social behaviour of ants in order tofind the shortest route from nest to food source In the antcolony algorithm each ant performs four basic activitiesin the process of route construction (1) select the nextcustomer based on the probable function of the distancefrom the current location to the customer and the routestrength on the arc (2) save the taboo list of the customersin the current route (3) update the residual capacity of thevehicle and (4) update the track intensity on the accessarc and use the method of local search to improve thequality of the solution Finally the taboo lists are deletedand a new iteration is started When the ant colony al-gorithm solves the MILP model the specific steps are asfollows

Step 1 importing data and setting basic parameters

Step 2 calculating the distance between customernodes and the cost and time of distance betweencustomer pointsStep 3 initializing and iterating in order to find the bestroute

Step 4 terminating the algorithm and reporting the bestsolution

Figure 2 shows the traversing process of a single ant inthe iterative search for the best route

e meanings of the mathematical symbols involved inFigure 2 are explained as follows

Current the current location of antsAllowed(k)11138641113865 the collection of client nodes that havenot been accessed initially including all client nodesNext[i]11138641113865 the set of optional customer nodes when theelectric vehicle is in i-nodePnext[i]11138641113865 the collection of optional customer nodes forEV charging closest to i-node

4 Calculation Experiment and Cost Analysis

In order to verify the proposed MILP model the calculationexperiments are carried out based on the known benchmarkinstances and the ant colony algorithm is used to solve themodel

41 Test Examples e experimental data are from Solo-monrsquos VRPTW standard problem set and the data numberis R101 [29] which is characterized by uniform distributionof customer points and narrow time windows In this case avehicle is generally only responsible for the distribution ofseveral customer points and the vehicle route cost is greatlyaffected by the time windows so the data selection of the caseis reasonable In order to draw a clear road map this paperonly selects the first 26 data including 1 distribution centreand 25 customer nodes1 is the distribution centre 2ndash26 isthe customer node 27ndash31 is the charging stations node especific parameters of the example are shown in Table 1 andthe node information is shown in Table 2

In this paper according to the actual situation we madeassumptions about the required data in Table 1 and for thispart of the program design we reserved a data change areawhich is malleable

e MILP model is solved by MATLAB programmingIn order to reduce the influence of random factors as muchas possible this paper repeatedly tests the example 10 timesto get the total cost optimal solution (C) the number ofvehicles (N) route length (L) and penalty cost (P) when theoptimal solution is reached

As can be seen from Table 3 the optimal solution of thisexample is 728308 including the route length when theoptimal solution is reached at 27061 and Table 4 shows thatthe optimal allocation scheme includes 4 routes the routemap is shown in Figure 3

42 Cost Analysis Based on the calculation experiment ofthe Solomon benchmark example the sensitivity analysis ofthe cost affecting the electric vehicle route planning is carriedout

421 Use Cost and Transportation Cost First adjust the usecost from 1000 for each vehicle to 5000 for each vehicle keepthe other parameters unchanged repeat the test for 10 timesand see Table 5 for the results when the optimal solution isreached

It can be seen from Table 5 that after adjusting the usecost of vehicles from 1000 to 5000 after 10 times of oper-ation compared with Table 3 the number of vehicles isreduced from 4 to 2 which is 50 It can be seen that thehigher the use cost of vehicles is the smaller the number ofvehicles used isWhen the use cost of vehicles is much higherthan other costs the vehicle route distribution scheme withthe minimum number of vehicles will be preferred At thesame time the route length is only increased by 3 com-pared with the result in Table 3 while the time windowpenalty is increased by 52 is is understandable because

Advances in Operations Research 5

the proportion of vehicle use cost in the objective functionincreases so the algorithm will tend to find the solution withthe minimum vehicle use

Keep the cost of using vehicles at 5000 per vehicle andadjust the unit transportation cost from 2 to 10 while thepenalty factor of time windows remains unchanged Run theprogram 10 times and see Table 6 for relevant results whenthe optimal solution is reached

It can be seen from Table 6 that after adjusting vehicleuse cost and unit transportation cost at the same time thenumber of vehicles obtained is significantly reduced com-pared with Table 3 It can be seen that when vehicletransportation cost and use cost are much higher than othercosts the route distribution scheme with the least number ofvehicles will be preferred e route length in Table 6 issimilar to that in Table 3 but the penalty cost of timewindows is increased by 53 By increasing the factors ofvehicle use cost and unit freight in the objective function theproportion of time window penalty cost is greatly reducederefore the length of the route and the number of vehiclesare given priority in the result so the time window penalty isgreatly increased is shows the effectiveness of the algo-rithm again in this paper

Ants at current

Whether allowed (k) is

empty

Building Next [Current]

Whether Next [Current]

is empty

Index [] are allgreater than 0

Go to the nearest charging station of current for charging

build Pnext [Current]

Whether Pnext [Current] is

empty

Select j-node according to probability

Current = j

Direct return to distribution center

Current = 0

Return to the distribution center (or return to the distribution center after

charging)Current = 0

Select j-node according to probability

Current = j

Return to the distribution center and

output the total cost

Yes

No

No

Yes

No

No

Yes

Yes

Figure 2 Single ant traversal process to find the best route during iterative search

Table 1 Temperature and wildlife count in the three areas coveredby the test examples

Name ParameterMaximum loading capacity of vehicles 80 piecesUse cost of vehicles 1000 RMBvehicleUnit transportation cost 2 RMBkmSpeed of vehicles 40 kmhFull charge at the charging stations 60 kWhPower consumption per unit distance 1 kWhCost per battery replacement 30 RMBBattery replacement time once 31minService time per customer 10minPenalty coefficient of time windows (1 05 15 2)e customer tolerance level 05Maximum number of iterations 200

6 Advances in Operations Research

422 Time Window Penalty Cost Adjust the penalty co-efficient of the time windows from ρ1 1 ρ2 05 ρ3

15 and ρ4 2 to ρ1 5 ρ2 25 ρ3 75 and ρ4 10keep other parameters unchanged repeat the test 10 timesand see Table 7 for the results when the optimal solution isreached

After the penalty cost coefficient increases 5 times thecalculation results are shown in Table 7 e route length isreduced by 03 compared with the result in Table 3 but thenumber of optimal vehicles has increased from 4 to 7

Table 2 Node information

Number X-coordinate

Y-coordinate Demand Ready

timeDuedate

1 35 35 0 0 2302 41 49 10 161 1713 35 17 7 50 604 55 45 13 116 1265 55 20 19 149 1596 15 30 26 34 447 25 30 3 99 1098 20 50 5 81 919 10 43 9 95 10510 55 60 16 97 10711 30 60 16 124 13412 20 65 12 67 7713 50 35 19 63 7314 30 25 23 159 16915 15 10 20 32 4216 30 5 8 16 7117 10 20 19 75 8518 5 30 2 157 16719 20 40 12 87 9720 15 60 17 76 8621 45 65 9 126 13622 45 20 11 62 7223 45 10 18 97 10724 55 5 29 68 7825 65 35 3 153 16326 65 20 6 172 18227 10 32 0 0 23028 27 47 0 0 23029 40 30 0 0 23030 50 50 0 0 23031 60 10 0 0 230

Table 3 Related results of the test examples

Operation times C N L P

1 740418 4 27208 2372112 761371 4 27804 2544153 776436 3 26293 3814294 758694 4 28075 2669485 728308 4 27061 2238966 756774 3 25858 3629467 759047 3 26997 3617058 749176 4 26934 2314079 760367 3 27103 37248810 746696 3 26306 357825Average 753729 35 26964 305027

Table 4 Sequence of routes when the test examples reaches theoptimal solution

Vehicle Route number1 1ndash14ndash22ndash23ndash24ndash27ndash9ndash12 1ndash7ndash6ndash18ndash17ndash15ndash16ndash28ndash19ndash20ndash13 1ndash3ndash5ndash26ndash25ndash4ndash13ndash28ndash8ndash14 1ndash2ndash21ndash10ndash11ndash12ndash1

0 10 20 30 40 50 60 700

10

20

30

40

50

60

70

1

2

3

4

5

6 7

8

9

1011

12

13

14

1516

17

18

19

2021

22

2324

25

26

27

28

29

30

31

Figure 3 Corresponding route trajectory when the examplereaches the optimal solution

Table 5 Impact of adjusting use cost on results

Operation times N L P

1 2 28125 6036132 2 27501 6646813 2 26850 6809434 2 28149 6021615 2 28076 6722076 2 26862 6450827 2 27284 6257538 2 27415 5855419 2 28566 63446310 2 28063 602555Average 2 27689 631700

Table 6 Impact of adjusting use cost and unit transportation coston results

Operation times N L P

1 2 28125 6524182 2 27501 6646813 2 27241 6992544 2 28149 6021615 2 28123 6679206 2 26862 6593437 2 27284 6257538 2 27415 6323099 2 28538 63446310 2 28063 602555Average 2 27730 644086

