Proactive Two-Level Dynamic Distribution Routing Optimization …downloads.hindawi.com/journals/mpe/2018/5191637.pdf · 2,7 3) is the predicted value of the customer attribute using

Research ArticleProactive Two-Level Dynamic Distribution RoutingOptimization Based on Historical Data

Xianlong Ge 12 Guiqin Xue 1 and PengzheWen1

1School of Economics and Management Chongqing Jiaotong University Chongqing 400074 China2Key Laboratory of Intelligent Logistics Network Chongqing 400074 China

Correspondence should be addressed to Xianlong Ge gexianlongcqjtueducn and Guiqin Xue xuegqmail126com

Received 27 April 2018 Revised 24 September 2018 Accepted 30 October 2018 Published 21 November 2018

Academic Editor Konstantina Skouri

Copyright copy 2018 Xianlong Ge et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

In view of the dynamic dispersion of e-commerce logistics demand this paper uses the historical distribution data of logisticscompanies to study data-driven proactive vehicle routing optimization First based on the classic 2E-VRP problem a single-nodemultistage 2E-VRP mathematical model is constructed Then a framework for solving the proactive vehicle routingoptimization problem is proposed in combination with the characteristics of the proposed model including four modules data-driven demand forecasting methods customer clustering methods proactive demand quotas and replenishment strategies andvehicle routing optimization procedureThe significant feature of the proposed solution framework is that the response to dynamiccustomers is proactive rather than passive The solution is applied to the distribution practice of a large logistics company inChongqing The results show that the proposed method has better dynamic scene adaptability and customer response capabilitiesin traffic limit

1 Introduction

With the rise of cloud computing and big data technolo-gies the role of data-driven decision-making in commercialoperations has become increasingly prominent and providestechnical guidance to traditional distribution enterprisesfromapractical perspective At the same time the continuousimprovement of the Internet infrastructure also provides areliable source of data for business decision-making butmassive data has also led to data disasters to a certain extentOn the one hand diversification of data acquisition meansthat distribution enterprises can obtain customer data veryconveniently and tap customer potential based on the dataobtained to change or reshape customerrsquos demand behavioron the other hand even in a short period of time the amountof data gathered by large enterprises is staggering whichposes a serious challenge for data cleaning and data miningFor example the gradual opening of some cloud computingplatforms and tools such as Amazon Cloud and AlibabaCloud enables SMEs to take advantage of the powerful com-puting power of these cloud computing platforms to rapidlyrespond to changing market demands and shorten the lead

time of ordering so that the inconvenience of their customersrsquodemand for goods isminimized However in the distributionprocess enterprises can achieve proactive demand responseif we can tap out the potential law of dynamic demandoptimizing the allocation of existing logistics resources

Vehicle routing problem is one of the most extensiveand in-depth combinatorial optimization problems In recentyears the development of e-commerce has led to the trendof decentralization of demand dynamics which makes thesolution of vehicle routing problems more complicated (see[1ndash4]) In addition the vehicle restriction strategy is prevalentin major cities around the world Therefore in the currenturban distribution process vehicles with heavy loads areoften used to transport goods to the urban edge areas andtransport to smaller cities by vehicles with smaller loads tomeet the needs of the peoplersquos daily lives which led to theresearch on the two-level dynamic vehicle routing problem[5 6] However this strategy often neglects some potentialdynamic customers and lacks practical consideration

In this paper we propose a two-echelon proactive vehiclerouting problem based on the proactive scheduling methodwhich is one of the expanding problems of dynamic vehicle

HindawiMathematical Problems in EngineeringVolume 2018 Article ID 5191637 15 pageshttpsdoiorg10115520185191637

2 Mathematical Problems in Engineering

routing problem [7ndash9] 2E-PVRP generates a priori knowl-edge of dynamic customer changes based on the customerdata obtained by the delivery companies and uses the priorknowledge to process the dynamic demand informationduring the distribution process to form a robust vehiclescheduling solution Due to the complexity of the questionsraised this paper divides the solution into four modulesdata driven demand forecasting methods customer cluster-ing methods proactive demand quotas and replenishmentstrategies and vehicle routing optimization programs Thedata driven demand forecasting methods mainly excludesthe gross error points in the original data selects theappropriate measure dimension to evaluate the change ofcustomer attributes and then predicts the dynamic demandtrend The customer clustering methods will determine thecustomers who meet a certain distribution into the samecluster mainly based on the dynamic customer forecastingresults and static customer data The proactive demandquotas and replenishment strategies mainly evaluate thestatistical characteristics of customer needs in the clusterand allocate the distribution quotas of each stage reasonablyThe vehicle routing optimization program mainly adoptsthe exact or approximate path optimization algorithm togenerate the optimal delivery path plan for each clusterarea at different distribution stages To better illustrate thefeasibility of the framework system studied in this paper inview of the problems neglected by the current distributionenterprises this paper uses the logistics and distribution dataof large logistics company in Chongqing to test the proposedsolution The test results show that the solution has shownbetter results

The structure of the article is as follows In the secondpart the paper introduces the development of the vehiclerouting problem and its extension problem The third part isthe mathematical model of the problem The fourth part isthe realization process of the solution framework The fifthpart is the use of the enterprise empirical research data thesixth part is obtaining the management inspiration and theseventh part is the summary and future work

2 Literature Review

At present many scholars at home and abroad have made agreat deal of research on the 2E-VRP problem Among themdemand forecasting customer clusteringmethod and vehiclerouting solving algorithm in dynamic vehicle scheduling areclosely related to this paper Dynamic customer processingin dynamic vehicle routing has always been the focus ofresearch Wood [10] uses the three indicators of orderquantity order variation rate and order frequency as themeasure and uses the piecewise linear model to evaluatethe reliability of the demand forecast based on the dataThe test results show that in the case of small number oforders small differences in order quantity and lower orderfrequency the use of point-of-sale real-time shared data canachieve better forecasting results which is provided in thispaper by using multidimensional customer attribute datato predict dynamic customer demand Data-driven demandforecasting methods as an effective forecasting strategy are

also widely used by scholars Thomas [11] designed a real-time heuristic algorithm to predict future customer locationsand the probability of occurrence of demand resulting ina significant reduction in customer service latency Lima[12] takes customer needs and businesses on their own toleverage historical data and online data monitoring to antici-pate customer needs and improve customer responsivenessCabello [13] designed low cost forecasting algorithm foruncertain demand tomanage bank cash flow Jan [14] andMa[15] anticipate changes in customer demand in advance byconsidering demand forecasting and inventory control Sha[16] anticipates clientsrsquo expected waiting times significantlyusing historical demand data to proactively anticipate sparepart demand Willemai [17] and Porras [18] argue that inthe case of limited demand data sets the demand extreme(suddenly a large or small value) is unpredictable and thedemand dynamics affect the demand forecasting effect Inthis paper we propose a proactive demand quota method tosolve the failure of demand forecasting by using the strategyof multibatch and small-batch delivery That is to say acomplete service cycle is divided into initial delivery stage andmultiple replenishment stages If there is an extreme demandand a failure forecasting in the initial stage the shortfall ofdemandwill be supplemented through the late replenishmentphase to avoid the serious consequences of the forecastfailure

After acquiring the prior knowledge of dynamic clientsby using data-driven forecasting methods they need to bemerged with the original delivery customers to determine thecustomer base to be served during the full-service periodThe customer clustering method is to classify customers withsimilar attributes into the same type of clusters according toa certain rule and classify the clients with large differences inattributes into different clusters so as to realize the classifi-cation of customer behaviors Due to the effective customerclustering scheme in reducing logistics costs and improvingthe quality of service many scholars have adopted thestrategy of ldquoplanning route after clusteringrdquo to optimize thevehicle routing The authors in [19ndash25] analyzed the problemof service area allocation in the dynamic vehicle problemwithstochastic demand Ferrucci [26] assumed that the dynamiccustomer demand obeys Poisson distribution and dividedone cycle of distribution activities into several smaller gridsareas and calculated the Poisson distribution parametersof each grid area in different distribution stages Since thePoisson distribution parameters in the single grid area aresmall and cannot meet the delivery requirements the authoruses the maximum roaming radius and roaming time criteriato cluster the service subareas and optimize the distributionnetwork path The results show that the proactive schedul-ing method can effectively improve customer satisfactionFerrucci [27] expanded the space-time Poisson distributionmodelWang [28] discussed the customer clustering problemin 2E-VRP assumed that the location of Tier 1 and Tier 2facilities is determined and the customers are clustered intoa Tier 2 facility according to the set evaluation criteria Onthis basis this paper determines the waiting customer groupbased on the data-driven forecasting method and clusters thecustomer group to determine the service customer group of

Mathematical Problems in Engineering 3

each secondary facility so as to optimize the delivery route ofthe entire distribution system

The proactive two-level dynamic routing optimizationproblem studied in this paper belongs to the crossoverproblem of dynamic vehicle routing problem and secondarynetwork vehicle routing problem The above three problemsare unable to get a reasonable solution in polynomial timewhich is a typical NP-hard problem However the problemin this paper is more difficult to solve than the aboveproblem For the vehicle routing optimization problem themain problem is whether to use the exact algorithm orthe approximate algorithm For an introduction of VRPrsquosexact solution algorithm see [29ndash31] Santos [32] proposedbranch and bound algorithm and its solution to the weightedaverage method proposed by Santos [33] and Sahraeian anextended version of 2E-VRP that includes two optimizationgoals environmental costs and service satisfaction Howeverthe exact solution to the algorithm has poor adaptability tothe customer scale so the approximate solution algorithmis more favored by scholars when the problem scale islarger Commonly used approximate solution algorithmsinclude large neighborhood search algorithm [19 20 34]genetic algorithm [35] tabu search algorithm [36] simulatedannealing algorithm and ant colony algorithm Alonso [37]developed a tabu search algorithm to solve the multivehi-cle routing problem Maischberger [38] added perturbationmechanism to tabu search algorithm and used multicoreparallel technology both ensuring the diversity and opti-mization ability of algorithms and improving the efficiencyof solving Silvestrin [39] embedded tabu search algorithmsin iterative local search algorithms for better computationalresults Inspired by this considering that genetic algorithmhas a strong global search capability premature algorithmmay exist Tabu search algorithm has better local searchability but its solution performance is greatly affected byinitial solution Therefore the genetic algorithm is embeddedinto the tabu search algorithm to get the optimal solution ofthe proposed 2E-PVRP

The above research provides meaningful solutions forvehicle optimal scheduling in dynamic scenarios from differ-ent perspectives but there is still room for further improve-ment First the traditional dynamic VRP considers the first-level distribution network system from the vehicle yard tothe customer In the dynamic distribution scenario there isa long-term customer response distance which is difficult toadapt to the demanding requirements of customers secondthe research on urban distribution scheduling problem ismostly reactive scheduling and less use of prior knowledgecontained in historical data By refining the service areato develop a differentiated service strategy that takes intoaccount the differentiated characteristics of regional demandthe distribution process is less systematically optimized fromthe perspective of proactivereactive integration optimiza-tion

