research article designing a multistage supply chain...

Research ArticleDesigning a Multistage Supply Chain in Cross-StageReverse Logistics Environments Application of Particle SwarmOptimization Algorithms

Tzu-An Chiang1 Z H Che2 and Zhihua Cui34

1 Department of Business Administration National Taipei College of Business Taipei 10051 Taiwan2Department of Industrial Engineering and Management National Taipei University of Technology Taipei 10608 Taiwan3 Complex System and Computational Intelligent Laboratory Taiyuan University of Science and Technology Taiyuan 030024 China4 State Key Laboratory for Novel Software Technology Nanjing University Nanjing 210023 China

Correspondence should be addressed to Z H Che zhchentutedutw

Received 11 October 2013 Accepted 23 December 2013 Published 18 February 2014

Academic Editors C H Aladag and C-C Jane

Copyright copy 2014 Tzu-An Chiang et alThis 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

This study designed a cross-stage reverse logistics course for defective products so that damaged products generated in downstreampartners can be directly returned to upstream partners throughout the stages of a supply chain for rework and maintenance Tosolve this reverse supply chain design problem an optimal cross-stage reverse logistics mathematical model was developed Inaddition we developed a genetic algorithm (GA) and three particle swarm optimization (PSO) algorithms the inertia weightmethod (PSOA IWM) 119881Max method (PSOA VMM) and constriction factor method (PSOA CFM) which we employed to findsolutions to support this mathematical model Finally a real case and five simulative cases with different scopes were used tocompare the execution times convergence times and objective function values of the four algorithms used to validate the modelproposed in this study Regarding system execution time the GA consumed more time than the other three PSOs did Regardingobjective function value the GA PSOA IWM and PSOA CFM could obtain a lower convergence value than PSOA VMM couldFinally PSOA IWM demonstrated a faster convergence speed than PSOA VMM PSOA CFM and the GA did

1 Introduction

Intense competition within the global market has promptedenterprise competition to change from a competition amongcompanies to that among supply chains In addition to reduc-ing operating costs and improving competitiveness effec-tively integrating the upstream and downstream suppliersand manufacturers of a supply chain can reflect marketchanges and meet consumer needs efficiently

Previous studies on the design problems of supply net-works include [1ndash8] In addition Che and Cui [9] addressedthe network design on unbalanced supply chain system Forthe integrity of supply chain circulation reverse logisticsshould be implemented to form a complete logistics circula-tion Reverse logistics was first proposed by Stock [10] thenTrebilcock [11] indicated that in the past most enterprisesfocused only on forward logistics andmisunderstood reverselogistics as a nonprofitable activity

Cohen [12] suggested that enterprises could save 40ndash60 ofmanufacturing costs annually by adopting the remakemethod compared with using newmaterials In recent yearsenterprises have begun paying increased attention to reverselogistics activities such as customer returns product mainte-nance replacement and recyclingWhite et al [13] describedin detail the essential aspects and challenges in acquiringassessing disassembling and reprocessing computer equip-ment as it moves through this reversemanufacturing processProper planning of a comprehensive product recycling plancan reduce the environmental damage caused by disposingof used equipment

Based on literature review reverse logistics includesman-agement functions related to returned products depot repairrework material reprocessing material recycling and dis-posal of waste and hazardous materialsThese allow productsto be returned upstream for processing in a reverse logisticssystem thus the circulation of an integral supply chain can be

Hindawi Publishing Corporatione Scientific World JournalVolume 2014 Article ID 595902 19 pageshttpdxdoiorg1011552014595902

2 The Scientific World Journal

SupplierRaw materialsAssembly partsPackaging materialsParts manufactures

Processing programsInitial manufacturesRemanufacturingMaintenanceReutilizationResaleRecycle

Final productProductAlternate parts Distribution centers

RegionalityTerritoriality

Customer

DisposalBurialIncineration

Forward logistics

Reverse logistics

∙∙

∙∙

∙∙

∙∙

∙∙

∙∙

∙∙

∙∙

Figure 1 The reverse logistics flow of the products (Gattorna [14])

implemented The reverse logistics flow of products is shownin Figure 1

Many scholars have defined reverse logistics briefly andclearly [10 15ndash18] and some have studied the reverse logisticsnetwork design for different fields such as the steel industry[19] electronic equipment [20] sand recycling [21] reusablepackaging [22] and general recovery networks [23] Aminiet al [24] demonstrated how an effective and profitablereverse logistics operation for an RSSC was designed foran MDM in which customer operations demanded a quickrepair service Fleischmann et al [25] considered a logisticsnetwork design in a reverse logistics context and presented ageneric facility location model by discussing the differencescompared with traditional logistics settings This model wasthen used to analyze the impact of product return flow onlogistics networks

In addition Savaskan et al [26] developed a detailedunderstanding of the implications that a manufacturerrsquosreverse channel choice has on forward channel decisions andthe used product return rate from customers Chouinardet al [27] addressed problems related to integrating reverselogistics activities within an organization and to coordinat-ing this new system Kainuma and Tawara [28] proposedthe multiple-attribute utility theory method for assessing asupply chain including reusing and recycling throughout thelife cycle of products and services Nagurney and Toyasaki[29] developed a model linking these decisions to prices andmaterial shipments among end-of-life electronics sourcesrecyclers processors and suppliers for deterministic scenar-ios Nikolaidis [30] proposed a single-period mathematicalmodel for determining a reverse supply chain plan that con-siders procurement and returnsrsquo remanufacturing andNenesand Nikolaidis [31] extended Nikolaidisrsquos model to a multi-period model Salema et al [32] developed a multiperiodmultiproduct model for designing supply chain networksregarding reverse flowsMore recently Pinto-Varela et al [33]considered an environmental perspective to develop amixed-integer linear programming model for planning reversesupply chains Amin and Zhang [34] presented a mixed-integer linear programming model for designing a closed-loop supply chain network regarding product life cycles In

additionHuang et al [35] analyzed strategies of a closed-loopsupply chain containing a dual recycling channel Althoughcross-stage logistics in reverse supply chains generally existsin practice our research suggests that it has yet to be ade-quately addressed Hence the motivation of this study is todesign the reverse supply chain with cross-stage logistics