Advances in Operations Research 7

indicated an increase of 75 and we can see that thenumber of vehicles has increased significantly is isunderstandable for the change of the penalty cost coeffi-cient increases the penalty cost in the objective function sothe algorithm will tend to find more solutions for vehiclesto serve customers e increase in the number of vehicleswill inevitably lead to a decrease in the average drivingroute length which proves the effectiveness of the algo-rithm again erefore the higher the cost of fines is themore vehicles are required is has led logistics companiesto prepare more vehicles under strict time window con-ditions making the customerrsquos total demand unchanged oreven increased

423 Electricity Replenishment Cost e battery capacity is60 kWh the charging time needs 60min and the powerchange time is 31min e shortest power supply mode isselected erefore when the supplementary power is notmore than half quick charging is preferred Otherwisechoose the battery replacement strategy e charging costper unit time is 1 RMBmin and the cost of single batteryreplacement is 30 RMB Now the cost of power supply isincreasing e charging cost per unit time is 50 RMBminand the cost of single battery replacement is 1500 RMB eresults are shown in Table 8 and the vehicle route when theoptimal solution is reached is shown in Figure 4

It can be seen from Table 8 that after the unit charge costis adjusted from 1 to 50 and the single battery change cost isadjusted from 30 to 1500 after ten runs compared withTable 3 the number of vehicles increased from 4 to 5 ve-hicles indicated an increase of 25 At the same time it canbe seen that the number of charging stations passed inFigure 3 is 3 however the number of charging stationspassed in Figure 4 is 2 Increased costs have drived com-panies to choose more vehicles to avoid charging In ad-dition compared with Table 3 the route length is reduced by06 together with the penalty cost is reduced by 103And the increase in the number of vehicles serving cus-tomers leads to a reduction in the possibility of reducingtime penalties and costs is proves the effectiveness of thealgorithm erefore when the charging facilities are notperfect together with the power replenishment cost is highthe logistics companies tend to use more vehicles to avoidcharging as much as possible

5 Conclusions

At present most of the literature studies use a chargingstrategy and the customer tolerance is not considered whilestudying the customer time windows In this paper thecharging strategy of combining two charging ways isadopted the broken line soft time windows is used con-sidering the customer tolerance and the MILP model of theEVRPTW is finally established And through the calculationexperiment of the Solomon benchmark example the cost ofaffecting the route optimization of electric vehicle is ana-lysed the availability as well as effectiveness of data andalgorithm are proved and the management opinions on thepractical application of MILP model are put forward

(1) e higher the use cost and freight of vehicles are theless the number of vehicles used When the use costand freight of vehicles are much higher than othercosts the vehicle route distribution scheme with theleast number of vehicles is preferred

(2) e higher the penalty cost of time windows is thehigher the number of vehicles used for vehicle dis-tribution is In the case of strict time windows lo-gistics companies need to prepare more vehicles thanthe total demand of customers

Table 7 Impact of adjusting time window penalty costs on results

Operation times N L1 8 279772 7 234703 7 291224 7 245155 6 284256 6 271807 8 265798 6 259409 7 2897610 7 26766Average 69 26895

Table 8 Impact of adjusted electricity supplement costs on results

Operation times N L P

1 4 28415 3492102 5 27377 2099193 5 27284 2372204 5 26824 2601645 5 24432 2244606 5 25166 2644777 4 27103 3498758 5 26605 2281859 4 28159 35634810 5 26555 255216Average 47 26792 273507

0 10 20 30 40 50 60 700

10

20

30

40

50

60

70

1

2

3

4

5

6 7

8

9

101112

13

14

1516

17

18

19

2021

22

2324

25

26

27

28

29

30

31

Figure 4 Vehicle route at high electricity replenishment cost

8 Advances in Operations Research

(3) Logistics companies tend to use more EVs to avoidcharging as much as possible when charging facilitiesare not perfect and the cost of power supply is high

e model can help the logistics enterprises providesome suggestions for the route optimization help to pro-mote the application of EVs in the field of logistics andimprove energy efficiency energy conservation and emis-sion reduction e proposed MILP model is helpful toreduce the logistics cost However the traditional short-comings of VRP still exist in the EVRPTW model Forexample it is still a NP-hard and it is difficult to solve large-scale problems e focus of future research may be todeveloping more effective heuristic algorithm to solve large-scale problems consider the real-time changes of trafficconditions and expand the direction of the dynamic vehicleroute

Data Availability

e data used to support the findings of this study are in-cluded within the article

Conflicts of Interest

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

Acknowledgments

is research was funded by the National Natural ScienceFoundation of China grant no 71471061 and the Funda-mental Research Funds for the Central Universities grantno 2017MS171

References

[1] G B Dantzig and J H Ramser ldquoe truck dispatchingproblemrdquoManagement Science vol 6 no 1 pp 80ndash91 1959

[2] Y Xiao Q Zhao I Kaku and Y Xu ldquoDevelopment of a fuelconsumption optimization model for the capacitated vehiclerouting problemrdquo Computers amp Operations Research vol 39no 7 pp 1419ndash1431 2012

[3] J Zhang Y ZhaoW Xue and J Li ldquoVehicle routing problemwith fuel consumption and carbon emissionrdquo InternationalJournal of Production Economics vol 170 pp 234ndash242 2015

[4] N Norouzi M Sadegh-Amalnick and R Tavakkoli-Mog-haddam ldquoModified particle swarm optimization in a time-dependent vehicle routing problem minimizing fuel con-sumptionrdquo Optimization Letters vol 11 no 1 pp 121ndash1342017

[5] G Poonthalir and R Nadarajan ldquoA fuel efficient green vehiclerouting problem with varying speed constraint (F-GVRP)rdquoExpert Systems with Applications vol 100 pp 131ndash144 2018

[6] J Wang S Yao J Sheng and H Yang ldquoMinimizing totalcarbon emissions in an integrated machine scheduling andvehicle routing problemrdquo Journal of Cleaner Productionvol 229 pp 1004ndash1017 2019

[7] S-C Ma Y Fan J-F Guo J-H Xu and J Zhu ldquoAnalysingonline behaviour to determine Chinese consumersrsquo prefer-ences for electric vehiclesrdquo Journal of Cleaner Productionvol 229 pp 244ndash255 2019

[8] B G Pollet I Staffell and J L Shang ldquoCurrent status ofhybrid battery and fuel cell electric vehicles from electro-chemistry to market prospectsrdquo Electrochimica Acta vol 84pp 235ndash249 2012

[9] G Desaulniers F Errico S Irnich and M Schneider ldquoExactalgorithms for electric vehicle-routing problems with win-dowsrdquo Operations Research vol 64 no 6 pp 1177ndash15652016

[10] R A Fernandez ldquoAmore realistic approach to electric vehiclecontribution to greenhouse gas emissions in the cityrdquo Journalof Cleaner Production vol 172 pp 949ndash959 2018

[11] L C Casals E Martinez-Laserna B A Garcia and N NietoldquoSustainability analysis of the electric vehicle use in Europe forCO2 emissions reductionrdquo Journal of Cleaner Productionvol 127 pp 425ndash437 2016

[12] Z Wu M Wang J Zheng X Sun M Zhao and X WangldquoLife cycle greenhouse gas emission reduction potential ofbattery electric vehiclerdquo Journal of Cleaner Productionvol 190 pp 462ndash470 2018

[13] Y Xiao X Zuo I Kaku S Zhou and X Pan ldquoDevelopmentof energy consumption optimization model for the electricvehicle routing problem with time windowsrdquo Journal ofCleaner Production vol 225 pp 647ndash663 2019

[14] S-N YangW-S Cheng Y-C Hsu C-H Gan and Y-B LinldquoCharge scheduling of electric vehicles in highwaysrdquo Math-ematical and Computer Modelling vol 57 no 11-12pp 2873ndash2882 2013

[15] A Dogan andM Alci ldquoHeuristic optimization of EV chargingschedule considering battery degradation costrdquo Elektronika irElektrotechnika vol 24 no 6 pp 15ndash20 2018

[16] A Dogan S Bahceci F Daldaban and M Alci ldquoOptimi-zation of chargedischarge coordination to satisfy networkrequirements using heuristic algorithms in vehicle-to-gridconceptrdquo Advances in Electrical and Computer Engineeringvol 18 no 1 pp 121ndash130 2018

[17] V Aravinthan and W Jewell ldquoControlled electric vehiclecharging for mitigating impacts on distribution assetsrdquo IEEETransactions on Smart Grid vol 6 no 2 pp 999ndash1009 2015

[18] M Schucking P Jochem W Fichtner O Wollersheim andK Stella ldquoCharging strategies for economic operations ofelectric vehicles in commercial applicationsrdquo TransportationResearch Part D Transport and Environment vol 51pp 173ndash189 2017

