Resource Allocation Optimization Model of Collaborative...

Research ArticleResource Allocation Optimization Model of CollaborativeLogistics Network Based on Bilevel Programming

Xiao-feng Xu Wei-hong Chang and Jing Liu

College of Economics and Management China University of Petroleum Qingdao 266580 China

Correspondence should be addressed to Xiao-feng Xu xuxiaofengupceducn

Received 14 July 2016 Accepted 23 January 2017 Published 22 February 2017

Academic Editor Tomas Margalef

Copyright copy 2017 Xiao-feng Xu 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

Collaborative logistics network resource allocation can effectively meet the needs of customers It can realize the overall benefitmaximization of the logistics network and ensure that collaborative logistics network runs orderly at the time of creating valueTherefore this article is based on the relationship of collaborative logistics network supplier the transit warehouse and sellersand we consider the uncertainty of time to establish a bilevel programming model with random constraints and propose a geneticsimulated annealing hybrid intelligent algorithm to solve it Numerical example shows that the method has stronger robustnessand convergence it can achieve collaborative logistics network resource allocation rationalization and optimization

1 Introduction

Collaborative logistics network is a supply and demandnetwork which consists of supply collaboration nodes suchas rawmaterials and equipment and logistics function collab-oration nodes such as transportation and warehousing andeven road and relationship between nodes [1] The allocationof resource is to meet the supply and demand network Theaim is to collaborate logistics network enterprise internaland external resources and combine the supply chain systemeffectively which is composed of producers manufacturersand customers to realize the lowest cost and the best qualityservice [2] So reasonable resource allocation process is thebasis to realize the orderly operation of the whole logisticsnetworkHowever collaborative logistics network has suppli-ers transit warehouses vendors and other forms of logisticsnode and has some characteristics such as being dynamicopen and complex It leads to some uncertainty factors inthe process of allocating logistics resources that may have aneffect on the running time and operating costTherefore thisresearch about resource allocation of collaborative logisticsnetwork is how to select nodes in the numerous suppliersand transit warehouse under the condition of considering theinfluence of uncertainty factors to realize the optimal logisticssystem

The current research on collaborative logistics networkresource scheduling is not enough in depth and it is mainlyconcentrated in the delivery path optimization and distri-bution address selection as well as the relationship betweencollaboration node and so forth In terms of path selectionYu et al [3] established a scheduling model with time asconstraint and the shortest route as object and used artificialintelligence algorithms to solve the problem Najera [4]used evolutionary algorithm to study transportation routingproblem in consideration of capacity of vehicle Mir andAbolghasemi [5] took vehicle transportation situations ofencoring or not into account and proposed the optimalroute according to the customer location changes Chenet al [6] made full use of geographic information systemtechnology to select path under the constraint of the leastdistribution sites In terms of optimal location selectionCheng et al [7] study the impact of the rapid transit on thecapacity of current urban transportation system and a two-mode network capacity model including the travel modesof automobile and transit is developed based on the well-known road network capacity model Turskis and Zavadskas[8] used the fuzzy multiple criteria decision to describefuzziness of site selection of distribution center Nozick andTurnquist [9] established a location optimization decisionmodel from the aspects of cost and customer responsiveness

HindawiScientific ProgrammingVolume 2017 Article ID 4587098 8 pageshttpsdoiorg10115520174587098

2 Scientific Programming

Yang and Zhou [10] built the location selection model withequilibrium constraints considering facility competition onthe basis of the equilibrium theory and then applied geneticalgorithm and projection algorithm to solve the model Forthe relationship between collaboration points Qiu andWang[11] develop a robust optimization model for designing athree-echelon supply chain network that consists ofmanufac-turers distribution centers and retailers under both demanduncertainty and supply disruptions Liu et al [12] consideredthree-layer logistics service supply chain and studied theorder task allocation model between collaboration nodes

Integrating the documents we can find that the currentresearch focused on the microscopic aspects such as pathoptimization and site selection and used artificial intelligencealgorithm to solve the model But the ideal model cannotfully describe the collaborative allocation of resources dueto the networkrsquos complexity and some uncertainty factorsin the process of resource allocation Collaborative logisticsnetwork resource allocation process involves three levelswhich are suppliers transit warehouse and vendors so thebilevel programming model can be used to explain therelationship between every two levels of nods At the sametime the stochastic constrained programming can protectmodel against uncertain influence and it has been appliedto the system dynamics structural dynamics and financialand other fields [13ndash15] Therefore this article will set up thethree-level nodes relationship among the suppliers transitwarehouses and retailers and establish a bilevel program-ming model with chance constrained to control uncertaintyfactors so as to make the whole logistics network systemoptimal under meeting the nodesrsquo profit of both sides

Generally speaking the bilevel programming is NP-hardproblem Ben-Ayed and Blair (1988) have proved that [16]this problem does not have a polynomial algorithm so thesolution of it is very complicated Like genetic algorithm (GA)and Simulated Annealing Algorithm (Simulated AnnealingSA) Neural Network Algorithm (NNA) and so forth someintelligent algorithms were used to solve the bilevel program-ming problem Li et al [17] put forward a genetic algorithmthat can effectively solve bilevel programming problemIn this method they used constraint to transform bilevelproblem into a single-level one and designed the binarycoding to solve the multiplier and numerical experimentshows that the given algorithm can find the global optimalsolution in the least time Niwa et al [18] proposed a bilevelprogramming problem that the upper class has only onedecision-maker while the lower one has multiple decision-makers and a distribution of the genetic algorithm Li andWang [19] studied a special kind of linear quadratic bilevelprogramming problems and genetic algorithmwas proposedafter being converted into equivalent problem

Genetic algorithm by the ideas of the fittest in naturechooses an optimal individual for the solution of the modelby selection crossover and mutation genetic operationAlthough it has some characteristics such as simple oper-ation strong operability and problem space independenceit is easy to exhibit slow convergence speed and get onlylocal optimal value [20] Simulated annealing algorithm is theresult of logistics annealing principle of solid matter starting

from an initial temperature to find the optimal solution inthe solution space with the reduction of the temperatureparameters Although it can get the global optimal solutionit evolved slowly and has strong dependence on parameters[21] So there are advantages and disadvantages respectivelyof the two algorithms hybrid genetic simulated annealingalgorithms can compensate deficiency for each other theynot only can search the related areas of optimal solution inthe global but also can find the optimal solution in the regionof the optimal solution and there have been some scholarswho have done the related research Wang and Zheng [22]proposed a hybrid heuristic algorithm the algorithm mixedthe genetic algorithm and simulated annealing method andthe sampling process of simulated annealing method insteadof mutation operators of genetic algorithm and this algo-rithm improves the local search ability of genetic algorithmWang et al [23] assume that the drivers allmake route choicesbased on Stochastic User Equilibrium (SUE) principle Twomethods that is the sensitivity analysis-based method andgenetic algorithm (GA) are detailedly formulated to solve thebilevel reserve capacity problem Kong et al [24] establisha bilevel programming model of land use structure indexesvariables and use GASA to solve the problem and land androad area ratio should be improved by numerical exampleresults So in this paper designing the combination of geneticand simulated annealing hybrid algorithm to solve the bilevelprogramming problem is feasible