Reverse logistics is more complex than forward logisticsand this study aimed to develop a mathematical foundationfor modeling a cross-stage reverse logistics plan that enablesdefective products with differing degrees of damage to bereturned to upstream partners in the stages of a supply chainfor maintenance replacement or restructuring This cross-stage reverse logisticsmodel can help save time lessen unnec-essary deliveries and more importantly meet the conditionsof reverse logistics operation more efficiently

Recently GAs have been regarded as a novel approachto solving complex large-scale and real-world optimiza-tion problems [6 36ndash42] Moreover the PSO proposed byKennedy and Eberhart [43] was an iteration optimizationinstrument generating a group of initial solutions at thebeginning and then acquiring the optimal value throughiteration Liao and Rittscher [44] applied this instrumentto scheduling problems related to industrial piece workrequiring minimal completion time Zhang et al [45] appliedPSO to solve the minimization problems of the projectduration for resource-constrained scheduling Shi et al [46]applied a PSO to the traveling salesman problem Che [47]developed a PSO-based back-propagation artificial neuralnetwork for estimating the product and mold costs of plasticinjection molding and Che [48] proposed a modified PSOmethod for solving multiechelon unbalanced supply chainplanning problems Priya and Lakshmi [49] applied PSO forperforming the real time control of spherical tank systemand Ali et al [50] used the PSO for solving the constrainednumerical and engineering benchmark problems Otherrelated studies concerning the use of PSO for the optimizationproblems are [51ndash54]

In addition Dong et al [55] compared the improved PSOa combinatorial particle swarm optimization (CPSO) withGA and the results showed that the improved PSO was moreeffective in solving nonlinear problems Yin and Wang [56]

The Scientific World Journal 3

Stage 1 Stage 2 Stage 3 Stage 4

Demand

21

22

23

21

31

32

33

34

41

42

43

44

11

12

13

14

Reverse logisticsForward logistics

middot middot middot

Figure 2 The transportation model of reverse logistics

used PSO to solve nonlinear resource allocation problemsand compared PSO with the GA They found that theefficiency and potency of a PSO were higher than those ofa GA Salman et al [57] applied PSO to solve the efficiencyrates of tasks assigned to computers or parallel computersystems and compared the results with those of GA Theresults showed that PSOhas faster execution and convergencespeeds than the GA Based on our research no previous stud-ies have applied PSO to cross-stage reverse logistics problemstherefore to solve this problem this study used three updatedPSO methods the inertia weight method (PSOA IWM)constriction factor method (PSOA CFM) and 119881Max method(PSOA VMM) The results were then compared with thoseusing the GA regarding system execution time convergencetime and objective function value

The remainder of this paper is structured as followsSection 2 introduces the proposed mathematical foundationand solving algorithms for modeling and solving cross-stage reverse logistics problems Section 3 presents illustrativeexamples and the comparative and analytical results of thealgorithms Finally Section 4 provides the conclusion of thisstudy and offers suggestions for future research

2 Mathematical Foundation andSolving Models for Cross-Stage ReverseLogistics Problems

21 Problem Description Reverse logistics activities includerecycling rework replacement and waste disposal howeverthe reverse logistics activity of each function differs There-fore this study designed a forward and reverse cross-stagelogistics system for maintaining reassembling and packag-ing recycled defective products The structure is shown inFigure 2

When downstream partners generate defective productsthe products can be returned directly to upstream supplychain partners for maintenance to restore product functionand value based on the degree of damage Therefore thisstudy supposed that when defective products are generatedthey can be divided into N parts according to the averagevolume of defective products generated by a particularsupplier Downstream partners can then return defectiveproducts based on the divided quantity to upstreampartnersfor maintenance For example when the first partner of thefourth stage generates defective products the total defectiveamount is divided into three parts and then sent to the firstsecond and third stage partners separately in the supplychain thereby reducing general reverse logistics costs andtransportation time

For supply chain partner selection this study consideredproductivity restrictions transportation costs manufactur-ing costs transportation time manufacturing quality andother parameters The 119879-transfer approach is a common sta-tistical technology that is employed to integrate variables Inthis study the119879-transfer of transportation costs manufactur-ing costs transportation time andmanufacturing qualitywasintegrated into the objective function standards 119879-transferis a common statistics technology first proposed by McCall[58] it is defined as follows ldquo119879-Scores are a transformationof raw scores into a standard form where the transformationis made when there is no knowledge of the populationrsquosmean and standard deviationrdquo 119879-scores have a mean of 50and a standard deviation of 10 Che [59] considered themanufacturing cost and time transportation cost and timeproduct quality and green appraisal score in selecting greensuppliers when establishing a green supply chain and used119879-transfer technology to transform the data Cost timequality and green appraisal score aremeasurable criteria withdifferent units thus in this study the119879-transfer approachwas