In order to solve the problem of long response distance inthe traditional reactive dispatching mode of urban logisticsdistribution this paper uses the basic model of two-levelvehicle routing problem to construct a proactive two-leveldispatching mathematical model and its solution framework

based on historical data The aim of this step is to realizethe efficiency of urban logistics distribution service andenhance the ability of customer demand response in dynamicscenarios The contribution is as follows taking the two-levelvehicle routing problem as the basic model the distributioncycle is divided into initial phase and multiple dynamicreplenishment phase the customers with the same attributesare spatially clustered by using the customer spatial allocationfeature and the dynamic demand forecasting is performedaccording to the historical performance of the demandwithineach cluster At the same time differentiated services anddemand quota strategies are designed to optimize distribu-tion costs under different regional differentiation Due tothe two-level network design when a dynamic customer isgenerated it can be served by the transfer station of theclustering area which can reduce the spatial distance of thedynamic demand response and improve the flexibility ofdistribution scheduling Since the required data comes fromreal distribution enterprise the proposed method has certainpractical significance

3 Mathematical Model

31 Terms and Definitions (1) The two-level network refersto a distribution network consisting of a hub-type distribu-tion center to a distribution center (first-level network) anda distribution-type logistics center to a customer (second-level distribution network) Single-stage delivery divides thedelivery cycle into multiple time intervals each time intervalcorresponding to the delivery operation process Multistagedelivery includes the delivery process for many single-stagedelivery operations(2) Assume that the undirected graph 119866 = (119873119860)represents the distribution network 119873 = 1198730 cup 119873119865 cup 119873119878represents the node set and is composed of three typesof nodes hub-type distribution center 1198730 distribution-typelogistics center 119873119865 and customer 119873119878 119860 = 119860119865 cup 119860119878represents the set of arcs where 119860119865 represents the hubtype of a set of arcs between the logistics center 1198730 andthe distribution-type logistics center 119873119865 and 119860119878 representsa set of arcs between the distribution-type logistics center119873119865 and its service customer group 119873119878 The length of theconnection arc between any two nodes i and j in119860119865 and119860119878 isdenoted as 119889119894119895 and the decision variable 119887119894 is used to identifywhether node i belongs to the primary distribution networknode(3) Considering the problem of urban traffic limit thesame level distribution network should be used to deliverthe same type of vehicles different levels of networks shouldbe distributed using heterogeneous vehicles and the vehiclesshould not be used across levels that is the vehicles inthe primary distribution network should be prohibited frombeing secondary distribution networks in the delivery ofcustomer service Suppose the demand of any node 119894 is 119902119894 andthe model used in the first-class distribution network is 119870119865the capacity constraints of the vehicle kf is 119865119876 and the fixedcost is 119888119870119865 the second-class delivery network uses model119870119878the capacity constraints of the vehicle ks are 119878119876 and the fixedcost is 119888119878119865


(4) Given a level distribution network and nodes i j ifvehicle 119870119865 traverses the distribution type logistics centersi and j 119909119896119891119894119895 is assumed to be 1 otherwise it is 0 and thecorresponding secondary distribution network is denoted bythe symbol 119909119896119904119894119895(5) Let 119910119896119891119894 and 119910119896119904119894 denote the ownership relationshipbetween nodes and vehicles in the two-level distributionnetwork respectively If the ownership relationship is estab-lished the value is 1 otherwise it is 0

Since we divide the whole distribution cycle into multipledistribution phases and each distribution phase carries outcargo allocation through the proactive demand quota strat-egy we first establish a single-phase 2E-PVRP mathematicalmodel to describe the path optimization of each distributionphase On this basis a multistage 2E-VRP mathematicalmodel was established to optimize the path of the entiredistribution cycle

In the design of single-stage distributionmodel followingthe traditional VRP research model we do not consider theimpact of distribution center inventory costs on schedulingoperations but only consider the Path-Related costs Theoptimal solution of the model is to minimize the distributionoperation costs in the whole distribution phase in the pro-cess of multistage distribution because of the introductionof distribution logistics center for proactive inventory theoptimal solution of this model is that besides consideringthe minimum cost of each stage of distribution operationthe objective of minimum operation of distribution logisticscenter should be added

32 Single-Stage 2E-PVRPMathematicalModel To copewiththe changing dynamic customer demand this article dividesthe distribution cycle into the initial distribution phase andthe multiple replenishment phases A single distributionphase can be regarded as a static problem Therefore forany single distribution stage the mathematical model ofsingle-stage and two-level dynamic distribution problem isestablished with the minimum total cost of operation asobjective function The model is as follows

The objective function

min119885 = 119870119865sum119896119891=1

1198730cup119873119865sum119894=1

1198730cup119873119865sum119895=1

119909119896119891119894119895119888119896119891119894119895

+ 119870119878sum119896119904=1

119873119865cup119873119878sum119894=1

119873119865cup119873119878sum119895=1

119909119896119904119894119895119888119896119904119894119895 + [119873119865sum119894=1

119902119894119865119876] 119888119870119865

+ [119873119878sum119894=1

119902119894119904119876] 119888119878119865

(1)

Restrictions119873sum119894=1

119902119894119910119896119891119894 le 119865119876 (2)

119873sum119894=1

119902119894119910119896119904119894 le 119878119876 (3)

119873sum119894=1

1198871198941199091198961198911198940 = 119873sum119894=1

1198871198941199091198961198910119894 (4)

119873sum119894=1

(1 minus 119887119894) 119909119896119904119894119895 = 119873sum119894=1

(1 minus 119887119894) 119909119896119904119895119894 forall119895 isin 119873119865 (5)

119873sum119894=1

119873sum119895=1

(1 minus 119887119894) 119909119896119904119894119895 = 119873sum119894=1

119873sum119895=1

(1 minus 119887119894) 119909119896119904119895119894 (6)

119873sum119894=1

119873sum119895=1

119887119894119909119896119891119894119895 = 119873sum119894=1

119873sum119895=1

119887119894119909119896119891119895119894 (7)

119873119865sum119894=1

119910119896119891119894 = 1 (8)

119873119878sum119894=1

119910119896119904119894 = 1 (9)

119873sum119894=1

119887119894119902119894 ge 119873sum119894=1

(1 minus 119887119894) 119902119894 (10)

forall119894 119895 isin 119873119865119909119896119891119894119895 = 1 997904rArr 119865119876 minus

119873119865sum119894=1

119910119896119891119894119902119894 ge 119902119895 (11)


119873119878sum119894=1

119910119896119904119894119902119894 ge 119902119895 (12)

119889119894119895 + 119889119895119896 minus 119889119894119896 gt 0 forall119894 = 119895 = 119896 isin 119873 (13)

119887119894119909119896119891119894119895 (1 minus 119909119896119891119894119895) = (1 minus 119887119894) 119909119896119904119894119895 (1 minus 119909119896119904119894119895) = 0forall119894 = 119895 isin 119873 119896119904 isin 119870119878 119896119891 isin 119870119865 (14)

119887119894119910119896119891119894 (1 minus 119910119896119891119894) = (1 minus 119887119894) 119910119896119904119894 (1 minus 119910119896119904119894) = 0forall119894 isin 119873 119896119904 isin 119870119878 119896119891 isin 119870119865 (15)

119887119894 (1 minus 119887119894) = 0 forall119894 isin 119873 (16)

Formula (1) is the minimum objective function of totaloperating cost which consists of three items the first is thetotal distribution cost of the two-level distribution networkthe second is the fixed vehicle cost of the first-level distribu-tion network and the third is the fixed vehicle cost of thesecond-level distribution network Formulas (2) and (3) arethe vehicle load constraints in the two-level distribution net-work formula (4) is the access constraint between the hub-type logistics center and the distribution-type logistics centerformula (5) is the access constraint between the distribution-type logistics centers and their services formulas (6) and(7) represent the access constraints between nodes in a two-level network formula (8) shows that each distribution-typelogistics center in a level-1 distribution network can only be


accessed by a vehicle once formula (9) represents that twocustomers in the distribution network can only be accessedby the vehicle once formula (10) provides that secondarydistribution network demand is not greater than the totalamount of a distribution network supply formulas (11) and(12) specify that the remaining load is not less than the currentdemand of the node when the vehicle goes to a node formula(13) shows that the distance between nodes should meetthe triangular inequality formulas (14) to (16) represent thegeneral constraints followed by binary decision variables

33 Multistage 2E-PVRP Mathematical Model T The num-ber of stages of a complete distribution cycle119867119876119879 Service ability of hub logistics center119863119894119876119879 Service capability of distribution logistics center119885119905 Operation cost of T in a distribution stage119910119905119896119904119895 The customer J in the distribution stage T whether itis from the vehicle KS service then take 1 otherwise take 0119867119905119894 119880119905119894 The shortage of T in distribution logistics center Iat the delivery stage119880119905119894 The profit margin of distribution logistics center i atthe delivery stage t119888 Rental cost of distribution logistics center I119888ℎ119894 119888119906119894 Unit shortage cost and unit excess cost

Therefore a multistage 2E-PVRP mathematical modelwith the objective of minimizing the total vehicle dispatchingcost of each distribution stage and the operation cost of thedistribution logistics center is established as follows

min119885119879 = 119888119873119865 + 119879sum119905=1

(119885119905 +119873119865sum119894=1

(119867119905119894 119888ℎ119894 + 119880119905119894 119888119906119894 )) (17)

In addition to the constraints specified by the single stage2E-PVRP issue the following constraints need to be fulfilled

119873119865sum119894=1

119863119894119876119879 le 119867119876119879 (18)

119879sum119905=1

119873119878sum119895=1

119910119905119896119904119895119902119895 le 119863119894119876119879 forall119894 isin 119873119865 forall119895 isin 119873119878 (19)

1 le 119879sum119905=1

119910119905119896119891119894 le 119879 119894 isin 1198730 cup 119873119865 (20)

119879sum119905=1

119910119905119896119904119894 = 1 119894 isin 119873119878 (21)

forall119905 isin 119879 119894 isin 119873119865119867119905119894 = 0 lArrrArr 119880119905119894 = 0 (22)

119888 gt 0 119888ℎ119894 ge 0 119888119906119894 ge 0 (23)

Equation (17) is the minimum total cost of operationobjective function in each stage the first one is the Leaseholdcost of distribution logistics center the second one is thevehicle dispatching cost of each stage and the shortage andsurplus cost of distribution logistics center Equation (18)

is the constraint that secondary network service capabilityis not greater than the primary network service capabilityEquation (19) indicates that each distribution type logisticscenter needs less than its service Equation (20) representsthe number of times each distribution type logistics centeris visited throughout the entire distribution cycle (the initialdelivery phase needs to access all the distribution typelogistics centers) Equation (21) indicates that any customercan only be served once during the entire service period andno customer needs replenishment Equivalents (22) denotethat at any distribution stage t distribution logistics centerI does not have both shortage and surplus Equivalents (23)denote non-negative variable constraints

4 Solution Framework

The proposed method consists of four modules (1) Data-driven demand forecasting method the historical perfor-mance of dynamic demand is evaluated by using deter-ministic linguistic value and triangular fuzzy number andthe potential dynamic customer demand is predicted basedon the assessment results (2) Customer clustering methodthrough the method of clustering algorithm proactive parti-tioning is divided and then the distribution logistics centeris determined (3) Proactive demand quotas and replen-ishment strategies analyzing the historical performance ofcustomer demand data in each proactive subregion anddetermining the initial and replenishment supply quotas totimely meet customer needs (4) Vehicle path optimizationprocedure using scan operator to get the initial solution ofthe delivery path and embedding it into the designed tabusearch algorithm to obtain the optimal scheduling scheme ofdistribution network at all levels