2 Considering Uncertainty ResourceDeployment of Bilevel Programming Model

21 Bilevel Programming Model Bilevel programming (BP)[25] model was presented by Bracken andMcGill in 1973 thelower decision-maker makes decision in the first place theupper policymakers must predict the possible reaction of thelower ones and then the lower one reacts according to thedecision of the upper one to optimize the objective functionof the individual The general model is

min119909isin119883

119865 (119909 119910)st 119866 (119909 119910) le 0min119910isin119884

119891 (119909 119910)st 119892 (119909 119910) le 0

(1)

Among them 119909 isin 1198771198991 and 119910 isin 1198771198992 The upper variable is119909 isin 1198771198991 and the lower variable is 119910 isin 1198771198992 Also the functions119865 1198771198991 times 1198771198992 rarr 119877 and 119891 1198771198991 times 1198771198992 rarr 119877 are the upper andthe lower objective function respectively and vector-valuedfunctions 119866 1198771198991 times 1198771198992 rarr 1198771198981 and 119892 1198771198991 times 1198771198992 rarr 1198771198982 arerespectively the upper and the lower constraint conditions

22 Chance Constrained Programming Model Chance Con-strained Programming [26] is a method of stochastic pro-gramming put forward by Charnes and Cooper in 1959 Itallows decision value within a certain range of fluctuations

Scientific Programming 3

considering the possibility that decision-making process maynot meet the constraint conditions but the probability of theconstraint set-up must not be less than a certain confidencelevel 120572 which is small enough The general model is

min 119885 (119909) = 119899sum119895=1

119888119895119909119895st Pr[[

119899sum119895=1

1198861119895119909119895 ge 1198871 119899sum119895=1

119886119898119895119909119895 ge 119887119898]] ge 120572119909119895 ge 0 119895 = 1 2 119899

(2)

Among them Pr[ ] is the probability of the event set-up 120572is the confidence probability for the condition 119887119898 are randomvariables that obey a certain distribution and 119886 and 119887 obey119873(1205831 12059021) and119873(1205832 12059022) respectively23 The Model of Collaborative Logistics Network ResourceAllocation considering Uncertainty This paper researches onthe resource allocation optimization decision ofmultiple sup-pliers and multiple warehouse transfer nodes and retailersThe raw materials price and transportation fee that each sup-pliers charge are different and it is a key issue for the retailersto select the optimization suppliers and carry resources moreeffectively to their warehouses transfer node At the sametime the retailers compare the transit fees cost of eachwarehouse choosing the lowest one or more warehouses toallocation according to their own requirements which needto focus on every step of the whole logistics network Thiskind of relationship can be explained by bilevel programmingmodel Described in this paper the upper programmingrsquosgoal is how the suppliers realize the profit maximizationof their own on the condition of meeting the warehouserequirements the lower level programming describes thelowest cost during the process of warehouse transit center andretailer

In order to understand better we can use mathematicallanguage to describe the problem as follows

Assume that the logistics network119873 consists of suppliers119878119894 | 119894 = 1 2 119899119894 transit warehouses 119872119895 | 119895 =

1 2 119899119895 retailers 119875119896 | 119896 = 1 2 119899119896 and links betweeneach node 119877 | 119877 isin 119877119878119894119872119895 cup 119877119872119895119875119896 including logistics nodes119874 | 119874 isin 119878 cup 119872 cup 119875 When retailer 119875119896 sends the demandquantity119863119875119896

119897of resource 119897 | 119897 = 1 2 119899119897 the resource will

be transported to 119875119896 from warehouses119872119895 119883119897119872119895119875119896 stands forthe quantity of products 119897 that are distributed to the retailers119875119896 from the warehouses 119872119895 119883119897119878119894119872119895 stands for the quantityof raw materials that are distributed to the warehouses 119872119895from the suppliers 119878119894 119864(119877) | 119864(119877) isin 119864(119877119878119894119872119895) cup 119864(119877119872119895119875119896)stand for the distance between all logistics nodes Due tothe different location of logistics nodes the product feesof transportation storage packaging and processing foreach unit are also different Therefore 119862(119877) | 119862(119877) isin119862(119877119897119878119894119872119895) cup 119862(119877119897119872119895119875119896) stand for the cost of each unit distancebetween different logistics nodes to transport resources 119897119862(119891119897119874) and 119862(119892119897119874) stand for the unit cost of storage andprocessing (including labor) for all logistics nodes Suppliersas the disclosing party charge transit warehouses 119862(119883119897119878119894119872119895)for the resources 119897 Considering that all logistic nodes have acertain amount of time requirement to order processing anddistribution of resources the times of delivery requirementfrom warehouses to retailers and supplies to warehousesrespectively are119879119897119872119895119875119896 and119879119897119878119894119872119895 the times of order processing

and production processing respectively are 119879119897119872119895119875119896 1015840 119879119897119878119894119872119895 1015840119879119897119872119895119875119896 10158401015840 and 119879119897119872119895119875119896 10158401015840 transport vehicle maximum loadingcapacities respectively are 119866119872119895119877119896 and 119866119878119894119872119895

In the process of research the assumptions made are asfollows for the purpose of simplified model

(1) All land transportation is between all logistics nodes(2) The logistics node routes and distance have to be

known and are fixed(3) Vehicle average speed is 119881 during the process of

transportation between various logistics nodes

231 The Upper Programming considering the Relationshipbetween Suppliers and Warehouse Transit Centers

max1198651 = 119899sum119895=1

119899sum119896=1

119899sum119897=1

119899sum119894=1

(119862 (119883119897119878119894119872119895) minus 119862 (119877119897119878119894119872119895)119864 (119877119878119894119872119895) minus 119862 (119891119897119878119894) minus 119862 (119892119897119878119894))119883119897119878119894119872119895119906119894 (3)

119899sum119894=1

119906119894 ge 1 (4)

119866119878119894119872119895 ge 119883119897119878119894119872119895 (5)

Pr[[119879119897119878119894119872119895

1015840 + 119879119897119878119894119872119895 10158401015840 + 119864 (119877119878119894119872119895)119881 le 119879119897119878119894119872119895]] = 120572 (6)

119906119894119883119897119878119894119872119895 = 119883119897119872119895119875119896 (7)


119883119897119878119894119872119895 ge 0 119894 = 1 2 119899 119895 = 1 2 119899 (8)

119906119894 isin 0 1 (9)