[19] J D Adler and P B Mirchandani ldquoOnline routing andbattery reservations for electric vehicles with swappablebatteriesrdquo Transportation Research Part B Methodologicalvol 70 pp 285ndash302 2014

[20] J Yang and H Sun ldquoBattery swap station location-routingproblem with capacitated electric vehiclesrdquo Computers ampOperations Research vol 55 pp 217ndash232 2015

[21] Q Dai T Cai S Duan and F Zhao ldquoStochastic modeling andforecasting of load demand for electric bus battery-swapstationrdquo IEEE Transactions on Power Delivery vol 29 no 4pp 1909ndash1917 2014

[22] D Margaritis A Anagnostopoulou A Tromaras andM Boile ldquoElectric commercial vehicles practical perspectivesand future research directionsrdquo Research in TransportationBusiness amp Management vol 18 pp 4ndash10 2016

[23] MM Solomon and J Desrosiers ldquoSurvey paper-time windowconstrained routing and scheduling problemsrdquo Trans-portation Science vol 22 no 1 pp 1ndash13 1988

[24] A G Qureshi E Taniguchi and T Yamada ldquoAn exact so-lution approach for vehicle routing and scheduling problemswith soft time windowsrdquo Transportation Research Part E

Advances in Operations Research 9

Logistics and Transportation Review vol 45 no 6 pp 960ndash977 2009

[25] D Goeke ldquoGranular tabu search for the pickup and deliveryproblem with time windows and electric vehiclesrdquo EuropeanJournal of Operational Research vol 278 no 3 pp 821ndash8362019

[26] M Keskin and B Ccedilatay ldquoPartial recharge strategies for theelectric vehicle routing problem with time windowsrdquoTransportation Research Part C Emerging Technologiesvol 65 pp 111ndash127 2016

[27] M Schneider A Stenger and D Goeke ldquoe electric vehicle-routing problem with time windows and recharging stationsrdquoTransportation Science vol 48 no 4 pp 500ndash520 2014

[28] G Hiermann J Puchinger S Ropke and R F Hartl ldquoeelectric fleet size and mix vehicle routing problem with timewindows and recharging stationsrdquo European Journal of Op-erational Research vol 252 no 3 pp 995ndash1018 2016

[29] Solomon benchmark problems httpwcbaneuedusimmsolomonr101htm

10 Advances in Operations Research

the proportion of vehicle use cost in the objective functionincreases so the algorithm will tend to find the solution withthe minimum vehicle use

Keep the cost of using vehicles at 5000 per vehicle andadjust the unit transportation cost from 2 to 10 while thepenalty factor of time windows remains unchanged Run theprogram 10 times and see Table 6 for relevant results whenthe optimal solution is reached

It can be seen from Table 6 that after adjusting vehicleuse cost and unit transportation cost at the same time thenumber of vehicles obtained is significantly reduced com-pared with Table 3 It can be seen that when vehicletransportation cost and use cost are much higher than othercosts the route distribution scheme with the least number ofvehicles will be preferred e route length in Table 6 issimilar to that in Table 3 but the penalty cost of timewindows is increased by 53 By increasing the factors ofvehicle use cost and unit freight in the objective function theproportion of time window penalty cost is greatly reducederefore the length of the route and the number of vehiclesare given priority in the result so the time window penalty isgreatly increased is shows the effectiveness of the algo-rithm again in this paper

Ants at current

Whether allowed (k) is

empty

Building Next [Current]

Whether Next [Current]

is empty

Index [] are allgreater than 0

Go to the nearest charging station of current for charging

build Pnext [Current]

Whether Pnext [Current] is

empty

Select j-node according to probability

Current = j

Direct return to distribution center

Current = 0

Return to the distribution center (or return to the distribution center after

charging)Current = 0

Select j-node according to probability

Current = j

Return to the distribution center and

output the total cost

Yes

No

No

Yes

No

No

Yes

Yes

Figure 2 Single ant traversal process to find the best route during iterative search

Table 1 Temperature and wildlife count in the three areas coveredby the test examples

Name ParameterMaximum loading capacity of vehicles 80 piecesUse cost of vehicles 1000 RMBvehicleUnit transportation cost 2 RMBkmSpeed of vehicles 40 kmhFull charge at the charging stations 60 kWhPower consumption per unit distance 1 kWhCost per battery replacement 30 RMBBattery replacement time once 31minService time per customer 10minPenalty coefficient of time windows (1 05 15 2)e customer tolerance level 05Maximum number of iterations 200

6 Advances in Operations Research

422 Time Window Penalty Cost Adjust the penalty co-efficient of the time windows from ρ1 1 ρ2 05 ρ3

15 and ρ4 2 to ρ1 5 ρ2 25 ρ3 75 and ρ4 10keep other parameters unchanged repeat the test 10 timesand see Table 7 for the results when the optimal solution isreached

After the penalty cost coefficient increases 5 times thecalculation results are shown in Table 7 e route length isreduced by 03 compared with the result in Table 3 but thenumber of optimal vehicles has increased from 4 to 7

Table 2 Node information

Number X-coordinate

Y-coordinate Demand Ready

timeDuedate

1 35 35 0 0 2302 41 49 10 161 1713 35 17 7 50 604 55 45 13 116 1265 55 20 19 149 1596 15 30 26 34 447 25 30 3 99 1098 20 50 5 81 919 10 43 9 95 10510 55 60 16 97 10711 30 60 16 124 13412 20 65 12 67 7713 50 35 19 63 7314 30 25 23 159 16915 15 10 20 32 4216 30 5 8 16 7117 10 20 19 75 8518 5 30 2 157 16719 20 40 12 87 9720 15 60 17 76 8621 45 65 9 126 13622 45 20 11 62 7223 45 10 18 97 10724 55 5 29 68 7825 65 35 3 153 16326 65 20 6 172 18227 10 32 0 0 23028 27 47 0 0 23029 40 30 0 0 23030 50 50 0 0 23031 60 10 0 0 230

Table 3 Related results of the test examples

Operation times C N L P

1 740418 4 27208 2372112 761371 4 27804 2544153 776436 3 26293 3814294 758694 4 28075 2669485 728308 4 27061 2238966 756774 3 25858 3629467 759047 3 26997 3617058 749176 4 26934 2314079 760367 3 27103 37248810 746696 3 26306 357825Average 753729 35 26964 305027

Table 4 Sequence of routes when the test examples reaches theoptimal solution

Vehicle Route number1 1ndash14ndash22ndash23ndash24ndash27ndash9ndash12 1ndash7ndash6ndash18ndash17ndash15ndash16ndash28ndash19ndash20ndash13 1ndash3ndash5ndash26ndash25ndash4ndash13ndash28ndash8ndash14 1ndash2ndash21ndash10ndash11ndash12ndash1

0 10 20 30 40 50 60 700

10

20

30

40

50

60

70

1

2

3

4

5

6 7

8

9

1011

12

13

14

1516

17

18

19

2021

22

2324

25

26

27

28

29

30

31

Figure 3 Corresponding route trajectory when the examplereaches the optimal solution

Table 5 Impact of adjusting use cost on results

Operation times N L P

1 2 28125 6036132 2 27501 6646813 2 26850 6809434 2 28149 6021615 2 28076 6722076 2 26862 6450827 2 27284 6257538 2 27415 5855419 2 28566 63446310 2 28063 602555Average 2 27689 631700

Table 6 Impact of adjusting use cost and unit transportation coston results

Operation times N L P

1 2 28125 6524182 2 27501 6646813 2 27241 6992544 2 28149 6021615 2 28123 6679206 2 26862 6593437 2 27284 6257538 2 27415 6323099 2 28538 63446310 2 28063 602555Average 2 27730 644086

Advances in Operations Research 7

indicated an increase of 75 and we can see that thenumber of vehicles has increased significantly is isunderstandable for the change of the penalty cost coeffi-cient increases the penalty cost in the objective function sothe algorithm will tend to find more solutions for vehiclesto serve customers e increase in the number of vehicleswill inevitably lead to a decrease in the average drivingroute length which proves the effectiveness of the algo-rithm again erefore the higher the cost of fines is themore vehicles are required is has led logistics companiesto prepare more vehicles under strict time window con-ditions making the customerrsquos total demand unchanged oreven increased

423 Electricity Replenishment Cost e battery capacity is60 kWh the charging time needs 60min and the powerchange time is 31min e shortest power supply mode isselected erefore when the supplementary power is notmore than half quick charging is preferred Otherwisechoose the battery replacement strategy e charging costper unit time is 1 RMBmin and the cost of single batteryreplacement is 30 RMB Now the cost of power supply isincreasing e charging cost per unit time is 50 RMBminand the cost of single battery replacement is 1500 RMB eresults are shown in Table 8 and the vehicle route when theoptimal solution is reached is shown in Figure 4