41 Data-Driven Demand Forecasting Methods First if thefirm evaluates the customerrsquos historical performance fromx dimensions then the historical performance data for nclients can be represented by matrix A = (11988611 11988612 119886111990911988621 11988622 1198862119909 1198861198991 1198861198992 119886119899119909) To ensure that the description ofhistorical customer needs is closer to the actual applicationscenario different dynamic client attributes are described bydetermining language values and triangular fuzzy numbersrespectively The symbol 119909119863 is used to identify the partof the customer demand attribute that can be accuratelydescribed and the symbol 119909119865 is used to identify the part ofthe customer demand attribute that can only be measured byvague language values The prediction of demand attributesis determined by expert scoring method Assuming that thepredicted value of the attribute dimension x of the custom i is119901119909119894 and the measured mean value of the attribute dimensionin customers within multiple delivery cycles is119898119909119894 the logicaldistance 119897119889119909119894 between the current forecast value and themultiple measured actual mean values can be expressed asfollows119897119889119909119894=

119901119909119894 minus 119898119909119894 119909 isin 119909119863radic 10038161003816100381610038161003816(1199011199091198941 minus 1198981199091198941)210038161003816100381610038161003816 + 10038161003816100381610038161003816(1199011199091198942 minus 1198981199091198942)210038161003816100381610038161003816 + 10038161003816100381610038161003816(1199011199091198943 minus 1198981199091198943)2100381610038161003816100381610038163 119909 isin 119909119865

(24)


(1199011199091198941 1199011199091198942 1199011199091198943) is the predicted value of the customerattribute using the triangular fuzzy number and (1198981199091198941 11989811990911989421198981199091198943) is the average of the customer attributes using thetriangular fuzzy number If a dynamic customer attributevalue ranges from 1 to n its triangular fuzzy number iscalculated as

119901119909119894 = (max(119897 minus 1119899 0) 119897119899 min(119897 + 1119899 1)) 119897 isin [1 119899]

(25)

According to the theory of foreground the decision-maker has the risk preference when the expected evaluationvalue is greater than the actual measurement value (119901119909119894 gt119898119909119894 ) When the expected evaluation value is smaller thanthe actual measurement value (119901119909119894 lt 119898119909119894 ) the decision-maker will take the initiative to avoid the risk Because ofthe difference of decision-makersrsquo cognition of risk aversionin different situations the risk factors 1205831 and 1205832 are set inthe process of calculating the foreground value reflectingthe decision preferences of different decision-makers Thedynamic demand foreground value can be calculated byformula (25)

119865119881 = 1205831119897119889119909119894 119901119909119894 gt 1198981199091198941205832119897119889119909119894 119901119909119894 lt 119898119909119894 (26)

Obviously when the dynamic demand foreground is pos-itive the larger the value of 1205831 is with the same foregroundvaluation the more optimistic the decision-maker customerselection decision is When the dynamic demand foregroundis negative the larger the value of 1205832 is with the sameforeground valuation the more pessimistic the decision-maker clients choose to make their decisions

42 CustomerClusteringMethods Considering that dynamicclients are obtained by proactive risk assessment and cannotensure certainty in the process of delivery clustering con-strained only with actual demand will lead to the ineffectiveclustering expansion from the regional boundaries There-fore adding to the clustering algorithm the service radiusexpansion factor u and the load expansion factor v allowsthe demand in the cluster area (including the exact knownstatic customer demand and possible dynamic customerdemand) to be greater than the vehicle load However thevehicle is not allowed to be overloaded when leaving thedistribution center at every distribution stage On this basisthe proactive divisional scheduling strategy under the servicearea is divided as follows

Step 1 Calculate the adjacency matrix between the distri-bution center and all the customers based on the knowncustomer coordinate data

Step 2 Search eachnode i as a centerwithin the service radiusR record the client nodes falling within the range and selectthe circle to which the node with the largest number of clientnodes belongs as the proactive service subregion

Step 3 Generate proactive service subarea

Step 31 Center of gravity to determine the subregion proac-tive scheduling center

Step 32 Determine whether the total customer demand QD(iter) within the initial service subarea is greater than thevehicle load Q if yes execute Step 33 if less go Step 34

Step 33 If the result of Step 32 is true calculate the distancebetween the customer and the proactive scheduling centerfalling within the subregion to obtain the client sequenceM sorted in descending order and the first element of thesequence M removed get QD (iter + 1) to implement Step35 judgment conditions

Step 34 Expand the search radius to uR to determinewhether it is true or not and Step 32 is executed if falseStep 4 is executed

Step 35 Determine whether QD (iter) lt Q ltQ (iter + 1)is true and if true Step 4 is performed if false Step 32 isexecuted

Step 4 Remove the clients contained in the service subregiongenerated in Step 3 and go to Step 5

Step 5 Judge whether all the customers have been includedin all clusters if the judgment result is false execute Step 2 ifthe judgment result is true the algorithm is terminated

As vehicle overloading is not allowed in practical appli-cations the estimated load in the cluster partition generatedby the clustering algorithm is likely to exceed the actual loadTherefore considering the practical application scenario thestrategy of replenishing the replenishment vehicle betweenthe distribution center and each proactive dispatch center isadopted to solve the distribution difference problem that theactual delivery demand is greater than the subregion of thevehicle load

43 Proactive Demand Quotas and Replenishment StrategiesSince each distribution logistics center covers a relativelystable service area the key to optimizing the primary dis-tribution path is to evaluate the likely value of demandin that area The long-term distribution practice of urbandistribution companies accumulated a wealth of historicaldistribution data and it provides a basis for the assessmentof the demand for each distribution subregion

It is assumed that the average historical demand of adistribution-type logistics center is 120583119894 the variance is 120590119894and the customer dynamic degree is introduced to evaluatethe customer changes in each cluster area The calculationformula of regional dynamic degree is

119863119863119894 = 119899119889119910119899119899119904119905119886 + 119899119889119910119899 (27)

119899119889119910119899 contains predicted dynamic customers and unpre-dicted dynamic customers and 119899119904119905119886 is a static customer in thedelivery system


During the delivery process due to the new demand inthe subarea the supply of the initial delivery plan is smallerthan the actual demand in the subarea and the design of thereplenishment path must be supplemented with the failure ofdynamic customer forecasting

Therefore the set replenishment probability threshold119901119886119888119888119890119901119905 determines whether the distribution type logisticscenter i is a replenishment subarea and the formula is asfollows

119886119894 = 1 119901119894 ge 1199011198861198881198881198901199011199050 119901119894 lt 119901119886119888119888119890119901119905 (28)

After determiningwhether a distribution logistics centerrsquoscovering subarea is a replenishment subarea considering thedifferences in demand levels in the respective areas and theirdistance from the distribution center the design is configuredto allocate demand quotas for each subarea of the initial pathplanning based on the historical demand method

119902119888119894 = 119903119886119899119889 (120583119894 120583119894 + 3120590) 119886119894 = 0120583119894 119886119894 = 1 (29)

where rand (a b) denotes the random number in theinterval [a b] and min [a b] denotes the smaller of the two

44 Vehicle Routing Optimization Program

(1) Scan Operator Due to the large dependence of tabusearch algorithm on initial solution the initial solutionof scanning method is chosen and the initial solution isoptimized by using tabu search algorithm to obtain higherperformance solution The specific steps for constructing theinitial solution of the scan operator are as follows first of alltaking the distribution center as the origin and any customeras the starting point to build the polar coordinates of thestarting vector taking the distribution center as a startingpoint and the other client as the destination vector to calculatethe angle between the vector and the starting vector thevector angles are sorted first and then the initial customersequence is generated based on the path constraints

(2) Construct Temporary Solution In the process of taboosearch the neighborhood of the current solution is trans-formed and the scope of the solution space that can besearched out is expanded to increase the optimization abilityof the algorithm This paper defines the following four kindsof neighborhood optimization operator

T1 Randomly selected customers are removed from thevehicle and reinserted randomly

T2 Randomly exchange two randomly selected cus-tomers

T3 Randomly select two subroute segments to exchangewith each other

T4 Choose two customers at random and reverse all thecustomers located between the two customers

For each neighborhood operation the following twoacceptance strategies are used Strategy A the first improve-ment stopping the optimization after the first improvement

obtained after the neighborhood transformation Strategy Bthe best improvement repeating the same operator run ntimes and choosing the best improvement that appears duringthe experiment If running n operations the current solutionhas not been improved Then terminate this neighborhoodoperation

For each customer on each path and path five kinds oflocal optimization operators and one of the two acceptancestrategies are randomly and independently selected with auniform probability (14 and 12 respectively) Search depthis N times

(3) Construct Contraindications and Taboos To avoid thealgorithm getting into the local optimum we need to judgewhether the neighborhood solution is better than the his-torical optimal solution If the neighborhood solution issuperior to the historical optimal solution the historicaloptimal solution is updated and the neighborhood is treatedas a taboo object And then determine whether the tabootable is full if the taboo table is full remove the first elementof taboo table move the other elements to the left by oneand insert the taboo object into the tail of taboo table iftaboo table is not full the taboo object is directly insertedinto the first nonzero position If the neighborhood solutionis worse than the historical optimal solution the depth ofsearchwill be increased by 1 to continue to determinewhetherthe solution of the next neighborhood satisfies the taboocondition

(4) Quality Evaluation and Processing Method of SolutionsThe algorithm does not accept the transformation of theinfeasible solution and discards it directly that is if the totalamount of the distribution path exceeds the vehiclersquos nuclearload requirement it is regarded as an infeasible solution andis directly removed from the solution space

To sum up the tabu search routing optimization proce-dure designed in this paper is shown in Figure 1

5 Numerical Test

51 Data Description To illustrate the feasibility of the pro-posed method we use the distribution data of large logisticscompany in Chongqing China Chongqing is an importantcity in southwestern China and is in the middle and upperreaches of the Yangtze River Its port trade is well developedOur selected logistics and distribution company is a largerauto parts distribution company in Chongqing with up to35 service customers as shown in Figure 2 The distributioncompany has two different types of ZA and HAparts systemsthe customer may need one of two major categories ofparts or at the same time need two major categories ofparts The two types of vehicles owned by the enterprise aremarked as B207 and CD101 and their authorized weightsare 300 and 150 Due to the fragmented distribution ofcustomers and the dynamic changes in demand the hublocated at the headquarters of the enterprise is located at(520 280) in Figure 2 Establish distribution logistics centerin a few more concentrated areas of customers The partsproduced by the company are first transported from the


Start

Initial solution

Generate neighborhood solution R

Neighborhood operator

Tabu List

Current best solution Rlowast

End

R better than Rlowast

Tabu Rlowast

R isin Tabu List Update best solution R and add it to Tabu List

Output best solution R

Yes

No

YesNo

Yes

No

Delete R

Figure 1 Tabu search algorithm path optimization diagram

total customers in a whole cycle

1

23

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

50 100 150 200 250 300 350 400 450 50000

50

100

150

200

250

300

350

400

Figure 2 All customer space profiles for the full cycle

B207 vehicle to the distribution logistics center and then theCD101 vehicle is used from the distribution logistics centerto deliver the customerrsquos required parts to the correspondingcustomer

Customers that have appeared in the delivery systemat the start of delivery are called static customers andnonappearing customers use data-driven demand forecastingmethods to decide whether to include them in the deliverysystemThe static customer for each cycle is identified by thecustomerrsquos production plan and is known at the beginning ofthe cycle Table 1 is a distribution cycle customer informationform

52 Data-Driven Dynamic Customer Identification

(1) Customer Demand Forecast According to the historicaldemand of each customer collected by the enterprise for atotal of 30 days the mean and standard deviation are shownin the following table Using KS nonparametric test to testthe historical demand of each customer in historical datawe found that the normal distribution can better reflect thechange of the demand of historical data The fitting resultsare shown in Table 2