Establish the database of multistage supply chain with cross-stage

reverse logistics

Develop the optimal mathematical model for multistage supply chain

with cross-stage reverse logistics

Information of supply chain

Production costManufacture defective product rateTransportation costTransportation loss rateTransportation timeManufacturing qualityUpper and lower limits of productivity

hellip

Develop four solving models to solve the optimal mathematical

modelSolving algorithms

GAPSOA_VMMPSOA_IWMPSOA_CFM Analyze and compare the solving

performances for four solving models

Performance indicators

Execution timeConvergence timeObjective function value

Statistical techniques

ANOVA

Obtain the optimal multistage supply chain plan with cross-stage

reverse logistics

Optimal mathematical model

ObjectiveMinimize

Constraints

lowast

lowast

lowast

lowast

lowast

lowast

lowast

lowast

lowast

lowast

lowast

lowast

lowastlowast

lowast

lowast

Z = wPC(fPC + rPC) + wTC(fTC + rTC) minus

wPQ(fPQ+ rPQ) + wTS(fTS + rTS)

+

RUnminus1((rsj)(si)) le MaxCP(si)

JS

rs = s + 1 j = 1

sum sum

(MinCP(si) le Un((sminus1j)(si)) 1 minus TFR((sminus1j)(si))

J

j = 1

sum )

Scheff e method

Figure 3 The structure of this study

also employed to first transform the original scores of eachcriterion into a standard form and then to integrate them

To satisfy the conditions of the actual production situa-tion this study used transportation losses andmanufacturinglosses to construct an unbalanced supply chain network Inconsidering the characteristics of all the suppliers addressedin this study we developed a cross-stage reverse logisticscourse planning system for single-product and multiperiodprogramming

We programmed the reverse logistics for recycled defec-tive products which were returned directly to the upstreamsupply chain partners for maintenance reassembly andrepackaging through the cross-stage reverse logistics courseprogramming based on the degree and nature of the damageFor selecting supply chain partners this study consideredthe manufacturing characteristics (transportation costs pro-duction costs upper and lower limit of productivity man-ufacturerrsquos defective product rate transportation losses rateand manufacturing quality) to construct the reverse logisticsprogramming model Based on these data optimal manufac-turing quality with minimal production cost transportationcost and transportation time can be determined

In considering the different evaluation criteria this study119879-transferred the database and used theVisual Basic programlanguage to compile four solution models including GAPSOA IWM PSOA VMM and PSOA CFM The consid-ered parameters in the supplier database were combined todevelop a set for designing reverse logistics course planningsystems The framework of this study is shown in Figure 3

Analysis of variance (ANOVA) and Scheffe analyseswere per-formed to compare the objective function values (119879-score)convergence times and run times of the four algorithms toverify the validity of this study and the performance of thefour algorithms

22 Mathematical Foundation for Cross-Stage Reverse Logis-tics Problems The optimal mathematical model of cross-stage reverse logistics was developed as described in thefollowing steps The definitions of notations used in thismodel are listed as followsNotations for developing the optimal mathematical model

Parameters

119894 119895 Serial number of supplier119894 = 1 2 3 119868 119895 = 1 2 3 119869

119899 Production period 119899 = 1 2 3 119873

119904 119903119904 Stages of the supply chain network119904 = 1 2 3 119878 119903119904 = 1 2 3 119878

119868 119869 Total number of suppliers119873 Total production periods119878 Total stages of supply chain network119862119863119899

(119904119894) Customer requirement of supplier 119894 at

stage 119904 for period 119899

Min119862119875(119904119894)

Minimal starting up productivity ofsupplier 119894 at stage 119904

Max119862119875(119904119894)

Maximal starting up productivity ofsupplier 119894 at stage 119904


119875119862(119904119894)

Manufacturing cost of supplier 119894 atstage 119904

119875119876(119904119894)

Product quality of supplier 119894 at stage 119904119879119862((119904119894)(119904+1119895))

Transportation cost from supplier 119894 atstage 119904 to supplier 119895 at stage 119904 + 1

119879119878((119904119894)(119904+1119895))

Transportation time from supplier 119894 atstage 119904 to supplier 119895 at stage 119904 + 1

119875119862(119904119894)

Average manufacturing cost of supplier119894 at stage 119904

119875119876119904119894 Average product quality of supplier 119894 at

stage 119904119879119862((119904119894)(119904+1119895))

Average transportation cost fromsupplier 119894 at stage 119904 to supplier 119895 at stage119904 + 1

119879119878((119904119894)(119904+1119895))

Average transportation time fromsupplier 119894 at stage 119904 to supplier 119895 at stage119904 + 1

119879

119875119862(119904119894)

Manufacturing cost of supplier 119894 atstage 119904 after 119879-transfer

119879

119875119876119904119894 Product quality of supplier 119894 at stage 119904

after 119879-transfer119879

119879119862((119904119894)(119904+1119895))

Transportation cost from supplier 119894 atstage 119904 to supplier 119895 at stage 119904 + 1 after119879-transfer

119879

119879119878((119904119894)(119904+1119895))

Transportation time from supplier 119894 atstage 119904 to supplier 119895 at stage 119904 + 1 after119879-transfer

119878119866119875119862119904119894

Manufacturing cost standard deviationof supplier 119894 at stage 119904

119878119866119879119862((119904119894)(119904+1119895))

Transportation cost standard deviationof supplier 119894 at stage 119904 to supplier 119895 atstage 119904 + 1