Among them (3) is from the point of view of the suppli-ers which is pursuing of the profit maximization (4) ensureswarehouse transit centers at least choose one supplier (5)means the amount of resources that the suppliers providecannot exceed its maximum of vehicle loading capacity(6) stands for the probability that order processing timeprocessing time and shipping time of supplies cannot exceedthe longest time of warehouse transit centers which is 120572 (7)means the amount of resources that warehouse transit centersprovide is equal to what all suppliers provide (8) resourcedemand is a positive number (9) is supplierrsquos 0-1 variableconstraints which means that select supplier 119894 has a value of1 or a value of 0

232 The Lower Programming considering the Relationshipsbetween Warehouse Transit Centers and Retailers

min1198652= 119899sum119895=1

119899sum119896=1

119899sum119897=1

119899sum119895=1

(119862 (119877119897119872119895119875119896)119864 (119877119872119895119875119896) + 119862 (119891119897119872119895) + 119862 (119892119897119872119895))sdot 119883119897119872119895119875119896119906119895

(10)

119899sum119895=1

119906119895 ge 1 (11)

119899sum119895=1

119899sum119896=1

119899sum119895=1

119906119895119883119897119872119895119875119896 ge 119863119875119896119897 (12)

119866119872119895119877119896 ge 119883119897119872119895119875119896 (13)

Pr[[119879119897119872119895119875119896

1015840 + 119879119897119872119895119875119896 10158401015840 + 119864 (119877119872119895119875119896)119881 le 119879119897119872119895119875119896]] = 120573 (14)

119883119897119872119895119875119896 ge 0 119895 = 1 2 119899 119896 = 1 2 119899 (15)

119906119895 isin 0 1 (16)

Among them expression (10) stands for the warehousetransit center and distributors as a whole pursuing theminimizing cost including transportation and storage andproducing cost (11) ensures that retailers choose at leastone supply warehouse transit center (12) means the totalresources that product warehouse transit centers provideshould meet the demand of retailers 119875119896 (13) means theamount of resources that warehouse transit centers providecannot exceed its maximum of vehicle loading capacity (14)stands for the probability that the order processing timeprocessing time and shipping time of warehouse transitcenters cannot exceed the longest time of retailers which is120573 (15) means resource demand is a positive number (16)

is warehouse transit centersrsquo 0-1 variable constraints whichmeans that chosen warehouse 119895 has a value of 1 or value of 03 The Solution to the Resource

Allocation Bilevel Programming Modelconsidering Uncertainty

31 Random Planning Constraints Transformation As forthe uncertain factors during transportation and order pro-cessing we need to transform them into deterministic con-straints The solution method of stochastic programmingconstraint probably has two kinds one is transforming thestochastic programming into a deterministic mathematicalprogramming through certain changes and then using theexisting method that solves the deterministic mathematicalprogramming to solve the other method is to use theintelligent algorithm such as neural network based on theidea of approximation function

Due to solving bilevel programming after stochasticprogramming constraints transformation we take the firstmethod to research The order processing times 119879119897119872119895119875119896 1015840and 119879119897119878119894119872119895 1015840 respectively obey the normal distributions

119879119897119872119895119875119896 1015840 sim 119873(120583(119879119897119872119895119875119896 1015840) 120590(119879119897119872119895119875119896 1015840)2) and 119879119897119878119894119872119895 1015840 sim 119873(120583(119879119897119878119894119872119895 1015840)120590(119879119897119878119894119872119895 1015840)2) 119879119897119872119895119875119896 10158401015840 and 119879119897119878119894119872119895 10158401015840 respectively obey the nor-

mal distributions 119879119897119872119895119875119896 10158401015840 sim 119873(120583(119879119897119872119895119875119896 10158401015840) 120590(119879119897119872119895119875119896 10158401015840)2)and 119879119897119878119894119872119895 10158401015840 sim 119873(120583(119879119897119878119894119872119895 10158401015840) 120590(119879119897119878119894119872119895 10158401015840)2) 119864(119877119872119895119875119896)119881 and119864(119877119878119894119872119895)119881 respectively obey the normal distributions119864(119877119872119895119875119896)119881 sim 119873(120583(119864(119877119872119895119875119896)119881) 120590(119864(119877119872119895119875119896)119881)2) and119864(119877119878119894119872119895)119881 sim 119873(120583(119864(119877119878119894119872119895)119881) 120590(119864(119877119878119894119872119895)119881)2)

So the stochastic programming constraint (7)

Pr[[119879119897119878119894119872119895

1015840 + 119879119897119878119894119872119895 10158401015840 + 119864 (119877119878119894119872119895)119881 le 119879119897119878119894119872119895]] = 120572 (17)

can be transformed into

120583 (119879119897119878119894119872119895 1015840) + 120601minus1 (120572) 120590 (119879119897119878119894119872119895 1015840) + 120583 (119879119897119878119894119872119895 10158401015840)+ 120601minus1 (120572) 120590 (119879119897119878119894119872119895 10158401015840) + 120583(119864(119877119878119894119872119895)119881 )

+ 120601minus1 (120572) 120590(119864(119877119878119894119872119895)119881 ) le 119879119897119878119894119872119895(18)


Initialize the population and determinethe initial temperature

Comment on the current population

Convergence criterionis satisfied or not

Perform the GA duplication operation

Perform the GA crossover operation

Perform GA mutation operation

Get initial population GA and SA was carried out onthe individual search

Generated by the SA status function toproduce new individual

Accept the new individual in probability

SA sampling is stable or notAnnealingtemperatureoperation

The outputoptimization results

Yes

No

Yes No

Figure 1 The solving steps of genetic simulated annealing algorithm

and the stochastic programming constraint (14)

Pr[[119879119897119872119895119875119896

1015840 + 119879119897119872119895119875119896 10158401015840 + 119864 (119877119872119895119875119896)119881 le 119879119897119872119895119875119896]] = 120573 (19)


120583 (119879119897119872119895119875119896 1015840) + 120601minus1 (120573) 120590 (119879119897119872119895119875119896 1015840) + 120583 (119879119897119872119895119875119896 10158401015840)+ 120601minus1 (120573) 120590 (119879119897119872119895119875119896 10158401015840) + 120583(119864(119877119872119895119875119896)119881 )

+ 120601minus1 (120573) 120590(119864(119877119872119895119875119896)119881 ) le 119879119897119872119895119875119896 (20)

32 The Solving Thought of Genetic Simulated AnnealingAlgorithm The basic idea of genetic simulated annealingalgorithm is as follows firstly encoding the upper planningvariables and solving the lower programming to calculate thefitness of each string And then one can get the best seriesthrough copy crossover mutation and simulated annealingSpecific steps are shown as Figure 1

Step 1 Initialization

(1-1) Set parameters including the crossover probability ofgenetic algorithm 119875119888 mutation probability 119875119898 eachgeneration population of individuals (chromosomes)number119873 and largest evolution algebra Maxgen Setthe evolution algebra gen = 0

(1-2) Confirm the number of inner loops119872 and the initialvalue of the temperature 119879119900 of simulated annealingalgorithm let 119879 = 119879119900