(2) Dynamic Customer Evaluation To effectively describethe possible situation of dynamic customers in the servicearea the dynamic customer attributes are described by threeevaluation indexes customer dependence a1 payment speeda2 and demand a3 The corresponding weights of the threeindicators are 04 03 and 03 The above three assessmentmeasures belong to the fuzzy evaluation in which the cus-tomer dependency is divided into four categories dependentslightly dependent medium dependent and heavily depen-dentThe payment speed is divided into three levels procras-tination advancement and immediateness The expert givesthe prediction reference level fromhis experience that is the lvalue in formula (25) and then calculates the predicted valueof the attribute For the customer dependency and paymentspeed attributes selected in this paper formula (25) can beembodied as formulas (30) and (31) where the l value isconsistent with the definition order of the customer attribute


(30)


Table 1 Customer information form for complete delivery cycle

Customer type Customer Index The number of customers

Static customers 1256891112141516171820222425262730323435 23

Dynamic customer 347101319212328293133 12

Table 2 30 Day historical needs distribution all 35 clients

Customer Number Mean Standard deviation Customer Number Mean Standard deviation1 15 335 19 136 3042 2998 671 20 141 3153 157 351 21 102 2284 15 335 22 27 6045 1171 262 23 136 3046 105 235 24 2294 5137 17 38 25 20 4478 146 327 26 151 3389 2413 54 27 1165 2610 256 573 28 1811 40511 1506 337 29 13 29112 1633 365 30 1508 33713 1678 375 31 1297 2914 1331 298 32 1866 41715 13 291 33 1759 39316 167 374 34 199 44517 1582 354 35 186 41618 139 311


(31)

For customer demand the expert generates the forecastvalue of customer demand in the distribution cycle accordingto the statistical information of customer demand providedin Table 2 After getting the predicted value of the threeattributes the decision-maker uses formula (26) to evaluatethe dynamic customer and confirm whether to accept thedynamic customer according to the relationship betweenthe predicted value of the expert and the expected valueand the risk preference When calculating the foregroundvalue 1205831 = 1 1205832 = minus225 is taken since the customerrsquosattribute dimensions are different the data is normalizedTheprocessed dynamic customer foreground values are shown inTable 3 (note due to space limitations only the evaluationresults of the first stage dynamic customer prospect value areprovided) The dynamic customer evaluation formula is asfollows

119891 = 04 lowast 1198911 + 03 lowast 1198912 + 03 lowast 1198913 (32)

A negative forecasted value indicates that the predictedvalue of firm property is less than the previous averagevalue indicating that the decision-makerrsquos performance onthe clientrsquos property is more pessimistic the positive resultof the foreground value assessment indicates that the firmrsquos

forecast value of the clientrsquos property is higher than that of theprevious period indicating that the decision-maker is moreoptimistic about the customer service outlook Thereforein this paper dynamic customers with a foreground valuegreater than zero are included in the distribution networkcorresponding to 6 clients with indexes 3 7 28 29 31 and33 in Table 3 and determining the service attribution of eachcustomer through the customer clustering method

53 Customer Clustering and Demand Quotas As shown inFigure 2 and Table 3 the decision-makers are pessimisticabout the historical performance of customers 4 10 13 1921 and 23 The original distribution plan of this distributioncycle will not consider these customers only clustering thecustomers entering the distribution system The maximumservice radius bounded by the enterprise is 100 the serviceradius is 80 and the service radiusmaximum expansion scaleis 025 the expansion factor u has a step size of 005 the loadexpansion factor v has a step size of 01 and the maximumexpansion scale is 05 The customer clustering results areshown in Figure 3

After each cluster area and its customer base are servedit is necessary to determine the distribution quotas for thearea during the initial and replenishment phases basedon the historical performance of customer needs in thearea Since the demand of each customer point obeys anormal distribution the customerrsquos historical demand in


Table 3 Evaluation table of the dynamic client foreground value

DynamicCustomer Index

Customer Dependency (f1) Payment speed(f2) Demand (f3) Foreground valuePredictive value Past average Predictive value Past average Predictive value Past average

3 4 1 3 2 161 157 0434 1 3 1 3 161 15 -0277 1 4 3 1 161 17 01410 1 3 3 3 267 256 -02113 4 4 1 3 179 168 -01319 2 4 1 3 137 136 -02621 4 4 1 1 963 102 -00323 1 3 3 2 124 136 -00328 4 1 2 3 188 1811 02929 3 2 1 1 111 13 00331 3 2 3 2 1219 1297 01533 1 2 2 1 1785 1759 004

0 100 200 300 400 5000

50

100

150

200

250

300

350

400

450

500cluster result figure

1

2 3

4

class 1class 2class 3

class 4class central

Figure 3 Delivery system customer clustering results

each clustering subarea will be summed up for 30 daysand the mean and variance will be calculated Accordingto formula (28) for the distribution acceptence standardswhere 119901119886119888119888119890119901119905 = 035 then clusters 1 2 and 3 are dividedinto nonreplenishment subregions and region 4 is dividedinto replenishment subregions according to formula (29) todetermine the initial allocation of each region as shown inTable 4

54 Vehicle Scheduling Scheme After determining the cus-tomer base to be served in each cluster subarea the routingoptimization program described in Section 44 is used tooptimize the delivery path based on the initial allocationquota In the primary distribution network the initial dis-tribution phase transports the goods to the distribution typelogistics center (that is the distribution type logistics center)

starting from the hub-type center according to the distri-bution quota specified in Table 4 Secondary distributionnetwork traffic will start from the clustering center anddirectly provide delivery service for the customer accordingto each customerrsquos demandmdashstatic customers with its actualdemand distribution and distribution of dynamic customerto enterprise for its demand forecast

The whole distribution process is a complete distributionworkday consisting of eight hours which is divided into theinitial stage and replenishment stage each with four hoursthe initial stage is only static customer service and the expertexperience is used to conduct dynamic customer evaluationThe dynamic replenishment phase is enabled at half the time(that is the fourth hour) for static customers that have notyet been served and the dynamic customer service obtainedby the proposed method A complete cycle of distributionjob scheduling process is shown in Figure 4 Static customerswith their actual demand distribution dynamic customerswith expert predicted value of stock the actual demand isclear at the customer

The tabu search algorithm designed by 44 part is pro-grammed on the platform of Win 7 32 by using MATLAB2015B and the optimal distribution routing of 2E-VRP isgenerated with the design example data The algorithmparameters are as follows the taboo table length is 20 N =10 the maximum iterations number is 1000 and the initialsolution scale is 100 Table 5 shows the optimal initial andreplenishment routings for distribution centers to four clustercenters andTable 6 shows the initial distribution subpaths forfour cluster subregions

Under the accurate forecast result the distribution logis-tics centers in the nonreplenishment clustering area havedifferent levels of surplus stock from Table 6 while thereplenishment clustering area has a small amount of demanddifference At the same time due to the small difference indemand of cluster 4 dispatched vehicles may be worth morethan replenishing their replenishment However in practicalapplication scenarios prediction errors are inevitable Inaddition the analysis of the periodic distribution data found


Initial Phrase replenishment phrase

A whole cycle

Cluster

Hub

Cluster

Unserved staticCustomer

Expert

Dynamic CustomerStatic Customer

Start End4th hour

Figure 4 Schematic diagram of multistage distribution scheduling

Table 4 Clustering subarea parameter description table

Number Clustering 1 Clustering 2 Clustering 3 Clustering 4Cluster center coordinates (161318) (145125) (350110) (368290)The number of accepted customers 8 6 10 5The number of dynamic customers 2 2 3 4Dynamic value 02 025 03 044Daily average 13058 9852 16279 8059Daily variance 1111 763 1089 812Initial rationing 14307 11359 18031 8059Radius expansion scale u 01875 01875 01875 0Load expansion factor v -00462 -02427 02021 -04627

Table 5 A distribution network path table

Delivery phase Routing index Routing connection Routing mileage

Initial phase Routing 1 DC-1-2-DC 76044Routing 2 DC-3-4-DC 37364

Replenishment phase Routing 1 DC-4-DC 18083

that the forecast number 33 customers did not actuallygenerate demand and the number of 21 and 23 customerswhich were given up in the beginning of the distributiondue to decision-making risk aversion issued new distributionneeds in the distribution process Then the path of cluster3 and cluster 4 in the initial path is adjusted locally Theresults are shown in Table 7 The actual demand of 29customers involved in the distribution operation is shown inTable 8

Because the original intention of PVRP design is to putthe commodity closer to the customer the precondition ofits realization is that the distribution logistics center hasenough stock to serve the new dynamic customer in thereplenishment stage Therefore it is stipulated that unitshortage cost 119888ℎ119894 = 2 and unit excess cost 119888119906119894 = 1 from which

we can get a complete cycle of changes in the stock of goodsand the cost of each center as shown in Table 9

Given that the leasehold cost of distribution logisticscenter is 50 the total leasehold cost is 200 It is assumedthat the fixed cost of the model B207 is 1000 the unit costof use is 5 the fixed model cost of the model C101 is 600and the unit cost is 3 B207 and C101 were used for deliveryrespectively The results of comparison with the two-levelvehicle routing scheme designed in this paper are shown inTable 10

As shown in Table 10 the total cost of PVRP solutiondelivery is 1790335 in terms of delivery costs slightly higherthan the delivery of B207 bicycle and C101 However dueto the partition clustering algorithm the PVRP schemedesigned by the PVRPmethod has shorter running time than


Table 6 Distribution initial routing table for each cluster area

Cluster area number Routing connection Routing mileage Routing load Surplus loadCluster 1 c1-17-8-15-7-5-2-3-8-c1 3285 13287 102Cluster 2 c2-14-16-12-6-1-9-c2 40211 9597 1762

Cluster 3 c3-31-35-33-28-24-c3c3-22-18-20-25-27-c3

2377522564 17686 345

Cluster 4 c4-26-30-34-32-29-c4 17826 8174 -115

Table 7 Updated delivery path

Cluster area number Updated routing connection Updated routing mileageCluster 4 c4-21-23-c4 966

Table 8 All customer demand information sheets in the whole cycle

code 1 2 3 4 5 6 7 8 9real demand 1647 3323 1884 0 142 127 2033 1633 196forecast demand - - 161 161 - - 161 - -code 10 11 12 13 14 15 16 17 18real demand 0 126 167 0 163 1563 142 1433 145forecast demand 267 - - 179 - - - - -code 19 20 21 22 23 24 25 26 27real demand 0 168 144 141 169 216 1646 129 194forecast demand 137 - 963 - 124 - - - -code 28 29 30 31 32 33 34 35real demand 208 167 167 137 163 192 148 203forecast demand 188 111 - 1219 - 1785 148 -

the single-vehicle scheme Because the clustering center iscloser to the customer base especially the clustering areafarther away from the hub the proactive demand quota policycan dispatch the parts to its service from the distributedlogistics center faster