It can be seen from Table 8 that after the unit charge costis adjusted from 1 to 50 and the single battery change cost isadjusted from 30 to 1500 after ten runs compared withTable 3 the number of vehicles increased from 4 to 5 ve-hicles indicated an increase of 25 At the same time it canbe seen that the number of charging stations passed inFigure 3 is 3 however the number of charging stationspassed in Figure 4 is 2 Increased costs have drived com-panies to choose more vehicles to avoid charging In ad-dition compared with Table 3 the route length is reduced by06 together with the penalty cost is reduced by 103And the increase in the number of vehicles serving cus-tomers leads to a reduction in the possibility of reducingtime penalties and costs is proves the effectiveness of thealgorithm erefore when the charging facilities are notperfect together with the power replenishment cost is highthe logistics companies tend to use more vehicles to avoidcharging as much as possible

5 Conclusions

At present most of the literature studies use a chargingstrategy and the customer tolerance is not considered whilestudying the customer time windows In this paper thecharging strategy of combining two charging ways isadopted the broken line soft time windows is used con-sidering the customer tolerance and the MILP model of theEVRPTW is finally established And through the calculationexperiment of the Solomon benchmark example the cost ofaffecting the route optimization of electric vehicle is ana-lysed the availability as well as effectiveness of data andalgorithm are proved and the management opinions on thepractical application of MILP model are put forward

(1) e higher the use cost and freight of vehicles are theless the number of vehicles used When the use costand freight of vehicles are much higher than othercosts the vehicle route distribution scheme with theleast number of vehicles is preferred

(2) e higher the penalty cost of time windows is thehigher the number of vehicles used for vehicle dis-tribution is In the case of strict time windows lo-gistics companies need to prepare more vehicles thanthe total demand of customers

Table 7 Impact of adjusting time window penalty costs on results

Operation times N L1 8 279772 7 234703 7 291224 7 245155 6 284256 6 271807 8 265798 6 259409 7 2897610 7 26766Average 69 26895

Table 8 Impact of adjusted electricity supplement costs on results

Operation times N L P

1 4 28415 3492102 5 27377 2099193 5 27284 2372204 5 26824 2601645 5 24432 2244606 5 25166 2644777 4 27103 3498758 5 26605 2281859 4 28159 35634810 5 26555 255216Average 47 26792 273507

0 10 20 30 40 50 60 700

10

20

30

40

50

60

70

1

2

3

4

5

6 7

8

9

101112

13

14

1516

17

18

19

2021

22

2324

25

26

27

28

29

30

31

Figure 4 Vehicle route at high electricity replenishment cost

8 Advances in Operations Research

(3) Logistics companies tend to use more EVs to avoidcharging as much as possible when charging facilitiesare not perfect and the cost of power supply is high

e model can help the logistics enterprises providesome suggestions for the route optimization help to pro-mote the application of EVs in the field of logistics andimprove energy efficiency energy conservation and emis-sion reduction e proposed MILP model is helpful toreduce the logistics cost However the traditional short-comings of VRP still exist in the EVRPTW model Forexample it is still a NP-hard and it is difficult to solve large-scale problems e focus of future research may be todeveloping more effective heuristic algorithm to solve large-scale problems consider the real-time changes of trafficconditions and expand the direction of the dynamic vehicleroute

Data Availability

e data used to support the findings of this study are in-cluded within the article

Conflicts of Interest

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

Acknowledgments

is research was funded by the National Natural ScienceFoundation of China grant no 71471061 and the Funda-mental Research Funds for the Central Universities grantno 2017MS171

References

[1] G B Dantzig and J H Ramser ldquoe truck dispatchingproblemrdquoManagement Science vol 6 no 1 pp 80ndash91 1959

[2] Y Xiao Q Zhao I Kaku and Y Xu ldquoDevelopment of a fuelconsumption optimization model for the capacitated vehiclerouting problemrdquo Computers amp Operations Research vol 39no 7 pp 1419ndash1431 2012

[3] J Zhang Y ZhaoW Xue and J Li ldquoVehicle routing problemwith fuel consumption and carbon emissionrdquo InternationalJournal of Production Economics vol 170 pp 234ndash242 2015

[4] N Norouzi M Sadegh-Amalnick and R Tavakkoli-Mog-haddam ldquoModified particle swarm optimization in a time-dependent vehicle routing problem minimizing fuel con-sumptionrdquo Optimization Letters vol 11 no 1 pp 121ndash1342017

[5] G Poonthalir and R Nadarajan ldquoA fuel efficient green vehiclerouting problem with varying speed constraint (F-GVRP)rdquoExpert Systems with Applications vol 100 pp 131ndash144 2018

[6] J Wang S Yao J Sheng and H Yang ldquoMinimizing totalcarbon emissions in an integrated machine scheduling andvehicle routing problemrdquo Journal of Cleaner Productionvol 229 pp 1004ndash1017 2019

[7] S-C Ma Y Fan J-F Guo J-H Xu and J Zhu ldquoAnalysingonline behaviour to determine Chinese consumersrsquo prefer-ences for electric vehiclesrdquo Journal of Cleaner Productionvol 229 pp 244ndash255 2019

[8] B G Pollet I Staffell and J L Shang ldquoCurrent status ofhybrid battery and fuel cell electric vehicles from electro-chemistry to market prospectsrdquo Electrochimica Acta vol 84pp 235ndash249 2012

[9] G Desaulniers F Errico S Irnich and M Schneider ldquoExactalgorithms for electric vehicle-routing problems with win-dowsrdquo Operations Research vol 64 no 6 pp 1177ndash15652016

[10] R A Fernandez ldquoAmore realistic approach to electric vehiclecontribution to greenhouse gas emissions in the cityrdquo Journalof Cleaner Production vol 172 pp 949ndash959 2018

[11] L C Casals E Martinez-Laserna B A Garcia and N NietoldquoSustainability analysis of the electric vehicle use in Europe forCO2 emissions reductionrdquo Journal of Cleaner Productionvol 127 pp 425ndash437 2016

[12] Z Wu M Wang J Zheng X Sun M Zhao and X WangldquoLife cycle greenhouse gas emission reduction potential ofbattery electric vehiclerdquo Journal of Cleaner Productionvol 190 pp 462ndash470 2018

[13] Y Xiao X Zuo I Kaku S Zhou and X Pan ldquoDevelopmentof energy consumption optimization model for the electricvehicle routing problem with time windowsrdquo Journal ofCleaner Production vol 225 pp 647ndash663 2019

[14] S-N YangW-S Cheng Y-C Hsu C-H Gan and Y-B LinldquoCharge scheduling of electric vehicles in highwaysrdquo Math-ematical and Computer Modelling vol 57 no 11-12pp 2873ndash2882 2013

[15] A Dogan andM Alci ldquoHeuristic optimization of EV chargingschedule considering battery degradation costrdquo Elektronika irElektrotechnika vol 24 no 6 pp 15ndash20 2018

[16] A Dogan S Bahceci F Daldaban and M Alci ldquoOptimi-zation of chargedischarge coordination to satisfy networkrequirements using heuristic algorithms in vehicle-to-gridconceptrdquo Advances in Electrical and Computer Engineeringvol 18 no 1 pp 121ndash130 2018

[17] V Aravinthan and W Jewell ldquoControlled electric vehiclecharging for mitigating impacts on distribution assetsrdquo IEEETransactions on Smart Grid vol 6 no 2 pp 999ndash1009 2015

[18] M Schucking P Jochem W Fichtner O Wollersheim andK Stella ldquoCharging strategies for economic operations ofelectric vehicles in commercial applicationsrdquo TransportationResearch Part D Transport and Environment vol 51pp 173ndash189 2017

[19] J D Adler and P B Mirchandani ldquoOnline routing andbattery reservations for electric vehicles with swappablebatteriesrdquo Transportation Research Part B Methodologicalvol 70 pp 285ndash302 2014

[20] J Yang and H Sun ldquoBattery swap station location-routingproblem with capacitated electric vehiclesrdquo Computers ampOperations Research vol 55 pp 217ndash232 2015

[21] Q Dai T Cai S Duan and F Zhao ldquoStochastic modeling andforecasting of load demand for electric bus battery-swapstationrdquo IEEE Transactions on Power Delivery vol 29 no 4pp 1909ndash1917 2014

[22] D Margaritis A Anagnostopoulou A Tromaras andM Boile ldquoElectric commercial vehicles practical perspectivesand future research directionsrdquo Research in TransportationBusiness amp Management vol 18 pp 4ndash10 2016

[23] MM Solomon and J Desrosiers ldquoSurvey paper-time windowconstrained routing and scheduling problemsrdquo Trans-portation Science vol 22 no 1 pp 1ndash13 1988