(1-3) Determine a reasonable fitness function accordingto the objective function 1198651 of upper programmingdetermine the encodingway of the decision variable 119906of upper programming and randomly generate initialpopulation119883(1) = ( 119909119894(1) ) 119894 = 1 2 119873 letgen = 1

Step 2 Take 119883(gen) into lower programming to be UEdistribution calculation and calculate the fitness of eachindividual 119909119894(gen) (119894 = 1 2 119873) If gen = Maxgen thelargest fitness chromosome is the optimal solution of resourceallocation else turn to Step 3

Step 3 Copy group 119883(gen) according to the fitness distribu-tion


Step 4 It is crossover operation according to the crossoverprobability 119875119888Step 5 Perform mutation operation according to the muta-tion probability 119875119898 let gen = gen + 1 get a new population119883(gen) and then calculate the fitness of individuals of119883(gen)Step 6 For 119894 = 1 conducting the simulated annealing ofspecies119883(gen) is as follows(6-1) If 119894 = 119873 turn to Step 7 otherwise the cycle counting

round 119896 = 1 and turn to (6-2)(6-2) Get individual 119909119894(gen) by state function then decode

new individuals and conduct UE distribution calcu-lation under lower programming to get the objectivefunction value of the upper programming and calcu-late the fitness

(6-3) Accept new individual under Metropolis probabilityacceptance formula

(6-4) if 119896 = 119872 119894 = 119894 + 1 turn to (6-1) else 119896 = 119896 + 1 turnto (6-2)

Step 7 Annealing temperature let 119879 = 05119879 and turn toStep 2

Description is as follows

(1) The upper decision variables generally take binaryencoding multivariate encoding is as follows

decision variables 119906 = 1199061 1199062 sdot sdot sdot 119906119899mapping darr darr darr darr

Chromosome (string) 119909 = 0011 1011 0110 (21)

(2) In (1-3) the relationship between the length of thesubstring 120573 and the precision of decision variables 120587is

120573 ge log2 (119906max minus 119906min120587 + 1) (22)

(3) In a (6-2) SA state function can do random exchangeof two different genes positions of chromosome andreverse genes order of different random position ofchromosome such as

Decision variables 119906 = 1199061 1199062Genes Position 2 5 3 7Chromosome 119909 = 01100101 10110101 (23)

Assume that the random variable respectively positionsare 2 and 3 and 5 and 7 and the new individuals afterexchanging and reversing are

1199091 = 00101101 100101111199092 = 00011101 10010111 (24)

SuppliesTransit node

RetailersDistance between nodes(unit km)

S1

S2

S3

S4

M1

M2

M3

P1

100

100

100

100

100

120

120

80

180

180

200

220

260

40

Figure 2 Production and sale collaborative logistics network of onesneaker brand

Table 1 The distance between each supplier and transit warehouse

M1km M2km M3kmS1 200 240 infinS2 240 220 infinS3 infin 220 180S4 infin infin 180

4 The Sample Simulation

41 Sample Taking the collaborative logistics networkproduction-sales of one sneaker brand as an example aproduct retailer put forward a demand of 4000 pieces ofgoods to the transit warehouse according to the sales plan andproduct orders Assume that we can choose goods from foursuppliers and three transit warehouses that are available vehi-cle average speed is 40 kilometers per hour between variouslogistics nodes in the process of transportation the biggestload capacities from suppliers to the transit warehouses andfrom transit warehouses to retailers are respectively 2000and 3000 and specific arrangement is shown in Figure 2

The distance between all suppliers to the transit ware-house is shown in Table 1 the suppliersrsquo storage and pro-cessing fees for each unit are shown in Table 2 The distancebetween each transit warehouse to the retailer and the transitwarehousesrsquo storage and processing fees for each unit areshown in Table 3

42 Solving Example The actual material delivery time thatwarehouse transit node and retailer require is 10 hours and12 hours because of that the supplier and warehouse transitpoint have some uncertain factors such as the order process-ing and production time obeys the normal distribution asTable 4 shows there are also uncertainty factors on transportwhich obey the normal distribution table as shown in Table 5value interval is 120583 plusmn 3120590 namely the probability that thevalue points fall in the interval is 9973 and the probability


Table 2 The material charge and cost for each unit of storage andtransportation of suppliers

Materialcharges(RMB)

Storagecharges(RMB)

Processingcharges(RMB)

Transportationcharges(RMB)

S1 110 01 015 002S2 100 015 015 003S3 110 01 01 0035S4 100 015 01 0025

Table 3 The distance between retailer and transit warehouses andtransit warehousesrsquo cost for unit of storage and transportation

Distance(km)

Storagecharges(RMB)



M1 260 02 025 002M2 220 03 02 0025M3 280 02 015 0015

Table 4 The uncertain index value of the supplier and warehousetransfer pointrsquos order processing and production (unit hours)

Orderprocessing time

Production andprocessing time

Supplier 119873(01 5) 119873 (1 5)Storage andtransit point 119873(02 5) 119873 (05 5)Table 5 The uncertain index value of transport time range ofsuppliers to transit warehouse andwarehouse transfer to seller (unithours)

M1 M2 M3S1 119873(5 5) 119873 (6 5) infinS2 119873(6 5) 119873 (55 5) infinS3 infin 119873(55 5) 119873 (45 5)S4 infin infin 119873(45 5)Seller 119873(65 5) 119873 (55 5) 119873 (7 5)that ensures finishing the logistics tasks in the time of thewarehouse transit node and retailer is 90 which means 120572and 120573 both are 90

The parameters of the algorithm are as follows thepopulation size is 50 the crossover probability is 06 theprobability of mutation is 01 the cooling coefficient is 095and the initial temperature is 100 The result converges tothe optimal solution after 45 generations by using Matlab70for many times while traditional genetic algorithm iterationnumber is 64 as shown in Figure 3 The optimal solutionin the genetic simulated annealing algorithm is shown inTable 5

It can be seen as shown in Table 6 that supplier S1deployed 1000 unit materials to transit warehouse M1supplier S4 respectively deployed 199999 and 100001 unitmaterials toM2 andM3 on the basis of meeting the expected

GAGASA

Iterations

Fitn

ess

2484

2482

248

2478

2476

2474

2472

247

24681009080706050403020100

times10minus6

Figure 3 The convergence comparison chart of genetic simulatedannealing algorithm and genetic algorithm

Table 6The resources allocation for each supplier to the warehousetransfer point

M1 M2 M3S1 1000S2S3S4 199999 100001

delivery time and it makes the supplierrsquos profit maximum405000 Yuan while retailerrsquos cost is minimum about 19300Yuan while on the basis of traditional genetic algorithmthe maximum profit of suppliers is 404990 Yuan The resultindicates that the solution can maximize the interests of bothsides which verify the operability and optimization of themodel