119878119866119875119876119904119894

Product quality standard deviation ofsupplier 119894 at stage 119904

119878119866119879119878((119904119894)(119904+1119895))

Transportation time standard deviationof supplier 119894 at stage 119904 to supplier 119895 atstage 119904 + 1

119865119877(119904119894)

Defective product rates of supplier 119894 atstage 119904

119879119865119877((119904119894)(119904+1119895))

Transportation loss rate from supplier 119894at stage 119904 to supplier 119895 at stage 119904 + 1

119908119875119862

119908119879119862

119908119879119878

119908119875119876

Weights of manufacturing costtransportation cost transportationtime and product quality

Integer function for obtaining theinteger value of the real number byeliminating its decimal

Decision Variables

119880119899

((119904119894)(119904+1119895)) Transportation quantity from supplier 119894 at

stage 119904 to supplier 119895 at stage 119904 + 1 for period119899

119877119880119899

((119903119904119895)(119904119894)) Defective products quantity from supplier

119895 at stage 119903119904 to supplier 119894 at stage 119904 stage forterm 119899

Notations for developing the update models for the positionand velocity of each particle

1198881 1198882 Learning factors

119870 Constriction factorrand() Random numbers between 0 and 1119904lowast

119894 Pbest memory value of particle 119894

119904119894 Gbest memory value of particle 119894

119904new119894

New position of particle 119894Vold119894 Original velocity of particle 119894

Vnew119894

New velocity of particle 119894Vmax The set maximal velocity119908 Inertia weight

120601Totaling of cognition parameter and socialparameter which must exceed 4

Notations for performing hypotheses on the objective func-tion value convergence time and completion time amongfour proposed approaches

119862119879GA Convergence time of GA119862119879PSOA IWM Convergence time of PSOA IWM119862119879PSOA VMM Convergence time of PSOA VMM119862119879PSOA CFM Convergence time of PSOA CFM119865119879GA Completion time of GA119865119879PSOA IWM Completion time of PSOA IWM119865119879PSOA VMM Completion time of PSOA VMM119865119879PSOA CFM Completion time of PSOA CFMObjGA Objective function value of GAObjPSOA IWM Objective function value of PSOA IWMObjPSOA VMM Objective function value of PSOA VMMObjPSOA CFM Objective function value of PSOA CFM

Acquire the minimization of manufacturing costs trans-portation costs and transportation time as well as themaximization of the manufacturing quality of the differentsuppliers at various stages of forward and reverse logistics

Manufacturing cost for forward logistics

119891119875119862

=

119873

sum

119899=1

119878

sum

119904=1

119868

sum

119894=1

119879

119875119862(119904119894)

times [

[

100381710038171003817100381710038171003817100381710038171003817

119880119899

((119904119894)(119904+11))

1 minus 119865119877(119904119894)

100381710038171003817100381710038171003817100381710038171003817

+

119869

sum

119895=2

10038171003817100381710038171003817119880119899

((119904minus1119895)(119904119894))(1minus119879119865119877

((119904minus1119895)(119904119894)))10038171003817100381710038171003817]

]

(1)

Transportation cost for forward logistics

119891119879119862 =

119873

sum

119899=1

119878

sum

119904=1

119868

sum

119894=1

119869

sum

119895=1

119879

119879119862(119904119894)(119904+1119895)

119880119899

((119904119894)(119904+1119895)) (2)


Product quality for forward logistics

119891119875119876

=

119873

sum

119899=1

119878

sum

119904=1

119868

sum

119894=1

119879

119875119876(119904119894)

times [

[

100381710038171003817100381710038171003817100381710038171003817

119880119899

((119904119894)(119904+11))

1 minus 119865119877(119904119894)

100381710038171003817100381710038171003817100381710038171003817

+

119869

sum

119895=2

10038171003817100381710038171003817119880119899

((119904minus1119895)(119904119894))(1minus119879119865119877

((119904minus1119895)(119904119894)))10038171003817100381710038171003817]

]

(3)

Transportation time for forward logistics

119891119879119878 =

119873

sum

119899=1

119878

sum

119904=1

119868

sum

119894=1

119869

sum

119895=1

119879

119879119878(119904119894)(119904+1119895)

119880119899

((119904119894)(119904+1119895)) (4)

Manufacturing cost for reverse logistics

119903119875119862 =

119873

sum

119899=2

119878minus1

sum

119904=1

119868

sum

119894=1

119879

119875119862(119904119894)

119878

sum

119903119904=119904+1

119869

sum

119895=1

119877119880119899

((119903119904119895)(119904119894)) (5)

Transportation cost for reverse logistics

119903119879119862 =

119873

sum

119899=2

119878

sum

119904=1

119868

sum

119894=1

119879

119879119862((119903119904119895)(119904119894))

119878

sum

119903119904=119904+1

119869

sum

119895=1

119877119880119899

((119903119904119895)(119904119894)) (6)

Product quality for reverse logistics

119903119875119876 =

119873

sum

119899=2

119878minus1

sum

119904=1

119868

sum

119894=1

119879

119875119876(119904119894)

119878

sum

119903119904=119904+1

119869

sum

119895=1

119877119880119899

((119903119904119895)(119904119894)) (7)

Transportation time for reverse logistics

119903119879119878 =

119873

sum

119899=2

119878

sum

119904=1

119868

sum

119894=1

119879

119879119878((119903119904119895)(119904119894))

119878

sum

119903119904=119904+1

119869

sum

119895=1

119877119880119899

((119903119904119895)(119904119894)) (8)