55 Algorithm Performance Evaluation To avoid the stochas-tic error of the algorithm the C101 model the customer dis-tribution shown in Figure 2 and the corresponding customerdemand mean in Table 2 are used to form the example dataThe stability of the proposed algorithm is verified by using thesame tabu search algorithm parameters as those in the abovescheduling scheme At the same time the genetic algorithmis used to solve the example to verify the relative accuracythe two algorithms are run 20 times respectively and theresults are compared as shown in Figure 5 It shows that theoptimal solution of tabu search algorithm is 387633 and theoptimal solution obtained by genetic algorithm is 397356which improves by 24 According to the statistical mean of20 algorithms the average value of tabu search algorithm is395799 and the average value of genetic algorithm is 404789which improves by 22 When the variance of the twoalgorithms is statistically found the standard deviation of thetabu search algorithm is 6248 and the standard deviation ofthe genetic algorithm is 4052 It can be seen that the stabilityof the solution is slightly worse than the genetic algorithmbut considering the quality of the solution is better than thegenetic algorithm It is proved that the proposed algorithm is

0 108642 12 14 16 18 20Counts

3800

3850

3900

3950

4000

4050

4100

4150

4200

The B

est V

alue

Tabu Search AlgorithmGenetic Algorithm

Figure 5 Comparison of the genetic algorithm and the tabu searchalgorithm in this paper

superior to the genetic algorithm in the quality and stabilityof the solution and can better realize the routing optimizationtasks in each stage


Table 9 Stock quantity and cost analysis of each center in a complete cycle

Cluster number Stock quantity Initial phase Replenishment phase CostPath load Margin Path load Replenishment quantity Margin

Cluster 1 14307 12590 171700 0 0 1717 3434Cluster 2 11359 9597 176200 0 0 1762 3524Cluster 3 18031 17286 74500 15501 0 2530 3275Cluster 4 8059 6070 198900 91 104 0 1989

Table 10 Path costs of other programs

Scheduling scheme Single- typeB207

Single- typeC101

PVRPB207 C101

Scheduling times 2 6 3 6Mileage 301377 462983 131491 146886Distance cost 1706885 1748949 957455 800658Stock cost 0 0 0 12222Leasehold cost of distribution logistics center - - - 200Total cast 1706885 1748949 1790335

6 Management Insights

Since the problem to be solved comes from the actualapplication scenario we can obtain the following inspirationfrom the optimization results of this article

Data analysis is an important means for enterprises toobtain profits and tap the potential benefits It not only helpsenterprises to understand the historical operating conditionsbut also helps enterprises to analyze the laws of customersand discover the intrinsic dynamics of customer needsIn our forecasting method based on the data analysis ofthe past 30 days we found that customer historical datacan be effectively fit with normal distribution and give thedistribution parameters of each customer This is very usefulfor enterprises to grasp the trend of changes in customerdemand and we also consider that the two indicators ofpayment speed and customer reliance to comprehensivelymeasure the dynamic customer can be accepted The data-driven demand forecasting method proposed by the actualenterprise data validation can effectively identify dynamicclients Because of the unavoidable prediction errors twodynamic clients are not predicted in the example of this paperwith the more conservative customer selection decision andthere is a customer that failed to predict Therefore wecan make the following judgment (1) when there are alarge number of available historical data nonparametric testcan be used to analyze the distribution characteristics ofhistorical data and find the optimal distribution among themso as to achieve effective prediction of customer demand(2) The dynamic customerrsquos choice is related to the decisionpreference When the decision has the risk preference someclients with lower probability of occurrence may be includedin the distribution network In this way more customers maybe considered in the distribution system but may also bringadditional scheduling costs When the decision-making isrisk-averse the choice of service customer group will tendto be conservative and some dynamic customers may be

ignored However this article effectively prevents this bydesigning a proactive demand quota strategy

The combination of customer clustering and demandquotas is equivalent to directing vehicles to areas wherecustomer needs are more concentrated If the dynamicdemand occurs in the local area and the vehicle response tothe dynamic demand from the hub center may require higherservice and time cost the vehicle responding to the dynamicdemand promptly from the distribution center has the greatsignificance for improving customer satisfaction Proactivedemand quotas allow distribution centers to have more cargothan the current phase of demand In the event of a failedforecast or a transient customer the quantity of cargo stockedby the distribution logistics center ensures its ability to adaptto minor fluctuations in regional demand In addition whenthe dynamic demand in the region is too large and thelogistics center is short of supply the replenishment phasewill start with the volume of cargo that is not replenishedand the replenishment scope will be drastically reduced ThePVRP method designed in this paper is less significant interms of delivery costs However with vehicle collocation andsecondary network design it is well adapted to the currenttraffic restrictions in urban management Although the useof larger vehicles has some cost advantages it is less flexiblein complex transport networks and may require additionaldelivery of customer goods due to traffic limit When usingsmaller models the limited number of customers with one-off service due to the low vehicle load leads to a larger totalpath length of the vehicle thereby increasing the workloadand working hours of the drivers and lacking of humanisticconcern

7 Conclusion and Outlook

This paper presents a 2E-PVRP problem with four modulesdata driven demand forecasting method customer cluster-ing method proactive demand quotas and replenishment


strategy and vehicle routing optimization procedure Theconclusions are as follows (1) Data driven demand fore-casting method is helpful to give full play to the value ofthe existing historical data in the enterprise to identify thedynamic customers in the distribution process and reducethe impact of the uncertainty in the delivery process onthe delivery work (2) Customer clustering and demandquota design can guide the vehicles in the areas wherecustomers are more concentrated and respond to dynamiccustomers faster (3) 2E-PVRP adopts two-level networkand multivehicle design which enhances the adaptability ofdistribution system to traffic policy and pays more atten-tion to the humanistic concern of drivers In the futurewe will continue to study the site selection mechanism ofdistribution logistics centers that take social and economicfactors into consideration The case study shows that thereis a problem that the real delivery rate of the replenish-ment vehicles is too low when the regional replenishmentvolume is small Ministry will consider the introduction ofmultivehicle matching strategy in the first-class distributionnetwork to achieve the optimal allocation of distributionresources

Data Availability

(1) Basic data the simulation data needs a distribution centerand several customers to be distributed The researcher canuse the simulationmethod to randomly generate the dynamiccustomers in the text and simulate the simulation networkcomposed of the data in Figure 2 and Table 1 (2)The genera-tion of historical data the example of this paper comes fromthe statistical analysis of enterprise data The researchers cansimulate the historical performance of dynamic customers byrandomly generating data The distribution model obtainedfrom the simulated data may not be consistent with thenormal distribution of the results of this paper However thisdoes not affect the generation of the final result Regardlessof the distribution the purpose is to forecast the customerdemand It is also advisable for the researcher to obtainother distributions that can effectively reflect the customerrsquoshistorical performance (3) Dynamic customer evaluationusing the assessment indicators provided in this paper andformula (30) and formula (31) to obtain the forecast value ofthe indicator and thenusing formula (32) to comprehensivelyevaluate the three indicators to generate the prospect valueof dynamic customers (4) The customer clustering anddemand quotas can be implemented according to the methodproposed in the article Afterwards the emergency searchpath optimization program designed by the article can beused to obtain the desired result Again the data in thisarticle cannot be disclosed to the public because it involvescommercial secrets If the subsequent researchers need toverify or redevelop the results of this paper follow themethodologies provided in the third part of the articlersquossolution framework for data processing to get the desiredresults In addition we will be honored if the researchers canmake personal innovations on the basis of the results of thispaper

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

This study is supported by the National Natural ScienceFoundation of China (71502021 71602015) funded by theMinistry of Education of Humanities and Social ScienceFundProject (2014YJC6300382015XJC630007) supported byPostdoctoral Science Foundation (2016T90862) funded bythe Chongqing Foundation and Frontier Research Project(cstc2016jcyjA0160) Chongqing City Board of EducationHumanities and Social Science Research Project (17SKG073)and the Chongqing Municipal Science and TechnologyResearch Project (KJ1500702)

References

[1] BH Yang ldquoA survey on the real time vehicle routing problemsrdquoScience vol 125 no 3244 pp 383ndash387 2008

[2] G Laporte ldquoScheduling issues in vehicle routingrdquo Annals ofOperations Research vol 236 no 2 pp 1ndash12 2013

[3] C Y Shi and H Huang ldquoVehicle routing problem researchstatus and prospectrdquo Logistics Sci-Tech 2014

[4] K Braekers K Ramaekers and I Van Nieuwenhuyse ldquoThevehicle routing problem State of the art classification andreviewrdquo Computers amp Industrial Engineering vol 99 no 9 pp300ndash313 2016

[5] Y Rahmani W R Cherifkhettaf and A Oulamara ldquoThe two-echelon multi-products location-routing problem with pickupand delivery Formulation and heuristic approachesrdquo Interna-tional Journal of Production Research vol 54 no 4 pp 1ndash212016

[6] R Liu Y Tao Q Hu and X Xie ldquoSimulation-based optimisa-tion approach for the stochastic two-echelon logistics problemrdquoInternational Journal of Production Research vol 55 no 1 pp 1ndash15 2017

[7] V Pillac C Gueret and AMedaglia ldquoDynamic vehicle routingproblems state of the art and prospectsrdquo Dynamic VehicleRouting 2011

[8] V Pillac M Gendreau C Gueret and A L Medaglia ldquoAreview of dynamic vehicle routing problemsrdquo European Journalof Operational Research vol 225 no 1 pp 1ndash11 2013

[9] H N Psaraftis M Wen and C A Kontovas ldquoDynamic vehiclerouting problems Three decades and countingrdquo Networks vol67 no 1 pp 3ndash31 2016

[10] C Wood and K Hartzel ldquoFactors that affect the improvementof demand forecast accuracy through point-of-sale reportingrdquoEuropean Journal of Operational Research vol 26 no 1 pp 171ndash182 2016

[11] B W Thomas ldquoWaiting strategies for anticipating servicerequests from known customer locationsrdquo Informs 2007

[12] C A F Lima B M Luz S T Takemoto et al ldquoStrategicmodeling for the characterization of the conditions that allowthe anticipation of the consumerrsquos requestsrdquo Open Journal ofSocial Sciences vol 3 no 10 pp 146ndash160 2015

[13] H Cabello and F J Lobillo ldquoSound branch cash managementfor less a low-cost forecasting algorithm under uncertaindemandrdquo Omega vol 70 no 3 pp 118ndash134 2016


[14] J Huiskonen ldquoService parts management demand forecastingand inventory controlrdquo Production Planning amp Control vol 25no 6 pp 489ndash494 2011

[15] S Ma and R Fildes ldquoA retail store SKU promotions opti-mizationmodel for categorymulti-period profitmaximizationrdquoEuropean Journal of Operational Research vol 26 no 2 pp680ndash692 2017

[16] Z Sha R Dekker W V Jaarsveld et al ldquoAn improved methodfor forecasting spare parts demand using extreme value theoryrdquoEuropean Journal of Operational Research vol 26 no 1 pp 169ndash181 2017

[17] T R Willemain C N Smart and H F Schwarz ldquoA newapproach to forecasting intermittent demand for service partsinventoriesrdquo International Journal of Forecasting vol 20 no 3pp 375ndash387 2004

[18] E Porras and R Dekker ldquoAn inventory control system for spareparts at a refinery an empirical comparison of different re-orderpoint methodsrdquo European Journal of Operational Research vol184 no 1 pp 101ndash132 2008

[19] H Lei G Laporte and B Guo ldquoDistricting for routingwith stochastic customersrdquo Euro Journal on Transportation ampLogistics vol 1 no 12 pp 67ndash85 2012

[20] H Lei G Laporte and B Guo ldquoA generalized variable neigh-borhood search heuristic for the capacitated vehicle routingproblem with stochastic service timesrdquo TOP vol 20 no 1 pp99ndash118 2012