[24] A G Qureshi E Taniguchi and T Yamada ldquoAn exact so-lution approach for vehicle routing and scheduling problemswith soft time windowsrdquo Transportation Research Part E

Advances in Operations Research 9

Logistics and Transportation Review vol 45 no 6 pp 960ndash977 2009

[25] D Goeke ldquoGranular tabu search for the pickup and deliveryproblem with time windows and electric vehiclesrdquo EuropeanJournal of Operational Research vol 278 no 3 pp 821ndash8362019

[26] M Keskin and B Ccedilatay ldquoPartial recharge strategies for theelectric vehicle routing problem with time windowsrdquoTransportation Research Part C Emerging Technologiesvol 65 pp 111ndash127 2016

[27] M Schneider A Stenger and D Goeke ldquoe electric vehicle-routing problem with time windows and recharging stationsrdquoTransportation Science vol 48 no 4 pp 500ndash520 2014

[28] G Hiermann J Puchinger S Ropke and R F Hartl ldquoeelectric fleet size and mix vehicle routing problem with timewindows and recharging stationsrdquo European Journal of Op-erational Research vol 252 no 3 pp 995ndash1018 2016

[29] Solomon benchmark problems httpwcbaneuedusimmsolomonr101htm

10 Advances in Operations Research

422 Time Window Penalty Cost Adjust the penalty co-efficient of the time windows from ρ1 1 ρ2 05 ρ3

15 and ρ4 2 to ρ1 5 ρ2 25 ρ3 75 and ρ4 10keep other parameters unchanged repeat the test 10 timesand see Table 7 for the results when the optimal solution isreached

After the penalty cost coefficient increases 5 times thecalculation results are shown in Table 7 e route length isreduced by 03 compared with the result in Table 3 but thenumber of optimal vehicles has increased from 4 to 7

Table 2 Node information

Number X-coordinate

Y-coordinate Demand Ready

timeDuedate

1 35 35 0 0 2302 41 49 10 161 1713 35 17 7 50 604 55 45 13 116 1265 55 20 19 149 1596 15 30 26 34 447 25 30 3 99 1098 20 50 5 81 919 10 43 9 95 10510 55 60 16 97 10711 30 60 16 124 13412 20 65 12 67 7713 50 35 19 63 7314 30 25 23 159 16915 15 10 20 32 4216 30 5 8 16 7117 10 20 19 75 8518 5 30 2 157 16719 20 40 12 87 9720 15 60 17 76 8621 45 65 9 126 13622 45 20 11 62 7223 45 10 18 97 10724 55 5 29 68 7825 65 35 3 153 16326 65 20 6 172 18227 10 32 0 0 23028 27 47 0 0 23029 40 30 0 0 23030 50 50 0 0 23031 60 10 0 0 230

Table 3 Related results of the test examples

Operation times C N L P

1 740418 4 27208 2372112 761371 4 27804 2544153 776436 3 26293 3814294 758694 4 28075 2669485 728308 4 27061 2238966 756774 3 25858 3629467 759047 3 26997 3617058 749176 4 26934 2314079 760367 3 27103 37248810 746696 3 26306 357825Average 753729 35 26964 305027

Table 4 Sequence of routes when the test examples reaches theoptimal solution

Vehicle Route number1 1ndash14ndash22ndash23ndash24ndash27ndash9ndash12 1ndash7ndash6ndash18ndash17ndash15ndash16ndash28ndash19ndash20ndash13 1ndash3ndash5ndash26ndash25ndash4ndash13ndash28ndash8ndash14 1ndash2ndash21ndash10ndash11ndash12ndash1

0 10 20 30 40 50 60 700

10

20

30

40

50

60

70

1

2

3

4

5

6 7

8

9

1011

12

13

14

1516

17

18

19

2021

22

2324

25

26

27

28

29

30

31

Figure 3 Corresponding route trajectory when the examplereaches the optimal solution

Table 5 Impact of adjusting use cost on results

Operation times N L P

1 2 28125 6036132 2 27501 6646813 2 26850 6809434 2 28149 6021615 2 28076 6722076 2 26862 6450827 2 27284 6257538 2 27415 5855419 2 28566 63446310 2 28063 602555Average 2 27689 631700

Table 6 Impact of adjusting use cost and unit transportation coston results

Operation times N L P

1 2 28125 6524182 2 27501 6646813 2 27241 6992544 2 28149 6021615 2 28123 6679206 2 26862 6593437 2 27284 6257538 2 27415 6323099 2 28538 63446310 2 28063 602555Average 2 27730 644086

Advances in Operations Research 7

indicated an increase of 75 and we can see that thenumber of vehicles has increased significantly is isunderstandable for the change of the penalty cost coeffi-cient increases the penalty cost in the objective function sothe algorithm will tend to find more solutions for vehiclesto serve customers e increase in the number of vehicleswill inevitably lead to a decrease in the average drivingroute length which proves the effectiveness of the algo-rithm again erefore the higher the cost of fines is themore vehicles are required is has led logistics companiesto prepare more vehicles under strict time window con-ditions making the customerrsquos total demand unchanged oreven increased

423 Electricity Replenishment Cost e battery capacity is60 kWh the charging time needs 60min and the powerchange time is 31min e shortest power supply mode isselected erefore when the supplementary power is notmore than half quick charging is preferred Otherwisechoose the battery replacement strategy e charging costper unit time is 1 RMBmin and the cost of single batteryreplacement is 30 RMB Now the cost of power supply isincreasing e charging cost per unit time is 50 RMBminand the cost of single battery replacement is 1500 RMB eresults are shown in Table 8 and the vehicle route when theoptimal solution is reached is shown in Figure 4

It can be seen from Table 8 that after the unit charge costis adjusted from 1 to 50 and the single battery change cost isadjusted from 30 to 1500 after ten runs compared withTable 3 the number of vehicles increased from 4 to 5 ve-hicles indicated an increase of 25 At the same time it canbe seen that the number of charging stations passed inFigure 3 is 3 however the number of charging stationspassed in Figure 4 is 2 Increased costs have drived com-panies to choose more vehicles to avoid charging In ad-dition compared with Table 3 the route length is reduced by06 together with the penalty cost is reduced by 103And the increase in the number of vehicles serving cus-tomers leads to a reduction in the possibility of reducingtime penalties and costs is proves the effectiveness of thealgorithm erefore when the charging facilities are notperfect together with the power replenishment cost is highthe logistics companies tend to use more vehicles to avoidcharging as much as possible

5 Conclusions

At present most of the literature studies use a chargingstrategy and the customer tolerance is not considered whilestudying the customer time windows In this paper thecharging strategy of combining two charging ways isadopted the broken line soft time windows is used con-sidering the customer tolerance and the MILP model of theEVRPTW is finally established And through the calculationexperiment of the Solomon benchmark example the cost ofaffecting the route optimization of electric vehicle is ana-lysed the availability as well as effectiveness of data andalgorithm are proved and the management opinions on thepractical application of MILP model are put forward

(1) e higher the use cost and freight of vehicles are theless the number of vehicles used When the use costand freight of vehicles are much higher than othercosts the vehicle route distribution scheme with theleast number of vehicles is preferred

(2) e higher the penalty cost of time windows is thehigher the number of vehicles used for vehicle dis-tribution is In the case of strict time windows lo-gistics companies need to prepare more vehicles thanthe total demand of customers

Table 7 Impact of adjusting time window penalty costs on results

Operation times N L1 8 279772 7 234703 7 291224 7 245155 6 284256 6 271807 8 265798 6 259409 7 2897610 7 26766Average 69 26895

Table 8 Impact of adjusted electricity supplement costs on results

Operation times N L P

1 4 28415 3492102 5 27377 2099193 5 27284 2372204 5 26824 2601645 5 24432 2244606 5 25166 2644777 4 27103 3498758 5 26605 2281859 4 28159 35634810 5 26555 255216Average 47 26792 273507

0 10 20 30 40 50 60 700

10

20

30

40

50

60

70

1

2

3

4

5

6 7

8

9

101112

13

14

1516

17

18

19

2021

22

2324

25

26

27

28

29

30

31

Figure 4 Vehicle route at high electricity replenishment cost

8 Advances in Operations Research

(3) Logistics companies tend to use more EVs to avoidcharging as much as possible when charging facilitiesare not perfect and the cost of power supply is high

e model can help the logistics enterprises providesome suggestions for the route optimization help to pro-mote the application of EVs in the field of logistics andimprove energy efficiency energy conservation and emis-sion reduction e proposed MILP model is helpful toreduce the logistics cost However the traditional short-comings of VRP still exist in the EVRPTW model Forexample it is still a NP-hard and it is difficult to solve large-scale problems e focus of future research may be todeveloping more effective heuristic algorithm to solve large-scale problems consider the real-time changes of trafficconditions and expand the direction of the dynamic vehicleroute