5 Conclusion

Collaborative logistics network is a virtual organizationwhich is led by manufacturingservice companies or inde-pendent third-party logistics enterprise It is a supply anddemand network made up of supply collaboration nodesfunction of logistics nodes and the link road and relationshipbetween nodes the core task is overall plan and deploymentaccess of the network node resources to realize the overallinterests andmeet the customer serviceTherefore this paperestablishes a supply-sales network on the basis of collab-orative logistics network resource allocation model whichincludes collaborative logistics network suppliers warehousetransit nodes retailers and their node link From retailerrsquosdemand as a starting point considering the shipping time andquantity and distribution cost factors we establish a bilevelprogramming model with uncertainty factors On this basis


we use the genetic simulated annealing algorithm to analyzeand solve the model which can get the optimal scheme thatcan not only meet suppliers benefit maximization but alsomake cost minimum to retailers The analysis results showthe feasibility and validity of the model which can providethe optimal resource allocation decisions and plans

Competing Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This research was supported by the National Natural ScienceFoundation of China (Grant no 71501188) the NaturalScience Foundation of Shandong Province China (Grant noZR2015GQ006) and the Fundamental Research Funds forthe Central Universities China (Grant no 15CX04100B)

References

[1] X-F Xu J-L Zhao and J-K Song ldquoUncertain control opti-mization of resource planning for collaborative logistics net-work about complex manufacturingrdquo System Engineering The-ory amp Practice vol 32 no 4 pp 799ndash806 2012

[2] L H Shan and Z Y Zhang ldquoAnalysis on logistics network sys-tem operation mode based on dissipative structurerdquo LogisticsScience-Technology vol 12 no 28 pp 86ndash89 2014

[3] B Yu Z Z Yang and B Z Yao ldquoA hybrid algorithm for vehiclerouting problem with time windowsrdquo Expert Systems withApplications vol 38 no 1 pp 435ndash441 2011

[4] A G Najera ldquoThe vehicle routing problem with backhauls amulti-objective evolutionary approachrdquoEvolutionaryComputa-tion in Combinatorial Optimization vol 7245 no 42 pp 255ndash266 2012

[5] H S A Mir and N Abolghasemi ldquoAparticle swarm opti-mization algorithm for open vehicle routing problemrdquo ExpertSystems with Applications vol 38 no 9 pp 11547ndash11551 2011

[6] Y Chen R Z Ruan and M C Yan ldquoAlgorithm of path opti-mization for physical distribution based on GISrdquo GeospatialInformation vol 2 no 10 pp 104ndash182 2012

[7] L Cheng M Du X Jiang and H Rakha ldquoModeling andestimating the capacity of urban transportation network withrapid transitrdquo Transport vol 29 no 2 pp 165ndash174 2014

[8] Z Turskis and E K Zavadskas ldquoA new fuzzy additive ratioassessment method (ARAS-F) Case study the analysis of fuzzymultiple criteria in order to select the logistic centers locationrdquoTransport vol 25 no 4 pp 423ndash432 2010

[9] L K Nozick and M A Turnquist ldquoInventory transportationservice quality and the location of distribution centersrdquo Euro-pean Journal of Operational Research vol 129 no 2 pp 362ndash3712001

[10] Y X Yang and G G Zhou ldquoStudy on location model of facilitycompetition for closed-loop supply chain network with randomdemandsrdquo Control and Decision vol 10 no 26 pp 1553ndash15612011

[11] R Qiu and Y Wang ldquoSupply chain network design underdemand uncertainty and supply disruptions a distributionally

robust optimization approachrdquo Scientific Programming vol2016 Article ID 3848520 15 pages 2016

[12] W H Liu S Y Qu and S Y Zhong ldquoOrder allocation inthree-echelon logistics service supply chain under stochasticenvironmentsrdquo Computer Integrated Manufacturing Systemsvol 2 no 18 pp 381ndash388 2012

[13] Q Zeng and X-Z Xu ldquoAssessing the reliability of a multistatelogistics network under the transportation cost constraintrdquoDiscrete Dynamics in Nature and Society vol 2016 Article ID2628950 8 pages 2016

[14] P Guo G H Huang and Y P Li ldquoAn inexact fuzzy-chance-constrained two-stage mixed-integer linear program-ming approach for flood diversion planning under multipleuncertaintiesrdquo Advances in Water Resources vol 33 no 1 pp81ndash91 2010

[15] B Aouni C Colapinto and D La Torre ldquoA cardinality con-strained stochastic goal programming model with satisfactionfunctions for venture capital investment decision makingrdquoAnnals of Operations Research vol 205 pp 77ndash88 2013

[16] X Zhang H Wang and W Wang ldquoBi-level programmingmodel and algorithms for stochastic network with elasticdemandrdquo Transport vol 30 no 1 pp 117ndash128 2015

[17] H Li Y Jiao and L Zhang ldquoOrthogonal genetic algorithm forsolving quadratic bi-level programming problemsrdquo Journal ofSystems Engineering and Electronics vol 21 no 5 pp 763ndash7702010

[18] KNiwa THayashidaM Sakawa andY Yang ldquoComputationalmethods for decentralized two level 0-1 programming problemsthrough distributed genetic algorithmsrdquo AIP Conference Pro-ceedings vol 1285 no 1 pp 1ndash13 2010

[19] H C Li and Y P Wang ldquoA genetic algorithm for solving linear-quadratic bi-level programming problemsrdquo in New Trends andApplications of Computer-Aided Material and Engineering pp626ndash630 Trans Tech Publications 2012

[20] S Yu Q Yang J Tao et al ldquoProduct modular design incorpo-rating life cycle issues-Group Genetic Algorithm(GGA) basedmethodrdquo Journal of Cleaner Production vol 19 no 9-10 pp1016ndash1032 2011

[21] B Sankararao and C K Yoo ldquoDevelopment of a robust multi-objective simulated annealing algorithm for solving multi-objective optimization problemsrdquo Industrial amp EngineeringChemistry Research vol 50 no 11 pp 6728ndash6742 2011

[22] L Wang and D-Z Zheng ldquoA modified evolutionary pro-gramming for flow shop schedulingrdquo International Journal ofAdvanced Manufacturing Technology vol 22 no 7 pp 522ndash5272003

[23] J Wang W Deng and J Zhao ldquoRoad network reserve capacitywith stochastic user equilibriumrdquo Transport vol 30 no 1 pp103ndash116 2015

[24] Z Kong X Guo and J Hou ldquoUrban land structure plan-ning model based on green transportation system principalrdquoin Proceedings of the 10th International Conference of Chi-nese Transportation ProfessionalsmdashIntegrated TransportationSystems Green Intelligent Reliable (ICCTP rsquo10) Beijing ChinaAugust 2010

[25] J Bracken and J T McGill ldquoMathematical programs withoptimization problems in the constraintsrdquoOperations Researchvol 21 pp 37ndash44 1973