[21] Y Wang X Ma and Y Lao ldquoA fuzzy-based customer clusteringapproach with hierarchical structure for logistics networkoptimizationrdquo Expert Systems with Applications vol 41 no 2pp 521ndash534 2014

[22] T Vidal M Battarra A Subramanian et al ldquoHybrid meta-heuristics for the clustered vehicle routing problemrdquoComputersamp Operations Research vol 58 pp 87ndash99 2015

[23] M Battarra G Erdogan andD Vigo ldquoExact algorithms for theclustered vehicle routing problemrdquoOperations Research vol 62no 1 pp 58ndash71 2014

[24] A H Marc L Fuksz P C Pop and D Danciulescu ldquoAnovel hybrid algorithm for solving the clustered vehicle routingproblemrdquo in Hybrid Artificial Intelligent Systems vol 9121 pp679ndash689 Springer International Publishing 2015

[25] H Lei G Laporte Y Liu and T Zhang ldquoDynamic design ofsales territoriesrdquo Computers amp Operations Research vol 56 no11 pp 84ndash92 2015

[26] F Ferrucci and S Bock ldquoReal-time control of express pickupand delivery processes in a dynamic environmentrdquo Transporta-tion Research Part B Methodological vol 63 no 4 pp 1ndash142014

[27] F Ferrucci and S Bock ldquoPro-active real-time routing inapplications with multiple request patternsrdquo European Journalof Operational Research vol 253 no 2 pp 356ndash371 2016

[28] Y Wang X Ma M Xu Y Wang and Y Liu ldquoVehicle routingproblem based on a fuzzy customer clustering approach forlogistics network optimizationrdquo Journal of Intelligent amp FuzzySystems Applications in Engineering and Technology vol 29 no4 pp 1427ndash1442 2015

[29] G Laporte H Mercure and Y Nobert ldquoAn exact algorithmfor the asymmetrical capacitated vehicle routing problemrdquoNetworks vol 16 no 1 pp 33ndash46 1986

[30] G Laporte ldquoExact algorithms for the traveling salesman prob-lem and the vehicle routing problemrdquo Progress in IndustrialMathematics at Ecmi pp 458ndash472 1998

[31] R Baldacci and R W Calvo ldquoAn exact algorithm for thetwo-echelon capacitated vehicle routing problemrdquo OperationsResearch vol 61 no 2 pp 298ndash314 2013

[32] F A Santos A S da Cunha and G R Mateus ldquoBranch-and-price algorithms for the two-echelon capacitated vehicle routingproblemrdquo Optimization Letters vol 7 no 7 pp 1537ndash1547 2013

[33] F A Santos G R Mateus and A S Da Cunha ldquoA branch-and-cut-and-price algorithm for the two-echelon capacitated vehiclerouting problemrdquoTransportation Science vol 49 no 2 pp 355ndash368 2015

[34] U Breunig V Schmid R F Hartl and T Vidal ldquoA large neigh-bourhood based heuristic for two-echelon routing problemsrdquoComputers amp Operations Research vol 76 pp 208ndash225 2016

[35] K Wang S Lan and Y Zhao ldquoA genetic-algorithm-basedapproach to the two-echelon capacitated vehicle routing prob-lem with stochastic demands in logistics servicerdquo Journal of theOperational Research Society vol 68 no 11 pp 1ndash13 2017

[36] J CordeauMGendreau andG Laporte ldquoA tabu search heuris-tic for periodic and multi-depot vehicle routing problemsrdquoNetworks vol 30 no 2 pp 105ndash119 2015

[37] F Alonso M J Alvarez and J E Beasley ldquoA tabu searchalgorithm for the periodic vehicle routing problem with mul-tiple vehicle trips and accessibility restrictionsrdquo Journal of theOperational Research Society vol 59 no 7 pp 963ndash976 2008

[38] M Maischberger ldquoA parallel iterated tabu search heuristic forvehicle routing problemsrdquo Computers amp Operations Researchvol 39 no 9 pp 2033ndash2050 2012

[39] P V Silvestrin and M Ritt ldquoAn iterated tabu search for themulti-compartment vehicle routing problemrdquo Computers ampOperations Research vol 81 pp 192ndash202 2017

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of


Mathematical Problems in Engineering

Applied MathematicsJournal of


Probability and StatisticsHindawiwwwhindawicom Volume 2018

Journal of


Mathematical PhysicsAdvances in

Complex AnalysisJournal of


OptimizationJournal of



Engineering Mathematics

International Journal of


Operations ResearchAdvances in

Journal of


Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

International Journal of Mathematics and Mathematical Sciences


Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Hindawiwwwhindawicom Volume 2018Volume 2018

Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

Nature and SocietyHindawiwwwhindawicom Volume 2018

Hindawiwwwhindawicom

Dierential EquationsInternational Journal of

Volume 2018


Decision SciencesAdvances in


AnalysisInternational Journal of


Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom


routing problem [7ndash9] 2E-PVRP generates a priori knowl-edge of dynamic customer changes based on the customerdata obtained by the delivery companies and uses the priorknowledge to process the dynamic demand informationduring the distribution process to form a robust vehiclescheduling solution Due to the complexity of the questionsraised this paper divides the solution into four modulesdata driven demand forecasting methods customer cluster-ing methods proactive demand quotas and replenishmentstrategies and vehicle routing optimization programs Thedata driven demand forecasting methods mainly excludesthe gross error points in the original data selects theappropriate measure dimension to evaluate the change ofcustomer attributes and then predicts the dynamic demandtrend The customer clustering methods will determine thecustomers who meet a certain distribution into the samecluster mainly based on the dynamic customer forecastingresults and static customer data The proactive demandquotas and replenishment strategies mainly evaluate thestatistical characteristics of customer needs in the clusterand allocate the distribution quotas of each stage reasonablyThe vehicle routing optimization program mainly adoptsthe exact or approximate path optimization algorithm togenerate the optimal delivery path plan for each clusterarea at different distribution stages To better illustrate thefeasibility of the framework system studied in this paper inview of the problems neglected by the current distributionenterprises this paper uses the logistics and distribution dataof large logistics company in Chongqing to test the proposedsolution The test results show that the solution has shownbetter results

The structure of the article is as follows In the secondpart the paper introduces the development of the vehiclerouting problem and its extension problem The third part isthe mathematical model of the problem The fourth part isthe realization process of the solution framework The fifthpart is the use of the enterprise empirical research data thesixth part is obtaining the management inspiration and theseventh part is the summary and future work

2 Literature Review

At present many scholars at home and abroad have made agreat deal of research on the 2E-VRP problem Among themdemand forecasting customer clusteringmethod and vehiclerouting solving algorithm in dynamic vehicle scheduling areclosely related to this paper Dynamic customer processingin dynamic vehicle routing has always been the focus ofresearch Wood [10] uses the three indicators of orderquantity order variation rate and order frequency as themeasure and uses the piecewise linear model to evaluatethe reliability of the demand forecast based on the dataThe test results show that in the case of small number oforders small differences in order quantity and lower orderfrequency the use of point-of-sale real-time shared data canachieve better forecasting results which is provided in thispaper by using multidimensional customer attribute datato predict dynamic customer demand Data-driven demandforecasting methods as an effective forecasting strategy are

also widely used by scholars Thomas [11] designed a real-time heuristic algorithm to predict future customer locationsand the probability of occurrence of demand resulting ina significant reduction in customer service latency Lima[12] takes customer needs and businesses on their own toleverage historical data and online data monitoring to antici-pate customer needs and improve customer responsivenessCabello [13] designed low cost forecasting algorithm foruncertain demand tomanage bank cash flow Jan [14] andMa[15] anticipate changes in customer demand in advance byconsidering demand forecasting and inventory control Sha[16] anticipates clientsrsquo expected waiting times significantlyusing historical demand data to proactively anticipate sparepart demand Willemai [17] and Porras [18] argue that inthe case of limited demand data sets the demand extreme(suddenly a large or small value) is unpredictable and thedemand dynamics affect the demand forecasting effect Inthis paper we propose a proactive demand quota method tosolve the failure of demand forecasting by using the strategyof multibatch and small-batch delivery That is to say acomplete service cycle is divided into initial delivery stage andmultiple replenishment stages If there is an extreme demandand a failure forecasting in the initial stage the shortfall ofdemandwill be supplemented through the late replenishmentphase to avoid the serious consequences of the forecastfailure

After acquiring the prior knowledge of dynamic clientsby using data-driven forecasting methods they need to bemerged with the original delivery customers to determine thecustomer base to be served during the full-service periodThe customer clustering method is to classify customers withsimilar attributes into the same type of clusters according toa certain rule and classify the clients with large differences inattributes into different clusters so as to realize the classifi-cation of customer behaviors Due to the effective customerclustering scheme in reducing logistics costs and improvingthe quality of service many scholars have adopted thestrategy of ldquoplanning route after clusteringrdquo to optimize thevehicle routing The authors in [19ndash25] analyzed the problemof service area allocation in the dynamic vehicle problemwithstochastic demand Ferrucci [26] assumed that the dynamiccustomer demand obeys Poisson distribution and dividedone cycle of distribution activities into several smaller gridsareas and calculated the Poisson distribution parametersof each grid area in different distribution stages Since thePoisson distribution parameters in the single grid area aresmall and cannot meet the delivery requirements the authoruses the maximum roaming radius and roaming time criteriato cluster the service subareas and optimize the distributionnetwork path The results show that the proactive schedul-ing method can effectively improve customer satisfactionFerrucci [27] expanded the space-time Poisson distributionmodelWang [28] discussed the customer clustering problemin 2E-VRP assumed that the location of Tier 1 and Tier 2facilities is determined and the customers are clustered intoa Tier 2 facility according to the set evaluation criteria Onthis basis this paper determines the waiting customer groupbased on the data-driven forecasting method and clusters thecustomer group to determine the service customer group of















min119885 = 119870119865sum119896119891=1

1198730cup119873119865sum119894=1

1198730cup119873119865sum119895=1

119909119896119891119894119895119888119896119891119894119895

+ 119870119878sum119896119904=1

119873119865cup119873119878sum119894=1

119873119865cup119873119878sum119895=1

119909119896119904119894119895119888119896119904119894119895 + [119873119865sum119894=1

119902119894119865119876] 119888119870119865

+ [119873119878sum119894=1

119902119894119904119876] 119888119878119865

(1)


119902119894119910119896119891119894 le 119865119876 (2)

119873sum119894=1

119902119894119910119896119904119894 le 119878119876 (3)

119873sum119894=1

1198871198941199091198961198911198940 = 119873sum119894=1

1198871198941199091198961198910119894 (4)

119873sum119894=1

(1 minus 119887119894) 119909119896119904119894119895 = 119873sum119894=1


119873sum119894=1

119873sum119895=1

(1 minus 119887119894) 119909119896119904119894119895 = 119873sum119894=1

119873sum119895=1

(1 minus 119887119894) 119909119896119904119895119894 (6)

119873sum119894=1

119873sum119895=1

119887119894119909119896119891119894119895 = 119873sum119894=1

119873sum119895=1

119887119894119909119896119891119895119894 (7)

119873119865sum119894=1

119910119896119891119894 = 1 (8)

119873119878sum119894=1

119910119896119904119894 = 1 (9)

119873sum119894=1

119887119894119902119894 ge 119873sum119894=1

(1 minus 119887119894) 119902119894 (10)


119873119865sum119894=1

119910119896119891119894119902119894 ge 119902119895 (11)