Data Availability

e data used to support the findings of this study are in-cluded within the article

Conflicts of Interest

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

Acknowledgments

is research was funded by the National Natural ScienceFoundation of China grant no 71471061 and the Funda-mental Research Funds for the Central Universities grantno 2017MS171

References

[1] G B Dantzig and J H Ramser ldquoe truck dispatchingproblemrdquoManagement Science vol 6 no 1 pp 80ndash91 1959

[2] Y Xiao Q Zhao I Kaku and Y Xu ldquoDevelopment of a fuelconsumption optimization model for the capacitated vehiclerouting problemrdquo Computers amp Operations Research vol 39no 7 pp 1419ndash1431 2012

[3] J Zhang Y ZhaoW Xue and J Li ldquoVehicle routing problemwith fuel consumption and carbon emissionrdquo InternationalJournal of Production Economics vol 170 pp 234ndash242 2015

[4] N Norouzi M Sadegh-Amalnick and R Tavakkoli-Mog-haddam ldquoModified particle swarm optimization in a time-dependent vehicle routing problem minimizing fuel con-sumptionrdquo Optimization Letters vol 11 no 1 pp 121ndash1342017

[5] G Poonthalir and R Nadarajan ldquoA fuel efficient green vehiclerouting problem with varying speed constraint (F-GVRP)rdquoExpert Systems with Applications vol 100 pp 131ndash144 2018

[6] J Wang S Yao J Sheng and H Yang ldquoMinimizing totalcarbon emissions in an integrated machine scheduling andvehicle routing problemrdquo Journal of Cleaner Productionvol 229 pp 1004ndash1017 2019

[7] S-C Ma Y Fan J-F Guo J-H Xu and J Zhu ldquoAnalysingonline behaviour to determine Chinese consumersrsquo prefer-ences for electric vehiclesrdquo Journal of Cleaner Productionvol 229 pp 244ndash255 2019

[8] B G Pollet I Staffell and J L Shang ldquoCurrent status ofhybrid battery and fuel cell electric vehicles from electro-chemistry to market prospectsrdquo Electrochimica Acta vol 84pp 235ndash249 2012

[9] G Desaulniers F Errico S Irnich and M Schneider ldquoExactalgorithms for electric vehicle-routing problems with win-dowsrdquo Operations Research vol 64 no 6 pp 1177ndash15652016

[10] R A Fernandez ldquoAmore realistic approach to electric vehiclecontribution to greenhouse gas emissions in the cityrdquo Journalof Cleaner Production vol 172 pp 949ndash959 2018

[11] L C Casals E Martinez-Laserna B A Garcia and N NietoldquoSustainability analysis of the electric vehicle use in Europe forCO2 emissions reductionrdquo Journal of Cleaner Productionvol 127 pp 425ndash437 2016

[12] Z Wu M Wang J Zheng X Sun M Zhao and X WangldquoLife cycle greenhouse gas emission reduction potential ofbattery electric vehiclerdquo Journal of Cleaner Productionvol 190 pp 462ndash470 2018

[13] Y Xiao X Zuo I Kaku S Zhou and X Pan ldquoDevelopmentof energy consumption optimization model for the electricvehicle routing problem with time windowsrdquo Journal ofCleaner Production vol 225 pp 647ndash663 2019

[14] S-N YangW-S Cheng Y-C Hsu C-H Gan and Y-B LinldquoCharge scheduling of electric vehicles in highwaysrdquo Math-ematical and Computer Modelling vol 57 no 11-12pp 2873ndash2882 2013

[15] A Dogan andM Alci ldquoHeuristic optimization of EV chargingschedule considering battery degradation costrdquo Elektronika irElektrotechnika vol 24 no 6 pp 15ndash20 2018

[16] A Dogan S Bahceci F Daldaban and M Alci ldquoOptimi-zation of chargedischarge coordination to satisfy networkrequirements using heuristic algorithms in vehicle-to-gridconceptrdquo Advances in Electrical and Computer Engineeringvol 18 no 1 pp 121ndash130 2018

[17] V Aravinthan and W Jewell ldquoControlled electric vehiclecharging for mitigating impacts on distribution assetsrdquo IEEETransactions on Smart Grid vol 6 no 2 pp 999ndash1009 2015

[18] M Schucking P Jochem W Fichtner O Wollersheim andK Stella ldquoCharging strategies for economic operations ofelectric vehicles in commercial applicationsrdquo TransportationResearch Part D Transport and Environment vol 51pp 173ndash189 2017

[19] J D Adler and P B Mirchandani ldquoOnline routing andbattery reservations for electric vehicles with swappablebatteriesrdquo Transportation Research Part B Methodologicalvol 70 pp 285ndash302 2014

[20] J Yang and H Sun ldquoBattery swap station location-routingproblem with capacitated electric vehiclesrdquo Computers ampOperations Research vol 55 pp 217ndash232 2015

[21] Q Dai T Cai S Duan and F Zhao ldquoStochastic modeling andforecasting of load demand for electric bus battery-swapstationrdquo IEEE Transactions on Power Delivery vol 29 no 4pp 1909ndash1917 2014

[22] D Margaritis A Anagnostopoulou A Tromaras andM Boile ldquoElectric commercial vehicles practical perspectivesand future research directionsrdquo Research in TransportationBusiness amp Management vol 18 pp 4ndash10 2016

[23] MM Solomon and J Desrosiers ldquoSurvey paper-time windowconstrained routing and scheduling problemsrdquo Trans-portation Science vol 22 no 1 pp 1ndash13 1988

[24] A G Qureshi E Taniguchi and T Yamada ldquoAn exact so-lution approach for vehicle routing and scheduling problemswith soft time windowsrdquo Transportation Research Part E

Advances in Operations Research 9

Logistics and Transportation Review vol 45 no 6 pp 960ndash977 2009

[25] D Goeke ldquoGranular tabu search for the pickup and deliveryproblem with time windows and electric vehiclesrdquo EuropeanJournal of Operational Research vol 278 no 3 pp 821ndash8362019

[26] M Keskin and B Ccedilatay ldquoPartial recharge strategies for theelectric vehicle routing problem with time windowsrdquoTransportation Research Part C Emerging Technologiesvol 65 pp 111ndash127 2016

[27] M Schneider A Stenger and D Goeke ldquoe electric vehicle-routing problem with time windows and recharging stationsrdquoTransportation Science vol 48 no 4 pp 500ndash520 2014

[28] G Hiermann J Puchinger S Ropke and R F Hartl ldquoeelectric fleet size and mix vehicle routing problem with timewindows and recharging stationsrdquo European Journal of Op-erational Research vol 252 no 3 pp 995ndash1018 2016

[29] Solomon benchmark problems httpwcbaneuedusimmsolomonr101htm

10 Advances in Operations Research

indicated an increase of 75 and we can see that thenumber of vehicles has increased significantly is isunderstandable for the change of the penalty cost coeffi-cient increases the penalty cost in the objective function sothe algorithm will tend to find more solutions for vehiclesto serve customers e increase in the number of vehicleswill inevitably lead to a decrease in the average drivingroute length which proves the effectiveness of the algo-rithm again erefore the higher the cost of fines is themore vehicles are required is has led logistics companiesto prepare more vehicles under strict time window con-ditions making the customerrsquos total demand unchanged oreven increased

423 Electricity Replenishment Cost e battery capacity is60 kWh the charging time needs 60min and the powerchange time is 31min e shortest power supply mode isselected erefore when the supplementary power is notmore than half quick charging is preferred Otherwisechoose the battery replacement strategy e charging costper unit time is 1 RMBmin and the cost of single batteryreplacement is 30 RMB Now the cost of power supply isincreasing e charging cost per unit time is 50 RMBminand the cost of single battery replacement is 1500 RMB eresults are shown in Table 8 and the vehicle route when theoptimal solution is reached is shown in Figure 4

It can be seen from Table 8 that after the unit charge costis adjusted from 1 to 50 and the single battery change cost isadjusted from 30 to 1500 after ten runs compared withTable 3 the number of vehicles increased from 4 to 5 ve-hicles indicated an increase of 25 At the same time it canbe seen that the number of charging stations passed inFigure 3 is 3 however the number of charging stationspassed in Figure 4 is 2 Increased costs have drived com-panies to choose more vehicles to avoid charging In ad-dition compared with Table 3 the route length is reduced by06 together with the penalty cost is reduced by 103And the increase in the number of vehicles serving cus-tomers leads to a reduction in the possibility of reducingtime penalties and costs is proves the effectiveness of thealgorithm erefore when the charging facilities are notperfect together with the power replenishment cost is highthe logistics companies tend to use more vehicles to avoidcharging as much as possible