[26] A Charnes and W W Cooper ldquoChance-constrained program-mingrdquoManagement Science vol 6 no 1 pp 73ndash79 1960

Submit your manuscripts athttpswwwhindawicom

Computer Games Technology

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Distributed Sensor Networks


Advances in

FuzzySystems

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014


ReconfigurableComputing

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014


Applied Computational Intelligence and Soft Computing

thinspAdvancesthinspinthinsp

Artificial Intelligence

HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014

Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Electrical and Computer Engineering

Journal of

Journal of

Computer Networks and Communications


Hindawi Publishing Corporation

httpwwwhindawicom Volume 2014

Advances in

Multimedia


Biomedical Imaging


ArtificialNeural Systems

Advances in


RoboticsJournal of



Computational Intelligence and Neuroscience

Industrial EngineeringJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in



Yang and Zhou [10] built the location selection model withequilibrium constraints considering facility competition onthe basis of the equilibrium theory and then applied geneticalgorithm and projection algorithm to solve the model Forthe relationship between collaboration points Qiu andWang[11] develop a robust optimization model for designing athree-echelon supply chain network that consists ofmanufac-turers distribution centers and retailers under both demanduncertainty and supply disruptions Liu et al [12] consideredthree-layer logistics service supply chain and studied theorder task allocation model between collaboration nodes

Integrating the documents we can find that the currentresearch focused on the microscopic aspects such as pathoptimization and site selection and used artificial intelligencealgorithm to solve the model But the ideal model cannotfully describe the collaborative allocation of resources dueto the networkrsquos complexity and some uncertainty factorsin the process of resource allocation Collaborative logisticsnetwork resource allocation process involves three levelswhich are suppliers transit warehouse and vendors so thebilevel programming model can be used to explain therelationship between every two levels of nods At the sametime the stochastic constrained programming can protectmodel against uncertain influence and it has been appliedto the system dynamics structural dynamics and financialand other fields [13ndash15] Therefore this article will set up thethree-level nodes relationship among the suppliers transitwarehouses and retailers and establish a bilevel program-ming model with chance constrained to control uncertaintyfactors so as to make the whole logistics network systemoptimal under meeting the nodesrsquo profit of both sides

Generally speaking the bilevel programming is NP-hardproblem Ben-Ayed and Blair (1988) have proved that [16]this problem does not have a polynomial algorithm so thesolution of it is very complicated Like genetic algorithm (GA)and Simulated Annealing Algorithm (Simulated AnnealingSA) Neural Network Algorithm (NNA) and so forth someintelligent algorithms were used to solve the bilevel program-ming problem Li et al [17] put forward a genetic algorithmthat can effectively solve bilevel programming problemIn this method they used constraint to transform bilevelproblem into a single-level one and designed the binarycoding to solve the multiplier and numerical experimentshows that the given algorithm can find the global optimalsolution in the least time Niwa et al [18] proposed a bilevelprogramming problem that the upper class has only onedecision-maker while the lower one has multiple decision-makers and a distribution of the genetic algorithm Li andWang [19] studied a special kind of linear quadratic bilevelprogramming problems and genetic algorithmwas proposedafter being converted into equivalent problem

Genetic algorithm by the ideas of the fittest in naturechooses an optimal individual for the solution of the modelby selection crossover and mutation genetic operationAlthough it has some characteristics such as simple oper-ation strong operability and problem space independenceit is easy to exhibit slow convergence speed and get onlylocal optimal value [20] Simulated annealing algorithm is theresult of logistics annealing principle of solid matter starting

from an initial temperature to find the optimal solution inthe solution space with the reduction of the temperatureparameters Although it can get the global optimal solutionit evolved slowly and has strong dependence on parameters[21] So there are advantages and disadvantages respectivelyof the two algorithms hybrid genetic simulated annealingalgorithms can compensate deficiency for each other theynot only can search the related areas of optimal solution inthe global but also can find the optimal solution in the regionof the optimal solution and there have been some scholarswho have done the related research Wang and Zheng [22]proposed a hybrid heuristic algorithm the algorithm mixedthe genetic algorithm and simulated annealing method andthe sampling process of simulated annealing method insteadof mutation operators of genetic algorithm and this algo-rithm improves the local search ability of genetic algorithmWang et al [23] assume that the drivers allmake route choicesbased on Stochastic User Equilibrium (SUE) principle Twomethods that is the sensitivity analysis-based method andgenetic algorithm (GA) are detailedly formulated to solve thebilevel reserve capacity problem Kong et al [24] establisha bilevel programming model of land use structure indexesvariables and use GASA to solve the problem and land androad area ratio should be improved by numerical exampleresults So in this paper designing the combination of geneticand simulated annealing hybrid algorithm to solve the bilevelprogramming problem is feasible

2 Considering Uncertainty ResourceDeployment of Bilevel Programming Model

21 Bilevel Programming Model Bilevel programming (BP)[25] model was presented by Bracken andMcGill in 1973 thelower decision-maker makes decision in the first place theupper policymakers must predict the possible reaction of thelower ones and then the lower one reacts according to thedecision of the upper one to optimize the objective functionof the individual The general model is

min119909isin119883

119865 (119909 119910)st 119866 (119909 119910) le 0min119910isin119884

119891 (119909 119910)st 119892 (119909 119910) le 0

(1)

Among them 119909 isin 1198771198991 and 119910 isin 1198771198992 The upper variable is119909 isin 1198771198991 and the lower variable is 119910 isin 1198771198992 Also the functions119865 1198771198991 times 1198771198992 rarr 119877 and 119891 1198771198991 times 1198771198992 rarr 119877 are the upper andthe lower objective function respectively and vector-valuedfunctions 119866 1198771198991 times 1198771198992 rarr 1198771198981 and 119892 1198771198991 times 1198771198992 rarr 1198771198982 arerespectively the upper and the lower constraint conditions

22 Chance Constrained Programming Model Chance Con-strained Programming [26] is a method of stochastic pro-gramming put forward by Charnes and Cooper in 1959 Itallows decision value within a certain range of fluctuations



min 119885 (119909) = 119899sum119895=1

119888119895119909119895st Pr[[

119899sum119895=1

1198861119895119909119895 ge 1198871 119899sum119895=1

119886119898119895119909119895 ge 119887119898]] ge 120572119909119895 ge 0 119895 = 1 2 119899

(2)













max1198651 = 119899sum119895=1

119899sum119896=1

119899sum119897=1

119899sum119894=1


119899sum119894=1

119906119894 ge 1 (4)

119866119878119894119872119895 ge 119883119897119878119894119872119895 (5)

Pr[[119879119897119878119894119872119895

1015840 + 119879119897119878119894119872119895 10158401015840 + 119864 (119877119878119894119872119895)119881 le 119879119897119878119894119872119895]] = 120572 (6)

119906119894119883119897119878119894119872119895 = 119883119897119872119895119875119896 (7)