119873119878sum119894=1

119910119896119904119894119902119894 ge 119902119895 (12)










min119885119879 = 119888119873119865 + 119879sum119905=1

(119885119905 +119873119865sum119894=1

(119867119905119894 119888ℎ119894 + 119880119905119894 119888119906119894 )) (17)


119873119865sum119894=1

119863119894119876119879 le 119867119876119879 (18)

119879sum119905=1

119873119878sum119895=1


1 le 119879sum119905=1

119910119905119896119891119894 le 119879 119894 isin 1198730 cup 119873119865 (20)

119879sum119905=1

119910119905119896119904119894 = 1 119894 isin 119873119878 (21)


119888 gt 0 119888ℎ119894 ge 0 119888119906119894 ge 0 (23)







(24)




(25)


119865119881 = 1205831119897119889119909119894 119901119909119894 gt 1198981199091198941205832119897119889119909119894 119901119909119894 lt 119898119909119894 (26)
















119863119863119894 = 119899119889119910119899119899119904119905119886 + 119899119889119910119899 (27)





119886119894 = 1 119901119894 ge 1199011198861198881198881198901199011199050 119901119894 lt 119901119886119888119888119890119901119905 (28)


119902119888119894 = 119903119886119899119889 (120583119894 120583119894 + 3120590) 119886119894 = 0120583119894 119886119894 = 1 (29)















5 Numerical Test



Start

Initial solution



Tabu List


End


Tabu Rlowast



Yes

No

YesNo

Yes

No

Delete R



1

23

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

50 100 150 200 250 300 350 400 450 50000

50

100

150

200

250

300

350

400








(30)









(31)











3 4 1 3 2 161 157 0434 1 3 1 3 161 15 -0277 1 4 3 1 161 17 01410 1 3 3 3 267 256 -02113 4 4 1 3 179 168 -01319 2 4 1 3 137 136 -02621 4 4 1 1 963 102 -00323 1 3 3 2 124 136 -00328 4 1 2 3 188 1811 02929 3 2 1 1 111 13 00331 3 2 3 2 1219 1297 01533 1 2 2 1 1785 1759 004

0 100 200 300 400 5000

50

100

150

200

250

300

350

400

450


1

2 3

4












A whole cycle

Cluster

Hub

Cluster


Expert


Start End4th hour
















Cluster 3 c3-31-35-33-28-24-c3c3-22-18-20-25-27-c3

2377522564 17686 345

Cluster 4 c4-26-30-34-32-29-c4 17826 8174 -115







0 108642 12 14 16 18 20Counts

3800

3850

3900

3950

4000

4050

4100

4150

4200

The B

est V

alue










Single- typeC101

PVRPB207 C101











Data Availability




Acknowledgments


References
















































Journal of












Journal of







Volume 2018






Volume 2018






















min119885 = 119870119865sum119896119891=1

1198730cup119873119865sum119894=1

1198730cup119873119865sum119895=1

119909119896119891119894119895119888119896119891119894119895

+ 119870119878sum119896119904=1

119873119865cup119873119878sum119894=1

119873119865cup119873119878sum119895=1

119909119896119904119894119895119888119896119904119894119895 + [119873119865sum119894=1

119902119894119865119876] 119888119870119865

+ [119873119878sum119894=1

119902119894119904119876] 119888119878119865

(1)


119902119894119910119896119891119894 le 119865119876 (2)

119873sum119894=1

119902119894119910119896119904119894 le 119878119876 (3)

119873sum119894=1

1198871198941199091198961198911198940 = 119873sum119894=1

1198871198941199091198961198910119894 (4)

119873sum119894=1

(1 minus 119887119894) 119909119896119904119894119895 = 119873sum119894=1


119873sum119894=1

119873sum119895=1

(1 minus 119887119894) 119909119896119904119894119895 = 119873sum119894=1

119873sum119895=1

(1 minus 119887119894) 119909119896119904119895119894 (6)

119873sum119894=1

119873sum119895=1

119887119894119909119896119891119894119895 = 119873sum119894=1

119873sum119895=1

119887119894119909119896119891119895119894 (7)

119873119865sum119894=1

119910119896119891119894 = 1 (8)

119873119878sum119894=1

119910119896119904119894 = 1 (9)

119873sum119894=1

119887119894119902119894 ge 119873sum119894=1

(1 minus 119887119894) 119902119894 (10)


119873119865sum119894=1

119910119896119891119894119902119894 ge 119902119895 (11)


119873119878sum119894=1

119910119896119904119894119902119894 ge 119902119895 (12)










min119885119879 = 119888119873119865 + 119879sum119905=1

(119885119905 +119873119865sum119894=1

(119867119905119894 119888ℎ119894 + 119880119905119894 119888119906119894 )) (17)


119873119865sum119894=1

119863119894119876119879 le 119867119876119879 (18)

119879sum119905=1

119873119878sum119895=1


1 le 119879sum119905=1

119910119905119896119891119894 le 119879 119894 isin 1198730 cup 119873119865 (20)

119879sum119905=1

119910119905119896119904119894 = 1 119894 isin 119873119878 (21)


119888 gt 0 119888ℎ119894 ge 0 119888119906119894 ge 0 (23)







(24)




(25)


119865119881 = 1205831119897119889119909119894 119901119909119894 gt 1198981199091198941205832119897119889119909119894 119901119909119894 lt 119898119909119894 (26)
















119863119863119894 = 119899119889119910119899119899119904119905119886 + 119899119889119910119899 (27)





119886119894 = 1 119901119894 ge 1199011198861198881198881198901199011199050 119901119894 lt 119901119886119888119888119890119901119905 (28)


119902119888119894 = 119903119886119899119889 (120583119894 120583119894 + 3120590) 119886119894 = 0120583119894 119886119894 = 1 (29)















5 Numerical Test



Start

Initial solution



Tabu List


End


Tabu Rlowast



Yes

No

YesNo

Yes

No

Delete R



1

23

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

50 100 150 200 250 300 350 400 450 50000

50

100

150

200

250

300

350

400








(30)









(31)











3 4 1 3 2 161 157 0434 1 3 1 3 161 15 -0277 1 4 3 1 161 17 01410 1 3 3 3 267 256 -02113 4 4 1 3 179 168 -01319 2 4 1 3 137 136 -02621 4 4 1 1 963 102 -00323 1 3 3 2 124 136 -00328 4 1 2 3 188 1811 02929 3 2 1 1 111 13 00331 3 2 3 2 1219 1297 01533 1 2 2 1 1785 1759 004

0 100 200 300 400 5000

50

100

150

200

250

300

350

400

450


1

2 3

4












A whole cycle

Cluster

Hub

Cluster


Expert


Start End4th hour
















Cluster 3 c3-31-35-33-28-24-c3c3-22-18-20-25-27-c3

2377522564 17686 345

Cluster 4 c4-26-30-34-32-29-c4 17826 8174 -115







0 108642 12 14 16 18 20Counts

3800

3850

3900

3950

4000

4050

4100

4150

4200

The B

est V

alue










Single- typeC101

PVRPB207 C101











Data Availability




Acknowledgments


References
















































Journal of












Journal of







Volume 2018






Volume 2018














min119885 = 119870119865sum119896119891=1

1198730cup119873119865sum119894=1

1198730cup119873119865sum119895=1

119909119896119891119894119895119888119896119891119894119895

+ 119870119878sum119896119904=1

119873119865cup119873119878sum119894=1

119873119865cup119873119878sum119895=1

119909119896119904119894119895119888119896119904119894119895 + [119873119865sum119894=1

119902119894119865119876] 119888119870119865

+ [119873119878sum119894=1

119902119894119904119876] 119888119878119865

(1)


119902119894119910119896119891119894 le 119865119876 (2)

119873sum119894=1

119902119894119910119896119904119894 le 119878119876 (3)

119873sum119894=1

1198871198941199091198961198911198940 = 119873sum119894=1

1198871198941199091198961198910119894 (4)

119873sum119894=1

(1 minus 119887119894) 119909119896119904119894119895 = 119873sum119894=1


119873sum119894=1

119873sum119895=1

(1 minus 119887119894) 119909119896119904119894119895 = 119873sum119894=1

119873sum119895=1

(1 minus 119887119894) 119909119896119904119895119894 (6)

119873sum119894=1

119873sum119895=1

119887119894119909119896119891119894119895 = 119873sum119894=1

119873sum119895=1

119887119894119909119896119891119895119894 (7)

119873119865sum119894=1

119910119896119891119894 = 1 (8)

119873119878sum119894=1

119910119896119904119894 = 1 (9)

119873sum119894=1

119887119894119902119894 ge 119873sum119894=1

(1 minus 119887119894) 119902119894 (10)


119873119865sum119894=1

119910119896119891119894119902119894 ge 119902119895 (11)


119873119878sum119894=1

119910119896119904119894119902119894 ge 119902119895 (12)










min119885119879 = 119888119873119865 + 119879sum119905=1

(119885119905 +119873119865sum119894=1

(119867119905119894 119888ℎ119894 + 119880119905119894 119888119906119894 )) (17)


119873119865sum119894=1

119863119894119876119879 le 119867119876119879 (18)

119879sum119905=1

119873119878sum119895=1


1 le 119879sum119905=1

119910119905119896119891119894 le 119879 119894 isin 1198730 cup 119873119865 (20)

119879sum119905=1

119910119905119896119904119894 = 1 119894 isin 119873119878 (21)


119888 gt 0 119888ℎ119894 ge 0 119888119906119894 ge 0 (23)







(24)




(25)


119865119881 = 1205831119897119889119909119894 119901119909119894 gt 1198981199091198941205832119897119889119909119894 119901119909119894 lt 119898119909119894 (26)
















119863119863119894 = 119899119889119910119899119899119904119905119886 + 119899119889119910119899 (27)





119886119894 = 1 119901119894 ge 1199011198861198881198881198901199011199050 119901119894 lt 119901119886119888119888119890119901119905 (28)


119902119888119894 = 119903119886119899119889 (120583119894 120583119894 + 3120590) 119886119894 = 0120583119894 119886119894 = 1 (29)















5 Numerical Test



Start

Initial solution



Tabu List


End


Tabu Rlowast



Yes

No

YesNo

Yes

No

Delete R



1

23

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

50 100 150 200 250 300 350 400 450 50000

50

100

150

200

250

300

350

400








(30)









(31)











3 4 1 3 2 161 157 0434 1 3 1 3 161 15 -0277 1 4 3 1 161 17 01410 1 3 3 3 267 256 -02113 4 4 1 3 179 168 -01319 2 4 1 3 137 136 -02621 4 4 1 1 963 102 -00323 1 3 3 2 124 136 -00328 4 1 2 3 188 1811 02929 3 2 1 1 111 13 00331 3 2 3 2 1219 1297 01533 1 2 2 1 1785 1759 004

0 100 200 300 400 5000

50

100

150

200

250

300

350

400

450


1

2 3

4












A whole cycle

Cluster

Hub

Cluster


Expert


Start End4th hour
















Cluster 3 c3-31-35-33-28-24-c3c3-22-18-20-25-27-c3

2377522564 17686 345

Cluster 4 c4-26-30-34-32-29-c4 17826 8174 -115







0 108642 12 14 16 18 20Counts

3800

3850

3900

3950

4000

4050

4100

4150

4200

The B

est V

alue










Single- typeC101

PVRPB207 C101











Data Availability




Acknowledgments


References
















































Journal of












Journal of







Volume 2018






Volume 2018












min119885119879 = 119888119873119865 + 119879sum119905=1

(119885119905 +119873119865sum119894=1

(119867119905119894 119888ℎ119894 + 119880119905119894 119888119906119894 )) (17)