The objective function is expressed as follows

Minimize 119885 = 119908119875119862

(119891119875119862 + 119903119875119862)

+ 119908119879119862

(119891119879119862 + 119903119879119862)

minus 119908119875119876

(119891119875119876 + 119903119875119876)

+ 119908119879119878

(119891119879119878 + 119903119879119878)

st

(9)

Upper and lower limits of productivity of all the suppliers

Min119862119875(119904119894)

le

119869

sum

119895=1

10038171003817100381710038171003817119880119899

((119904minus1119895)(119904119894))(1 minus 119879119865119877

((119904minus1119895)(119904119894)))10038171003817100381710038171003817

+

119878

sum

119903119904=119904+1

119869

sum

119895=1

119877119880119899minus1

((119903119904119895)(119904119894))le Max119862119875

(119904119894)

for 119899 = 1 2 3 119873

119904 = 2 3 119878 119894 = 1 2 3 119868

(10)

Min119862119875(119904119894)

le

119869

sum

119895=1

10038171003817100381710038171003817100381710038171003817100381710038171003817

119880119899

((119904119894)(119904+1119895))

1 minus 119865119877(119904119894)

10038171003817100381710038171003817100381710038171003817100381710038171003817

+

119878

sum

119903119904=119904+1

119869

sum

119895=1

119877119880119899minus1

((119903119904119895)(119904119894))le Max119862119875

(119904119894)

for 119899 = 1 2 3 119873 119904 = 1

119894 = 1 2 3 119868

(11)

Ensure the balance between the input and output of all part-ners by considering the transportation defective rate

119869

sum

119895=1

100381710038171003817100381710038171003817119880119899

((119904minus1119895)(119904119894))(1 minus 119879119865119877

((119904minus1119895)(119904119894)))100381710038171003817100381710038171003817

+

119878

sum

119903119904=119904+1

119869

sum

119895=1

119877119880119899minus1

((119903119904119895)(119904119894))

=

119869

sum

119895=1

119880119899

((119904+1119895)(119904119894))+

119904minus1

sum

119903119904=1

119869

sum

119895=1

119877119880119899

((119904119894)(119903119904119895))

for 119899 = 1 2 3 119873

119904 = 1 2 3 119878 119894 = 1 2 3 119868

(12)

119904

sum

119903119904=1

119869

sum

119895=1

119877119880119899

((119903119904119895)(119904119894))

=

10038171003817100381710038171003817100381710038171003817100381710038171003817

(

119869

sum

119895=1

10038171003817100381710038171003817119880119899

((119904minus1119895)(119904119894))(1 minus 119879119865119877

((119904minus1119895)(119904119894)))10038171003817100381710038171003817

+

119878

sum

119903119904=119904+1

119869

sum

119895=1

119877119880119899minus1

((119903119904119895)(119904119894)))119865119877(119904119894)

10038171003817100381710038171003817100381710038171003817100381710038171003817

for 119899 = 1 2 3 119873

119904 = 1 2 3 119878 119894 = 1 2 3 119868

(13)


The product quantity should meet customer requirements

119869

sum

119895=1

10038171003817100381710038171003817119880119899

((119904minus1119895)(119904119894))(1 minus 119879119865119877

((119904minus1119895)(119904119894)))10038171003817100381710038171003817

minus

119904minus1

sum

119903119904=1

119869

sum

119895=1

119877119880119899

((119904119894)(119904minus119903119904119895))= 119862119863

119899

(119904119894)

for 119899 = 1 2 3 119873 119904 = 119878

119894 = 1 2 3 119868

(14)

The weights of manufacturing cost transportation costtransportation time and product quality should be not lessthan 0 and not more than 1

0 le 119908119875119862

119908119879119862

119908119879119878 119908119875119876

le 1

119908119875119862

+ 119908119879119862

+ 119908119879119878

+ 119908119875119876

= 1

(15)

The defective products returned in the first period during themultiperiods of production number zero

119877119880119899

((119903119904119895)(119904119894))= 0 for 119899 le 0 119904 = 1 2 3 4 119878 minus 1

119903119904 = 119904 + 1 119878 119894 = 1 2 3 119868

119895 = 1 2 3 119869

(16)

The forward and reverse transportation volume must belarger than zero and be an integer

119880119899

((119904119894)(119904+1119895))ge 0 and 119880

119899

((119904119894)(119904+1119895))isin Integer

for 119899 = 1 2 3 119873 119904 = 1 2 3 119878

119894 = 1 2 3 119868 119895 = 1 2 3 119869

(17)

119877119880119899

((119903119904119895)(119904119894))ge 0 and 119880

119899

((119904119894)(119904+1119895))isin Integer

for 119904 = 1 2 3 119878 119903119904 = 119878 + 1 119878

119899 = 1 2 3 119873 119894 = 1 2 3 119868 119895 = 1 2 3 119869

(18)

Manufacturing costs transportation costs manufacturingquality and transportation time should be 119879-transferred

119879

119875119862(119904119894)

=119875119862(119904119894)

minus 119875119862(119904119894)

119878119866119875119862(119904119894)

10+ 50 for 119904 = 1 2 3 119878

119894 = 1 2 3 119868

119879

119879119862((119904119894)(119904+1119895))

=

119879119862((119904119894)(119904+1119895))

minus 119879119862((119904119894)(119904+1119895))

119878119866119879119862((119904119894)(119904+1119895))