5 Conclusions

At present most of the literature studies use a chargingstrategy and the customer tolerance is not considered whilestudying the customer time windows In this paper thecharging strategy of combining two charging ways isadopted the broken line soft time windows is used con-sidering the customer tolerance and the MILP model of theEVRPTW is finally established And through the calculationexperiment of the Solomon benchmark example the cost ofaffecting the route optimization of electric vehicle is ana-lysed the availability as well as effectiveness of data andalgorithm are proved and the management opinions on thepractical application of MILP model are put forward

(1) e higher the use cost and freight of vehicles are theless the number of vehicles used When the use costand freight of vehicles are much higher than othercosts the vehicle route distribution scheme with theleast number of vehicles is preferred

(2) e higher the penalty cost of time windows is thehigher the number of vehicles used for vehicle dis-tribution is In the case of strict time windows lo-gistics companies need to prepare more vehicles thanthe total demand of customers

Table 7 Impact of adjusting time window penalty costs on results

Operation times N L1 8 279772 7 234703 7 291224 7 245155 6 284256 6 271807 8 265798 6 259409 7 2897610 7 26766Average 69 26895

Table 8 Impact of adjusted electricity supplement costs on results

Operation times N L P

1 4 28415 3492102 5 27377 2099193 5 27284 2372204 5 26824 2601645 5 24432 2244606 5 25166 2644777 4 27103 3498758 5 26605 2281859 4 28159 35634810 5 26555 255216Average 47 26792 273507

0 10 20 30 40 50 60 700

10

20

30

40

50

60

70

1

2

3

4

5

6 7

8

9

101112

13

14

1516

17

18

19

2021

22

2324

25

26

27

28

29

30

31

Figure 4 Vehicle route at high electricity replenishment cost

8 Advances in Operations Research

(3) Logistics companies tend to use more EVs to avoidcharging as much as possible when charging facilitiesare not perfect and the cost of power supply is high

e model can help the logistics enterprises providesome suggestions for the route optimization help to pro-mote the application of EVs in the field of logistics andimprove energy efficiency energy conservation and emis-sion reduction e proposed MILP model is helpful toreduce the logistics cost However the traditional short-comings of VRP still exist in the EVRPTW model Forexample it is still a NP-hard and it is difficult to solve large-scale problems e focus of future research may be todeveloping more effective heuristic algorithm to solve large-scale problems consider the real-time changes of trafficconditions and expand the direction of the dynamic vehicleroute

Data Availability

e data used to support the findings of this study are in-cluded within the article

Conflicts of Interest

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

Acknowledgments

is research was funded by the National Natural ScienceFoundation of China grant no 71471061 and the Funda-mental Research Funds for the Central Universities grantno 2017MS171

References

[1] G B Dantzig and J H Ramser ldquoe truck dispatchingproblemrdquoManagement Science vol 6 no 1 pp 80ndash91 1959

[2] Y Xiao Q Zhao I Kaku and Y Xu ldquoDevelopment of a fuelconsumption optimization model for the capacitated vehiclerouting problemrdquo Computers amp Operations Research vol 39no 7 pp 1419ndash1431 2012

[3] J Zhang Y ZhaoW Xue and J Li ldquoVehicle routing problemwith fuel consumption and carbon emissionrdquo InternationalJournal of Production Economics vol 170 pp 234ndash242 2015

[4] N Norouzi M Sadegh-Amalnick and R Tavakkoli-Mog-haddam ldquoModified particle swarm optimization in a time-dependent vehicle routing problem minimizing fuel con-sumptionrdquo Optimization Letters vol 11 no 1 pp 121ndash1342017

[5] G Poonthalir and R Nadarajan ldquoA fuel efficient green vehiclerouting problem with varying speed constraint (F-GVRP)rdquoExpert Systems with Applications vol 100 pp 131ndash144 2018

[6] J Wang S Yao J Sheng and H Yang ldquoMinimizing totalcarbon emissions in an integrated machine scheduling andvehicle routing problemrdquo Journal of Cleaner Productionvol 229 pp 1004ndash1017 2019

[7] S-C Ma Y Fan J-F Guo J-H Xu and J Zhu ldquoAnalysingonline behaviour to determine Chinese consumersrsquo prefer-ences for electric vehiclesrdquo Journal of Cleaner Productionvol 229 pp 244ndash255 2019

[8] B G Pollet I Staffell and J L Shang ldquoCurrent status ofhybrid battery and fuel cell electric vehicles from electro-chemistry to market prospectsrdquo Electrochimica Acta vol 84pp 235ndash249 2012

[9] G Desaulniers F Errico S Irnich and M Schneider ldquoExactalgorithms for electric vehicle-routing problems with win-dowsrdquo Operations Research vol 64 no 6 pp 1177ndash15652016

[10] R A Fernandez ldquoAmore realistic approach to electric vehiclecontribution to greenhouse gas emissions in the cityrdquo Journalof Cleaner Production vol 172 pp 949ndash959 2018

[11] L C Casals E Martinez-Laserna B A Garcia and N NietoldquoSustainability analysis of the electric vehicle use in Europe forCO2 emissions reductionrdquo Journal of Cleaner Productionvol 127 pp 425ndash437 2016

[12] Z Wu M Wang J Zheng X Sun M Zhao and X WangldquoLife cycle greenhouse gas emission reduction potential ofbattery electric vehiclerdquo Journal of Cleaner Productionvol 190 pp 462ndash470 2018

[13] Y Xiao X Zuo I Kaku S Zhou and X Pan ldquoDevelopmentof energy consumption optimization model for the electricvehicle routing problem with time windowsrdquo Journal ofCleaner Production vol 225 pp 647ndash663 2019

[14] S-N YangW-S Cheng Y-C Hsu C-H Gan and Y-B LinldquoCharge scheduling of electric vehicles in highwaysrdquo Math-ematical and Computer Modelling vol 57 no 11-12pp 2873ndash2882 2013

[15] A Dogan andM Alci ldquoHeuristic optimization of EV chargingschedule considering battery degradation costrdquo Elektronika irElektrotechnika vol 24 no 6 pp 15ndash20 2018

[16] A Dogan S Bahceci F Daldaban and M Alci ldquoOptimi-zation of chargedischarge coordination to satisfy networkrequirements using heuristic algorithms in vehicle-to-gridconceptrdquo Advances in Electrical and Computer Engineeringvol 18 no 1 pp 121ndash130 2018

[17] V Aravinthan and W Jewell ldquoControlled electric vehiclecharging for mitigating impacts on distribution assetsrdquo IEEETransactions on Smart Grid vol 6 no 2 pp 999ndash1009 2015

[18] M Schucking P Jochem W Fichtner O Wollersheim andK Stella ldquoCharging strategies for economic operations ofelectric vehicles in commercial applicationsrdquo TransportationResearch Part D Transport and Environment vol 51pp 173ndash189 2017

[19] J D Adler and P B Mirchandani ldquoOnline routing andbattery reservations for electric vehicles with swappablebatteriesrdquo Transportation Research Part B Methodologicalvol 70 pp 285ndash302 2014

[20] J Yang and H Sun ldquoBattery swap station location-routingproblem with capacitated electric vehiclesrdquo Computers ampOperations Research vol 55 pp 217ndash232 2015

[21] Q Dai T Cai S Duan and F Zhao ldquoStochastic modeling andforecasting of load demand for electric bus battery-swapstationrdquo IEEE Transactions on Power Delivery vol 29 no 4pp 1909ndash1917 2014

[22] D Margaritis A Anagnostopoulou A Tromaras andM Boile ldquoElectric commercial vehicles practical perspectivesand future research directionsrdquo Research in TransportationBusiness amp Management vol 18 pp 4ndash10 2016

[23] MM Solomon and J Desrosiers ldquoSurvey paper-time windowconstrained routing and scheduling problemsrdquo Trans-portation Science vol 22 no 1 pp 1ndash13 1988

[24] A G Qureshi E Taniguchi and T Yamada ldquoAn exact so-lution approach for vehicle routing and scheduling problemswith soft time windowsrdquo Transportation Research Part E

Advances in Operations Research 9

Logistics and Transportation Review vol 45 no 6 pp 960ndash977 2009

[25] D Goeke ldquoGranular tabu search for the pickup and deliveryproblem with time windows and electric vehiclesrdquo EuropeanJournal of Operational Research vol 278 no 3 pp 821ndash8362019

[26] M Keskin and B Ccedilatay ldquoPartial recharge strategies for theelectric vehicle routing problem with time windowsrdquoTransportation Research Part C Emerging Technologiesvol 65 pp 111ndash127 2016

[27] M Schneider A Stenger and D Goeke ldquoe electric vehicle-routing problem with time windows and recharging stationsrdquoTransportation Science vol 48 no 4 pp 500ndash520 2014