119883119897119878119894119872119895 ge 0 119894 = 1 2 119899 119895 = 1 2 119899 (8)

119906119894 isin 0 1 (9)



min1198652= 119899sum119895=1

119899sum119896=1

119899sum119897=1

119899sum119895=1

(119862 (119877119897119872119895119875119896)119864 (119877119872119895119875119896) + 119862 (119891119897119872119895) + 119862 (119892119897119872119895))sdot 119883119897119872119895119875119896119906119895

(10)

119899sum119895=1

119906119895 ge 1 (11)

119899sum119895=1

119899sum119896=1

119899sum119895=1

119906119895119883119897119872119895119875119896 ge 119863119875119896119897 (12)

119866119872119895119877119896 ge 119883119897119872119895119875119896 (13)

Pr[[119879119897119872119895119875119896

1015840 + 119879119897119872119895119875119896 10158401015840 + 119864 (119877119872119895119875119896)119881 le 119879119897119872119895119875119896]] = 120573 (14)

119883119897119872119895119875119896 ge 0 119895 = 1 2 119899 119896 = 1 2 119899 (15)

119906119895 isin 0 1 (16)









Pr[[119879119897119878119894119872119895

1015840 + 119879119897119878119894119872119895 10158401015840 + 119864 (119877119878119894119872119895)119881 le 119879119897119878119894119872119895]] = 120572 (17)


120583 (119879119897119878119894119872119895 1015840) + 120601minus1 (120572) 120590 (119879119897119878119894119872119895 1015840) + 120583 (119879119897119878119894119872119895 10158401015840)+ 120601minus1 (120572) 120590 (119879119897119878119894119872119895 10158401015840) + 120583(119864(119877119878119894119872119895)119881 )

+ 120601minus1 (120572) 120590(119864(119877119878119894119872119895)119881 ) le 119879119897119878119894119872119895(18)













Yes

No

Yes No



Pr[[119879119897119872119895119875119896

1015840 + 119879119897119872119895119875119896 10158401015840 + 119864 (119877119872119895119875119896)119881 le 119879119897119872119895119875119896]] = 120573 (19)


120583 (119879119897119872119895119875119896 1015840) + 120601minus1 (120573) 120590 (119879119897119872119895119875119896 1015840) + 120583 (119879119897119872119895119875119896 10158401015840)+ 120601minus1 (120573) 120590 (119879119897119872119895119875119896 10158401015840) + 120583(119864(119877119872119895119875119896)119881 )

+ 120601minus1 (120573) 120590(119864(119877119872119895119875119896)119881 ) le 119879119897119872119895119875119896 (20)
























1199091 = 00101101 100101111199092 = 00011101 10010111 (24)



S1

S2

S3

S4

M1

M2

M3

P1

100

100

100

100

100

120

120

80

180

180

200

220

260

40











Storagecharges(RMB)



S1 110 01 015 002S2 100 015 015 003S3 110 01 01 0035S4 100 015 01 0025


Distance(km)

Storagecharges(RMB)



M1 260 02 025 002M2 220 03 02 0025M3 280 02 015 0015








GAGASA

Iterations

Fitn

ess

2484

2482

248

2478

2476

2474

2472

247

24681009080706050403020100

times10minus6



M1 M2 M3S1 1000S2S3S4 199999 100001


5 Conclusion




Competing Interests


Acknowledgments


References



































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in





min 119885 (119909) = 119899sum119895=1

119888119895119909119895st Pr[[

119899sum119895=1

1198861119895119909119895 ge 1198871 119899sum119895=1

119886119898119895119909119895 ge 119887119898]] ge 120572119909119895 ge 0 119895 = 1 2 119899

(2)













max1198651 = 119899sum119895=1

119899sum119896=1

119899sum119897=1

119899sum119894=1


119899sum119894=1

119906119894 ge 1 (4)

119866119878119894119872119895 ge 119883119897119878119894119872119895 (5)

Pr[[119879119897119878119894119872119895

1015840 + 119879119897119878119894119872119895 10158401015840 + 119864 (119877119878119894119872119895)119881 le 119879119897119878119894119872119895]] = 120572 (6)

119906119894119883119897119878119894119872119895 = 119883119897119872119895119875119896 (7)


119883119897119878119894119872119895 ge 0 119894 = 1 2 119899 119895 = 1 2 119899 (8)

119906119894 isin 0 1 (9)



min1198652= 119899sum119895=1

119899sum119896=1

119899sum119897=1

119899sum119895=1

(119862 (119877119897119872119895119875119896)119864 (119877119872119895119875119896) + 119862 (119891119897119872119895) + 119862 (119892119897119872119895))sdot 119883119897119872119895119875119896119906119895

(10)

119899sum119895=1

119906119895 ge 1 (11)

119899sum119895=1

119899sum119896=1

119899sum119895=1

119906119895119883119897119872119895119875119896 ge 119863119875119896119897 (12)

119866119872119895119877119896 ge 119883119897119872119895119875119896 (13)

Pr[[119879119897119872119895119875119896

1015840 + 119879119897119872119895119875119896 10158401015840 + 119864 (119877119872119895119875119896)119881 le 119879119897119872119895119875119896]] = 120573 (14)

119883119897119872119895119875119896 ge 0 119895 = 1 2 119899 119896 = 1 2 119899 (15)

119906119895 isin 0 1 (16)









Pr[[119879119897119878119894119872119895

1015840 + 119879119897119878119894119872119895 10158401015840 + 119864 (119877119878119894119872119895)119881 le 119879119897119878119894119872119895]] = 120572 (17)


120583 (119879119897119878119894119872119895 1015840) + 120601minus1 (120572) 120590 (119879119897119878119894119872119895 1015840) + 120583 (119879119897119878119894119872119895 10158401015840)+ 120601minus1 (120572) 120590 (119879119897119878119894119872119895 10158401015840) + 120583(119864(119877119878119894119872119895)119881 )

+ 120601minus1 (120572) 120590(119864(119877119878119894119872119895)119881 ) le 119879119897119878119894119872119895(18)













Yes

No

Yes No



Pr[[119879119897119872119895119875119896

1015840 + 119879119897119872119895119875119896 10158401015840 + 119864 (119877119872119895119875119896)119881 le 119879119897119872119895119875119896]] = 120573 (19)


120583 (119879119897119872119895119875119896 1015840) + 120601minus1 (120573) 120590 (119879119897119872119895119875119896 1015840) + 120583 (119879119897119872119895119875119896 10158401015840)+ 120601minus1 (120573) 120590 (119879119897119872119895119875119896 10158401015840) + 120583(119864(119877119872119895119875119896)119881 )

+ 120601minus1 (120573) 120590(119864(119877119872119895119875119896)119881 ) le 119879119897119872119895119875119896 (20)
























1199091 = 00101101 100101111199092 = 00011101 10010111 (24)



S1

S2

S3

S4

M1

M2

M3

P1

100

100

100

100

100

120

120

80

180

180

200

220

260

40











Storagecharges(RMB)