10+ 50

for 119904 = 1 2 3 119878 119894 = 1 2 3 119868

119895 = 1 2 3 119869

119879

119875119876(119904119894)

=119875119876(119904119894)

minus 119875119876(119904119894)

119878119866119875119876(119904119894)10

+ 50 for 119904 = 1 2 3 119878

119894 = 1 2 3 119868

119879

119879119878((119904119894)(119904+1119895))

=

119879119878((119904119894)(119904+1119895))

minus 119879119878((119904119894)(119904+1119895))

119878119866119879119878((119904119894)(119904+1119895))

10+ 50

for 119904 = 1 2 3 119878 119894 = 1 2 3 119868

119895 = 1 2 3 119869

(19)

23 Proposed Models for Solving Cross-Stage Reverse LogisticsProblems

231 GA-Solving Model The detailed procedures of a GA-solving model are described as follows

Step 1 The encoding of this study was performed accordingto the cross-stage reverse logistics problem including forwardand reverse transportation routes therefore one route is oneencoding value The scope is randomly generated based onthe demands and (10)ndash(14) The chromosome structure isshown in Figure 4 The gene cell index 11ndash21 in the figurerepresents the products sent from the first supplier of the firststage to the initial supplier of the second stage within thesupply chain structure whereas the gene value represents thetransportation volumes from upstream to downstream

Step 2 Substitute all the generated encoding values in theobjective function equation (1) of this study to acquire thefitness function value of each gene

Step 3 This study adopted the roulette wheel selectionproposed by Goldberg [60] which is performed beforecloning to solve the minimization problem of this studyIt then selects the reciprocal of fitness function generated inStep 2 and calculates the cumulative probability of each stripof chromosome the larger probability value indicates thatthis chromosome has a greater likelihood of being duplicatedOne probability value between 0 and 1 is generated thesuitable fitness function is determined and cloning is carriedout

Step 4 The crossover of this study involves using the single-point crossover method Randomly select two chromosomesfrom the parent body for crossover and generate onecrossover point then exchange the genes of the chromosomeThe crossover course is shown in Figure 5

Step 5 The mutation of this study also adopts a single-pointmutationmethod and treats the delivery route of one supplieras a ldquosingle-pointrdquo of valueThemutationmethod is shown inFigure 6

Step 6 The new filial generation was generated through thegene evolution of Steps 3ndash5 if the optimal fitness functionvalue of the filial generation is higher than that of the parental


Gene cell index 11ndash21 12ndash21 13ndash21 11ndash22 12ndash22 13ndash22 middot middot middot 31ndash46 32ndash46 33ndash46 34ndash46 35ndash46Gene value 236 224 115 75 55 69 middot middot middot 75 65 78 99 63

Figure 4 Chromosome structure

Parent-1Gene cell index 11ndash21 12ndash21 13ndash21 11ndash22 12ndash22 13ndash22 middot middot middot 31ndash46 32ndash46 33ndash46 34ndash46 35ndash46

Gene value 236 224 115 75 55 69 middot middot middot 75 65 78 99 63


89 56 32 63 99 96 middot middot middot 45 56 32 106 88Gene value

Child-1Gene cell index 11ndash21 12ndash21 13ndash21 11ndash22 12ndash22 13ndash22 middot middot middot 31ndash46 32ndash46 33ndash46 34ndash46 35ndash46




Crossover pointAfter crossover

Figure 5 Crossover process

OldGene cell index 11ndash21 12ndash21 13ndash21 11ndash22 12ndash22 13ndash22 middot middot middot 31ndash46 32ndash46 33ndash46 34ndash46 35ndash46


NewGene cell index 11ndash21 12ndash21 13ndash21 11ndash22 12ndash22 13ndash22 middot middot middot 31ndash46 32ndash46 33ndash46 34ndash46 35ndash46


Mutation point

After mutation

Figure 6 Mutation process

LineParticle 1 2 3 4 5 6 middot middot middot 60 61 62

Volume 103 27 30 140 158 18 middot middot middot 308 15 61

11minus22F 11minus22F 11minus23F 11minus24F 12minus21F 12minus22F middot middot middot 33minus46F 34minus46F 35minus46F

Figure 7 Particle swarm encoding for forward logistics

Particle 1 2 3 4 5 6 117 118 119Line

Volume 0 0 42 9 0 0 0 2 0

21minus11R 21minus12R 21minus13R 22minus11R 22minus12R 22minus13R middot middot middot



46minus33R 46minus34R 46minus35R

Figure 8 Particle swarm encoding for reverse logistics

generation then this would replace the parental generation asthe new parent generation otherwise the original parentalgeneration would be reserved to conduct the evolution of thenext generation

Step 7 This study sets the iteration times as the terminationcondition for gene evolution

232 PSO-Solving Models The detailed procedures involvedin PSO-solving models are described as follows

Step 8 Set the relative coefficients as particle populationvelocity weight and iteration times then all forward and

reverse transportation routes are viewed as one particle basedon the supply chain structure The forward and reverseparticle swarm encodings are shown in Figures 7 and 811ndash21F in Figure 7 represents the products sent from thefirst supplier of the first stage to the first supplier of thesecond stage and 21ndash11R in Figure 8 represents the productsreturned to the first suppliers of the first stage from the firstsuppliers of the second stage

The forward transportation volume produces the parentalgeneration solution adopting demand transportation lossmanufacturerrsquos defective products and (10)ndash(14) as the ran-dom variant scope for the particles Each particle has its own


initial parameters of velocity and position generated withinthe scope of 0ndash1The velocity and position would be renewedand the reverse part is delivered according to the proportionbased on the quantity of defective products generated bythe downstream suppliers of each stage For example thedefective products generated by the fourth stage retailerwould first be divided into 30 30 and 40 accordingto the proportion and then delivered to the suppliers of thethird second and first stages