[28] G Hiermann J Puchinger S Ropke and R F Hartl ldquoeelectric fleet size and mix vehicle routing problem with timewindows and recharging stationsrdquo European Journal of Op-erational Research vol 252 no 3 pp 995ndash1018 2016

[29] Solomon benchmark problems httpwcbaneuedusimmsolomonr101htm

10 Advances in Operations Research

(3) Logistics companies tend to use more EVs to avoidcharging as much as possible when charging facilitiesare not perfect and the cost of power supply is high

e model can help the logistics enterprises providesome suggestions for the route optimization help to pro-mote the application of EVs in the field of logistics andimprove energy efficiency energy conservation and emis-sion reduction e proposed MILP model is helpful toreduce the logistics cost However the traditional short-comings of VRP still exist in the EVRPTW model Forexample it is still a NP-hard and it is difficult to solve large-scale problems e focus of future research may be todeveloping more effective heuristic algorithm to solve large-scale problems consider the real-time changes of trafficconditions and expand the direction of the dynamic vehicleroute

Data Availability

e data used to support the findings of this study are in-cluded within the article

Conflicts of Interest

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

Acknowledgments

is research was funded by the National Natural ScienceFoundation of China grant no 71471061 and the Funda-mental Research Funds for the Central Universities grantno 2017MS171

References

[1] G B Dantzig and J H Ramser ldquoe truck dispatchingproblemrdquoManagement Science vol 6 no 1 pp 80ndash91 1959

[2] Y Xiao Q Zhao I Kaku and Y Xu ldquoDevelopment of a fuelconsumption optimization model for the capacitated vehiclerouting problemrdquo Computers amp Operations Research vol 39no 7 pp 1419ndash1431 2012

[3] J Zhang Y ZhaoW Xue and J Li ldquoVehicle routing problemwith fuel consumption and carbon emissionrdquo InternationalJournal of Production Economics vol 170 pp 234ndash242 2015

[4] N Norouzi M Sadegh-Amalnick and R Tavakkoli-Mog-haddam ldquoModified particle swarm optimization in a time-dependent vehicle routing problem minimizing fuel con-sumptionrdquo Optimization Letters vol 11 no 1 pp 121ndash1342017

[5] G Poonthalir and R Nadarajan ldquoA fuel efficient green vehiclerouting problem with varying speed constraint (F-GVRP)rdquoExpert Systems with Applications vol 100 pp 131ndash144 2018

[6] J Wang S Yao J Sheng and H Yang ldquoMinimizing totalcarbon emissions in an integrated machine scheduling andvehicle routing problemrdquo Journal of Cleaner Productionvol 229 pp 1004ndash1017 2019

[7] S-C Ma Y Fan J-F Guo J-H Xu and J Zhu ldquoAnalysingonline behaviour to determine Chinese consumersrsquo prefer-ences for electric vehiclesrdquo Journal of Cleaner Productionvol 229 pp 244ndash255 2019

[8] B G Pollet I Staffell and J L Shang ldquoCurrent status ofhybrid battery and fuel cell electric vehicles from electro-chemistry to market prospectsrdquo Electrochimica Acta vol 84pp 235ndash249 2012

[9] G Desaulniers F Errico S Irnich and M Schneider ldquoExactalgorithms for electric vehicle-routing problems with win-dowsrdquo Operations Research vol 64 no 6 pp 1177ndash15652016

[10] R A Fernandez ldquoAmore realistic approach to electric vehiclecontribution to greenhouse gas emissions in the cityrdquo Journalof Cleaner Production vol 172 pp 949ndash959 2018

[11] L C Casals E Martinez-Laserna B A Garcia and N NietoldquoSustainability analysis of the electric vehicle use in Europe forCO2 emissions reductionrdquo Journal of Cleaner Productionvol 127 pp 425ndash437 2016

[12] Z Wu M Wang J Zheng X Sun M Zhao and X WangldquoLife cycle greenhouse gas emission reduction potential ofbattery electric vehiclerdquo Journal of Cleaner Productionvol 190 pp 462ndash470 2018

[13] Y Xiao X Zuo I Kaku S Zhou and X Pan ldquoDevelopmentof energy consumption optimization model for the electricvehicle routing problem with time windowsrdquo Journal ofCleaner Production vol 225 pp 647ndash663 2019

[14] S-N YangW-S Cheng Y-C Hsu C-H Gan and Y-B LinldquoCharge scheduling of electric vehicles in highwaysrdquo Math-ematical and Computer Modelling vol 57 no 11-12pp 2873ndash2882 2013

[15] A Dogan andM Alci ldquoHeuristic optimization of EV chargingschedule considering battery degradation costrdquo Elektronika irElektrotechnika vol 24 no 6 pp 15ndash20 2018

[16] A Dogan S Bahceci F Daldaban and M Alci ldquoOptimi-zation of chargedischarge coordination to satisfy networkrequirements using heuristic algorithms in vehicle-to-gridconceptrdquo Advances in Electrical and Computer Engineeringvol 18 no 1 pp 121ndash130 2018

[17] V Aravinthan and W Jewell ldquoControlled electric vehiclecharging for mitigating impacts on distribution assetsrdquo IEEETransactions on Smart Grid vol 6 no 2 pp 999ndash1009 2015

[18] M Schucking P Jochem W Fichtner O Wollersheim andK Stella ldquoCharging strategies for economic operations ofelectric vehicles in commercial applicationsrdquo TransportationResearch Part D Transport and Environment vol 51pp 173ndash189 2017

[19] J D Adler and P B Mirchandani ldquoOnline routing andbattery reservations for electric vehicles with swappablebatteriesrdquo Transportation Research Part B Methodologicalvol 70 pp 285ndash302 2014

[20] J Yang and H Sun ldquoBattery swap station location-routingproblem with capacitated electric vehiclesrdquo Computers ampOperations Research vol 55 pp 217ndash232 2015

[21] Q Dai T Cai S Duan and F Zhao ldquoStochastic modeling andforecasting of load demand for electric bus battery-swapstationrdquo IEEE Transactions on Power Delivery vol 29 no 4pp 1909ndash1917 2014

[22] D Margaritis A Anagnostopoulou A Tromaras andM Boile ldquoElectric commercial vehicles practical perspectivesand future research directionsrdquo Research in TransportationBusiness amp Management vol 18 pp 4ndash10 2016

[23] MM Solomon and J Desrosiers ldquoSurvey paper-time windowconstrained routing and scheduling problemsrdquo Trans-portation Science vol 22 no 1 pp 1ndash13 1988

[24] A G Qureshi E Taniguchi and T Yamada ldquoAn exact so-lution approach for vehicle routing and scheduling problemswith soft time windowsrdquo Transportation Research Part E

Advances in Operations Research 9

Logistics and Transportation Review vol 45 no 6 pp 960ndash977 2009

[25] D Goeke ldquoGranular tabu search for the pickup and deliveryproblem with time windows and electric vehiclesrdquo EuropeanJournal of Operational Research vol 278 no 3 pp 821ndash8362019

[26] M Keskin and B Ccedilatay ldquoPartial recharge strategies for theelectric vehicle routing problem with time windowsrdquoTransportation Research Part C Emerging Technologiesvol 65 pp 111ndash127 2016

[27] M Schneider A Stenger and D Goeke ldquoe electric vehicle-routing problem with time windows and recharging stationsrdquoTransportation Science vol 48 no 4 pp 500ndash520 2014

[28] G Hiermann J Puchinger S Ropke and R F Hartl ldquoeelectric fleet size and mix vehicle routing problem with timewindows and recharging stationsrdquo European Journal of Op-erational Research vol 252 no 3 pp 995ndash1018 2016

[29] Solomon benchmark problems httpwcbaneuedusimmsolomonr101htm

10 Advances in Operations Research

Logistics and Transportation Review vol 45 no 6 pp 960ndash977 2009

[25] D Goeke ldquoGranular tabu search for the pickup and deliveryproblem with time windows and electric vehiclesrdquo EuropeanJournal of Operational Research vol 278 no 3 pp 821ndash8362019

[26] M Keskin and B Ccedilatay ldquoPartial recharge strategies for theelectric vehicle routing problem with time windowsrdquoTransportation Research Part C Emerging Technologiesvol 65 pp 111ndash127 2016

[27] M Schneider A Stenger and D Goeke ldquoe electric vehicle-routing problem with time windows and recharging stationsrdquoTransportation Science vol 48 no 4 pp 500ndash520 2014

[28] G Hiermann J Puchinger S Ropke and R F Hartl ldquoeelectric fleet size and mix vehicle routing problem with timewindows and recharging stationsrdquo European Journal of Op-erational Research vol 252 no 3 pp 995ndash1018 2016

[29] Solomon benchmark problems httpwcbaneuedusimmsolomonr101htm

10 Advances in Operations Research