S1 110 01 015 002S2 100 015 015 003S3 110 01 01 0035S4 100 015 01 0025


Distance(km)

Storagecharges(RMB)



M1 260 02 025 002M2 220 03 02 0025M3 280 02 015 0015








GAGASA

Iterations

Fitn

ess

2484

2482

248

2478

2476

2474

2472

247

24681009080706050403020100

times10minus6



M1 M2 M3S1 1000S2S3S4 199999 100001


5 Conclusion




Competing Interests


Acknowledgments


References



































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




119883119897119878119894119872119895 ge 0 119894 = 1 2 119899 119895 = 1 2 119899 (8)

119906119894 isin 0 1 (9)



min1198652= 119899sum119895=1

119899sum119896=1

119899sum119897=1

119899sum119895=1

(119862 (119877119897119872119895119875119896)119864 (119877119872119895119875119896) + 119862 (119891119897119872119895) + 119862 (119892119897119872119895))sdot 119883119897119872119895119875119896119906119895

(10)

119899sum119895=1

119906119895 ge 1 (11)

119899sum119895=1

119899sum119896=1

119899sum119895=1

119906119895119883119897119872119895119875119896 ge 119863119875119896119897 (12)

119866119872119895119877119896 ge 119883119897119872119895119875119896 (13)

Pr[[119879119897119872119895119875119896

1015840 + 119879119897119872119895119875119896 10158401015840 + 119864 (119877119872119895119875119896)119881 le 119879119897119872119895119875119896]] = 120573 (14)

119883119897119872119895119875119896 ge 0 119895 = 1 2 119899 119896 = 1 2 119899 (15)

119906119895 isin 0 1 (16)









Pr[[119879119897119878119894119872119895

1015840 + 119879119897119878119894119872119895 10158401015840 + 119864 (119877119878119894119872119895)119881 le 119879119897119878119894119872119895]] = 120572 (17)


120583 (119879119897119878119894119872119895 1015840) + 120601minus1 (120572) 120590 (119879119897119878119894119872119895 1015840) + 120583 (119879119897119878119894119872119895 10158401015840)+ 120601minus1 (120572) 120590 (119879119897119878119894119872119895 10158401015840) + 120583(119864(119877119878119894119872119895)119881 )

+ 120601minus1 (120572) 120590(119864(119877119878119894119872119895)119881 ) le 119879119897119878119894119872119895(18)













Yes

No

Yes No



Pr[[119879119897119872119895119875119896

1015840 + 119879119897119872119895119875119896 10158401015840 + 119864 (119877119872119895119875119896)119881 le 119879119897119872119895119875119896]] = 120573 (19)


120583 (119879119897119872119895119875119896 1015840) + 120601minus1 (120573) 120590 (119879119897119872119895119875119896 1015840) + 120583 (119879119897119872119895119875119896 10158401015840)+ 120601minus1 (120573) 120590 (119879119897119872119895119875119896 10158401015840) + 120583(119864(119877119872119895119875119896)119881 )

+ 120601minus1 (120573) 120590(119864(119877119872119895119875119896)119881 ) le 119879119897119872119895119875119896 (20)
























1199091 = 00101101 100101111199092 = 00011101 10010111 (24)



S1

S2

S3

S4

M1

M2

M3

P1

100

100

100

100

100

120

120

80

180

180

200

220

260

40











Storagecharges(RMB)



S1 110 01 015 002S2 100 015 015 003S3 110 01 01 0035S4 100 015 01 0025


Distance(km)

Storagecharges(RMB)



M1 260 02 025 002M2 220 03 02 0025M3 280 02 015 0015








GAGASA

Iterations

Fitn

ess

2484

2482

248

2478

2476

2474

2472

247

24681009080706050403020100

times10minus6



M1 M2 M3S1 1000S2S3S4 199999 100001


5 Conclusion




Competing Interests


Acknowledgments


References



































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in















Yes

No

Yes No



Pr[[119879119897119872119895119875119896

1015840 + 119879119897119872119895119875119896 10158401015840 + 119864 (119877119872119895119875119896)119881 le 119879119897119872119895119875119896]] = 120573 (19)


120583 (119879119897119872119895119875119896 1015840) + 120601minus1 (120573) 120590 (119879119897119872119895119875119896 1015840) + 120583 (119879119897119872119895119875119896 10158401015840)+ 120601minus1 (120573) 120590 (119879119897119872119895119875119896 10158401015840) + 120583(119864(119877119872119895119875119896)119881 )

+ 120601minus1 (120573) 120590(119864(119877119872119895119875119896)119881 ) le 119879119897119872119895119875119896 (20)
























1199091 = 00101101 100101111199092 = 00011101 10010111 (24)



S1

S2

S3

S4

M1

M2

M3

P1

100

100

100

100

100

120

120

80

180

180

200

220

260

40











Storagecharges(RMB)



S1 110 01 015 002S2 100 015 015 003S3 110 01 01 0035S4 100 015 01 0025


Distance(km)

Storagecharges(RMB)



M1 260 02 025 002M2 220 03 02 0025M3 280 02 015 0015








GAGASA

Iterations

Fitn

ess

2484

2482

248

2478

2476

2474

2472

247

24681009080706050403020100

times10minus6



M1 M2 M3S1 1000S2S3S4 199999 100001


5 Conclusion




Competing Interests


Acknowledgments


References



































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in



















1199091 = 00101101 100101111199092 = 00011101 10010111 (24)



S1

S2

S3

S4

M1

M2

M3

P1

100

100

100

100

100

120

120

80

180

180

200

220

260

40











Storagecharges(RMB)



S1 110 01 015 002S2 100 015 015 003S3 110 01 01 0035S4 100 015 01 0025


Distance(km)

Storagecharges(RMB)



M1 260 02 025 002M2 220 03 02 0025M3 280 02 015 0015








GAGASA

Iterations

Fitn

ess

2484

2482

248

2478

2476

2474

2472

247

24681009080706050403020100

times10minus6



M1 M2 M3S1 1000S2S3S4 199999 100001


5 Conclusion




Competing Interests


Acknowledgments


References



































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in






Storagecharges(RMB)



S1 110 01 015 002S2 100 015 015 003S3 110 01 01 0035S4 100 015 01 0025


Distance(km)

Storagecharges(RMB)



M1 260 02 025 002M2 220 03 02 0025M3 280 02 015 0015








GAGASA

Iterations

Fitn

ess

2484

2482

248

2478

2476

2474

2472

247

24681009080706050403020100

times10minus6



M1 M2 M3S1 1000S2S3S4 199999 100001


5 Conclusion




Competing Interests


Acknowledgments


References



































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in





Competing Interests


Acknowledgments


References



































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in










Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in



Resource Allocation Optimization Model of Collaborative...

Documents

Transcript of Resource Allocation Optimization Model of Collaborative...