Step 9 All particles received by the initial solutions of objec-tive function equation (1) are carried to conduct the opera-tion to achieve minimal transportation costs transportationtimes and manufacturing costs as well as maximizing themanufacturing quality for each granule particle

Step 10 The target value of each particle generated in Step 9is compared to receive Gbest

Step 11 Modify the Pbest andGbest If the Pbest is better thanthe Gbest then the Pbest would replace the Gbest

Step 12 For the renewal portion of this study the inertiaweight method (PSOA IWM) proposed by Eberhart and Shi[61] the constriction factor method (PSOA CFM) proposedby Clerc [62] and the119881Max method (PSOA VMM) proposedby Eberhart and Kennedy [43 63] were used to update theposition and velocity of each particleThe updated modes arelisted as follows (descriptions of notations are listed in theappendix)

(1) PSOA IWM (Eberhart and Shi [61])

Vnew119894

= 119908Vold119894

+ 1198881times rand () times (119904

lowast

119894minus 119904

old119894

) + 1198882

times rand () times (119904119894minus 119904

old119894

)

119904new119894

= 119904old119894

+ Vnew119894

(20)

(2) PSOA VMM (Eberhart and Kennedy [43 63])

Vnew119894

= Vold119894

+ 1198881times rand () times (119904

lowast

119894minus 119904

old119894

) + 1198882


old119894

)

119904new119894

= 119904old119894

+ Vnew119894

if V119894gt Vmax V

119894= Vmax

else if V119894lt minusVmax V

119894= minusVmax

(21)

When the particle velocity was too extreme it could beguided to the normal velocity vector

(3) PSOA CFM (Clerc [62])

Vnew119894

= 119896 times ⟨Vold119894

+ 1198881times rand () times (119904

lowast

119894minus 119904

old119894

)

+1198882times rand () times (119904

119894minus 119904

old119894

)⟩

119904new119894

= 119904old119894

+ Vnew119894

119870 =2

2 minus 120593 minus radic1205932 minus 4120593

120601 = 1198881+ 1198882 120601 gt 4

(22)

Step 13 After the velocity and position of the particles areupdated theymust be verified to determinewhether theymet(10)ndash(18) and the set maximal velocity if these conditions arenot met then the renewal formulae would be used until therenovation meets the restriction formula

Step 14 Steps 9ndash13 would be repeated based on iterationtimes the Gbest of each iteration time would be comparedand then the iteration times would be used as the conditionfor stopping the calculation The final algorithm presents thedelivery quantity and target value of the forward and reverseroutes

3 Illustrative Example and Results Analysis

This section presents an illustrative example involving a semi-conductor supply chain network to demonstrate the effective-ness of the proposed approaches A typical semiconductorsupply chain network is shown in Figure 9The chain includesa multistage process obtaining silicon material materialfabrication wafer fabrication and a final test In each stagethere are many enterprises that perform the productionprocesses to fulfill the demand of the customer

This case programmed one unbalanced supply chain net-work structure including forward and reverse logistics sothat downstream suppliers or retailers can return defectiveproducts directly to upstream supply chain partners Themanufacturer can restore a broken productrsquos functiondepending on the damage so that the productrsquos purpose isrecovered This case addressed forward and reverse logisticspartner selection and quantity delivery problems using a 3-4-5-6 network structure It also programmed a three-periodcustomer requirement list for a single productThis case sup-posed that the initial inventory of the first period waszero transportation losses were considered waste and cannotbe reproduced and different reverse logistics for defectiveproducts of different damage levels were programmed Forexample when 10 defective products were generated by thefirst supplier of the fourth stage this study assumes that 30were returned to the third stage 30 were returned to thesecond stage and the rest were returned to the first stageTherefore the reverse logistics of this study would generatea cross-stage reverse delivery status

This study considered the productivity restrictions man-ufacturing costs delivery costs manufacturing quality andtransportation time for all suppliers in selecting supply chainpartnersThis study also considered themanufacturerrsquos defec-tive product rate and the transportation loss rate of suppliersto form a so-called ldquounbalancedrdquo supply chain network Thedetails of all of the suppliers are shown in Figure 10 andTable 1 In addition the weights of manufacturing costs


Siliconmaterial

Materialsfabrication

Waferfabrication Assembly Final

test Customer

Manufacturing unit

Demand unitForward route

Reverse route

Figure 9 Typical supply chain network for semiconductor

transportation costs transportation time and product qual-ity were assumed to be equal

This study used GA PSOA IWM PSOA CFM andPSOA VMM both to solve the problem of the optimal math-ematical model of cross-stage reverse logistics constructed bythis study and to determine the optimal parameter valuesWe used the experimental design to determine the optimalparameter values and the parameters of the GA used in thisstudy refer to the proposal of Eiben et al [64] It is possibleto determine the optimal solution when the mutation rateis 0005ndash001 and the crossover rate is 075ndash095 This studyconducted 16 groups of experimental designs for the parentalbodies (10 20) crossover rates (06 095) mutation rates(002 005) and generation (1000 2000) Each group wasrepeated 10 times to obtain the average and the optimalparameter values were as follows parental generation (20)crossover rate (06) mutation rate (005) generation (2000)The experimental results are shown in Table 2