119873119865sum119894=1

119863119894119876119879 le 119867119876119879 (18)

119879sum119905=1

119873119878sum119895=1


1 le 119879sum119905=1

119910119905119896119891119894 le 119879 119894 isin 1198730 cup 119873119865 (20)

119879sum119905=1

119910119905119896119904119894 = 1 119894 isin 119873119878 (21)


119888 gt 0 119888ℎ119894 ge 0 119888119906119894 ge 0 (23)







(24)




(25)


119865119881 = 1205831119897119889119909119894 119901119909119894 gt 1198981199091198941205832119897119889119909119894 119901119909119894 lt 119898119909119894 (26)
















119863119863119894 = 119899119889119910119899119899119904119905119886 + 119899119889119910119899 (27)





119886119894 = 1 119901119894 ge 1199011198861198881198881198901199011199050 119901119894 lt 119901119886119888119888119890119901119905 (28)


119902119888119894 = 119903119886119899119889 (120583119894 120583119894 + 3120590) 119886119894 = 0120583119894 119886119894 = 1 (29)















5 Numerical Test



Start

Initial solution



Tabu List


End


Tabu Rlowast



Yes

No

YesNo

Yes

No

Delete R



1

23

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

50 100 150 200 250 300 350 400 450 50000

50

100

150

200

250

300

350

400








(30)









(31)











3 4 1 3 2 161 157 0434 1 3 1 3 161 15 -0277 1 4 3 1 161 17 01410 1 3 3 3 267 256 -02113 4 4 1 3 179 168 -01319 2 4 1 3 137 136 -02621 4 4 1 1 963 102 -00323 1 3 3 2 124 136 -00328 4 1 2 3 188 1811 02929 3 2 1 1 111 13 00331 3 2 3 2 1219 1297 01533 1 2 2 1 1785 1759 004

0 100 200 300 400 5000

50

100

150

200

250

300

350

400

450


1

2 3

4












A whole cycle

Cluster

Hub

Cluster


Expert


Start End4th hour
















Cluster 3 c3-31-35-33-28-24-c3c3-22-18-20-25-27-c3

2377522564 17686 345

Cluster 4 c4-26-30-34-32-29-c4 17826 8174 -115







0 108642 12 14 16 18 20Counts

3800

3850

3900

3950

4000

4050

4100

4150

4200

The B

est V

alue










Single- typeC101

PVRPB207 C101











Data Availability




Acknowledgments


References
















































Journal of












Journal of







Volume 2018






Volume 2018











(25)


119865119881 = 1205831119897119889119909119894 119901119909119894 gt 1198981199091198941205832119897119889119909119894 119901119909119894 lt 119898119909119894 (26)
















119863119863119894 = 119899119889119910119899119899119904119905119886 + 119899119889119910119899 (27)





119886119894 = 1 119901119894 ge 1199011198861198881198881198901199011199050 119901119894 lt 119901119886119888119888119890119901119905 (28)


119902119888119894 = 119903119886119899119889 (120583119894 120583119894 + 3120590) 119886119894 = 0120583119894 119886119894 = 1 (29)















5 Numerical Test



Start

Initial solution



Tabu List


End


Tabu Rlowast



Yes

No

YesNo

Yes

No

Delete R



1

23

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

50 100 150 200 250 300 350 400 450 50000

50

100

150

200

250

300

350

400








(30)









(31)











3 4 1 3 2 161 157 0434 1 3 1 3 161 15 -0277 1 4 3 1 161 17 01410 1 3 3 3 267 256 -02113 4 4 1 3 179 168 -01319 2 4 1 3 137 136 -02621 4 4 1 1 963 102 -00323 1 3 3 2 124 136 -00328 4 1 2 3 188 1811 02929 3 2 1 1 111 13 00331 3 2 3 2 1219 1297 01533 1 2 2 1 1785 1759 004

0 100 200 300 400 5000

50

100

150

200

250

300

350

400

450


1

2 3

4












A whole cycle

Cluster

Hub

Cluster


Expert


Start End4th hour
















Cluster 3 c3-31-35-33-28-24-c3c3-22-18-20-25-27-c3

2377522564 17686 345

Cluster 4 c4-26-30-34-32-29-c4 17826 8174 -115







0 108642 12 14 16 18 20Counts

3800

3850

3900

3950

4000

4050

4100

4150

4200

The B

est V

alue










Single- typeC101

PVRPB207 C101











Data Availability




Acknowledgments


References
















































Journal of












Journal of







Volume 2018






Volume 2018











119886119894 = 1 119901119894 ge 1199011198861198881198881198901199011199050 119901119894 lt 119901119886119888119888119890119901119905 (28)


119902119888119894 = 119903119886119899119889 (120583119894 120583119894 + 3120590) 119886119894 = 0120583119894 119886119894 = 1 (29)















5 Numerical Test



Start

Initial solution



Tabu List


End


Tabu Rlowast



Yes

No

YesNo

Yes

No

Delete R



1

23

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

50 100 150 200 250 300 350 400 450 50000

50

100

150

200

250

300

350

400








(30)









(31)











3 4 1 3 2 161 157 0434 1 3 1 3 161 15 -0277 1 4 3 1 161 17 01410 1 3 3 3 267 256 -02113 4 4 1 3 179 168 -01319 2 4 1 3 137 136 -02621 4 4 1 1 963 102 -00323 1 3 3 2 124 136 -00328 4 1 2 3 188 1811 02929 3 2 1 1 111 13 00331 3 2 3 2 1219 1297 01533 1 2 2 1 1785 1759 004

0 100 200 300 400 5000

50

100

150

200

250

300

350

400

450


1

2 3

4












A whole cycle

Cluster

Hub

Cluster


Expert


Start End4th hour
















Cluster 3 c3-31-35-33-28-24-c3c3-22-18-20-25-27-c3

2377522564 17686 345

Cluster 4 c4-26-30-34-32-29-c4 17826 8174 -115







0 108642 12 14 16 18 20Counts

3800

3850

3900

3950

4000

4050

4100

4150

4200

The B

est V

alue










Single- typeC101

PVRPB207 C101











Data Availability




Acknowledgments


References
















































Journal of












Journal of







Volume 2018






Volume 2018









Start

Initial solution



Tabu List


End


Tabu Rlowast



Yes

No

YesNo

Yes

No

Delete R



1

23

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

50 100 150 200 250 300 350 400 450 50000

50

100

150

200

250

300

350

400








(30)









(31)











3 4 1 3 2 161 157 0434 1 3 1 3 161 15 -0277 1 4 3 1 161 17 01410 1 3 3 3 267 256 -02113 4 4 1 3 179 168 -01319 2 4 1 3 137 136 -02621 4 4 1 1 963 102 -00323 1 3 3 2 124 136 -00328 4 1 2 3 188 1811 02929 3 2 1 1 111 13 00331 3 2 3 2 1219 1297 01533 1 2 2 1 1785 1759 004

0 100 200 300 400 5000

50

100

150

200

250

300

350

400

450


1

2 3

4












A whole cycle

Cluster

Hub

Cluster


Expert


Start End4th hour
















Cluster 3 c3-31-35-33-28-24-c3c3-22-18-20-25-27-c3

2377522564 17686 345

Cluster 4 c4-26-30-34-32-29-c4 17826 8174 -115







0 108642 12 14 16 18 20Counts

3800

3850

3900

3950

4000

4050

4100

4150

4200

The B

est V

alue










Single- typeC101

PVRPB207 C101











Data Availability




Acknowledgments


References
















































Journal of












Journal of







Volume 2018






Volume 2018
















(31)











3 4 1 3 2 161 157 0434 1 3 1 3 161 15 -0277 1 4 3 1 161 17 01410 1 3 3 3 267 256 -02113 4 4 1 3 179 168 -01319 2 4 1 3 137 136 -02621 4 4 1 1 963 102 -00323 1 3 3 2 124 136 -00328 4 1 2 3 188 1811 02929 3 2 1 1 111 13 00331 3 2 3 2 1219 1297 01533 1 2 2 1 1785 1759 004

0 100 200 300 400 5000

50

100

150

200

250

300

350

400

450


1

2 3

4












A whole cycle

Cluster

Hub

Cluster


Expert


Start End4th hour
















Cluster 3 c3-31-35-33-28-24-c3c3-22-18-20-25-27-c3

2377522564 17686 345

Cluster 4 c4-26-30-34-32-29-c4 17826 8174 -115







0 108642 12 14 16 18 20Counts

3800

3850

3900

3950

4000

4050

4100

4150

4200

The B

est V

alue










Single- typeC101

PVRPB207 C101











Data Availability




Acknowledgments


References
















































Journal of












Journal of







Volume 2018






Volume 2018












3 4 1 3 2 161 157 0434 1 3 1 3 161 15 -0277 1 4 3 1 161 17 01410 1 3 3 3 267 256 -02113 4 4 1 3 179 168 -01319 2 4 1 3 137 136 -02621 4 4 1 1 963 102 -00323 1 3 3 2 124 136 -00328 4 1 2 3 188 1811 02929 3 2 1 1 111 13 00331 3 2 3 2 1219 1297 01533 1 2 2 1 1785 1759 004

0 100 200 300 400 5000

50

100

150

200

250

300

350

400

450


1

2 3

4












A whole cycle

Cluster

Hub

Cluster


Expert


Start End4th hour
















Cluster 3 c3-31-35-33-28-24-c3c3-22-18-20-25-27-c3

2377522564 17686 345

Cluster 4 c4-26-30-34-32-29-c4 17826 8174 -115







0 108642 12 14 16 18 20Counts

3800

3850

3900

3950

4000

4050

4100

4150

4200

The B

est V

alue










Single- typeC101

PVRPB207 C101











Data Availability




Acknowledgments


References
















































Journal of












Journal of







Volume 2018






Volume 2018










A whole cycle

Cluster

Hub

Cluster


Expert


Start End4th hour
















Cluster 3 c3-31-35-33-28-24-c3c3-22-18-20-25-27-c3

2377522564 17686 345

Cluster 4 c4-26-30-34-32-29-c4 17826 8174 -115







0 108642 12 14 16 18 20Counts

3800

3850

3900

3950

4000

4050

4100

4150

4200

The B

est V

alue










Single- typeC101

PVRPB207 C101











Data Availability




Acknowledgments


References
















































Journal of












Journal of







Volume 2018






Volume 2018











Cluster 3 c3-31-35-33-28-24-c3c3-22-18-20-25-27-c3

2377522564 17686 345

Cluster 4 c4-26-30-34-32-29-c4 17826 8174 -115







0 108642 12 14 16 18 20Counts

3800

3850

3900

3950

4000

4050

4100

4150

4200

The B

est V

alue










Single- typeC101

PVRPB207 C101











Data Availability




Acknowledgments


References
















































Journal of












Journal of







Volume 2018






Volume 2018














Single- typeC101

PVRPB207 C101











Data Availability




Acknowledgments


References
















































Journal of












Journal of







Volume 2018






Volume 2018










Data Availability




Acknowledgments


References
















































Journal of












Journal of







Volume 2018






Volume 2018










































Journal of












Journal of







Volume 2018






Volume 2018















Journal of












Journal of







Volume 2018






Volume 2018








Documents

Proactive Two-Level Dynamic Distribution Routing Optimization …downloads.hindawi.com/journals/mpe/2018/5191637.pdf · 2,7 3) is the predicted value of the customer attribute using