For the PSO this study used PSOA IWM PSOA CFMand PSOA VMM to solve the problems PSOA IWM wassuggested by Eberhart and Shi [61] so when119882 was between09ndash125 it had a higher chance of achieving the optimal solu-tion the design of PSOA IWM parameters was as followsparticle population (10 20) velocity (30 50) weight (04 09)and generation (1000 2000) Sixteen groups of experimentswere designed and each group was repeated 10 times togain the average convergence value completion time andconvergence timeThe optimal parameters of the experimen-tal results were as follows particle 20 weight 04 veloc-ity 50 generation 2000 The experimental results are shownin Table 3 PSOA CFM refers to the 119888

1= 205 119888

2= 205 pro-

posed byClerc [62] 1198881= 28 119888

2= 13proposed byZhang et al

[45] the particle (10 20) and the generation (1000 2000)16 groups of experiments were designed respectively witheach group being repeated 10 times to acquire the averageconvergence value completion time and convergence timeThe optimal parameters of the experimental result were asfollows particle = 20 119888

1= 28 119888

2= 13 velocity = 50

and generation = 2000 The experimental results are shownin Table 4 PSOA VMM used the following values particle(10 20) velocity (30 50) and generation (1000 2000) toconduct eight groups of experimental designs respectivelywith each group repeated 10 times to acquire the averageconvergence value completion time and convergence timeThe optimal parameters of the experimental results were asfollows particle = 20 velocity = 50 generation = 2000 Theexperimental results are shown in Table 5

For the hardware configuration of this experiment theCPU was P4-30GHz and the RAM DDR was 512 MB Thisstudy used ANOVA and Scheffe to verify system operationtimes and convergence times and to select the indices for theGA and the three renovation methods The Scheffe methodwas first promoted by Scheffe [65] to assess the relationshipamong the selection factors ANOVA is a statistical techniquethat can be used to evaluate whether there are differencesbetween the average values or means across several popu-lation groups The Scheffe method one of the multiple-comparison approaches refers to tests designed to establishwhether there are differences between particular levels in anANOVA design that is to determine which variable amongseveral independent variables is statistically the most differ-ent The verification results are shown in Tables 6 7 and 8

Tables 6ndash8 show that all 1198670are rejected Finally the

Scheffe method was used to make multiple comparisons ofthe selection index system execution time and convergencetime of all the algorithms and their differences The Scheffeformula is presented as

(119909119894minus 119909119895minus radic(119896 minus 1) 119865

120572(119896minus1)(119899minus119896)radicMSE(

1

119899119894

+1

119899119895

)

119909119894minus 119909119895+ radic(119896 minus 1) 119865


1

119899119894

+1

119899119895

))

(23)


Table1Datao

ftranspo

rtationcostanddefectrate

Transportatio

nlin

e11ndash21

11ndash22

11ndash23

11ndash24

12ndash21

12ndash22

12ndash23

12ndash24

13ndash21

13ndash22

13ndash23

13ndash24

21ndash31

21ndash32

21ndash33

21ndash34

Transportatio

ndefectrate

001

003

002

002

002

001

004

005

004

003

005

001

003

002

001

004

Transportatio

ncost

56

103

75

64

43

510

45

34

Transportatio

nlin

e21ndash35

22ndash31

22ndash32

22ndash33

22ndash34

22ndash35

23ndash31

23ndash32

23ndash33

23ndash34

23ndash35

24ndash

31

24ndash

32

24ndash

33

24ndash

34

24ndash

35

Transportatio

ndefectrate

002

002

003

004

002

005

003

004

002

003

001

003

004

002

001

002

Transportatio

ncost

54

56

22

58

54

65

65

45

Transportatio

nlin

e31ndash41

31ndash42

31ndash43

31ndash44

31ndash45

31ndash46

32ndash41

32ndash42

32ndash43

32ndash44

32ndash45

32ndash46

33ndash41

33ndash42

33ndash43

33ndash44

Transportatio

ndefectrate

003

002

001

002

001

003

002

003

001

004

002

003

002

003

004

005

Transportatio

ncost

45

46

46

46

35

45

56

48

Transportatio

nlin

e33ndash45

33ndash46

34ndash

41

34ndash

42

34ndash

43

34ndash

44

34ndash

45

34ndash

46

35ndash41

35ndash42

35ndash43

35ndash44

35ndash45

35ndash46

Transportatio

ndefectrate

002

001

002

003

005

004

002

003

003

002

003

004

005

003

Transportatio

ncost

65

44

65

56

25

65

42


Stage 4

Stage 3

Stage 2

Stage 1


Q7PC20

30 = Q = 1700

Q9PC15

10 = Q = 1600

Q10PC12

20 = Q = 1800

Q9PC16

DR00220 = Q = 1550

Q7PC13

DR00310 = Q = 1700

Q8PC15

DR00215 = Q = 1650

Q9PC20

DR00130 = Q = 1700

Q7PC12

DR00220 = Q = 1700

Q6PC13

DR00330 = Q = 1600

Q8PC18

DR00125 = Q = 1350

Q7PC15

DR00230 = Q = 1500

Q8PC13

DR002150 = Q = 1600

Q6PC10

DR00330 = Q = 1350

Q10PC20

DR00120 = Q = 1500

Q8PC12

DR00225 = Q = 1400

Q7PC15

DR00126 = Q = 1250

Q9PC11

DR00320 = Q = 1450

Q7PC12

DR00330 = Q = 1500

Demand

11

12

13

21

22

23

24

31

32

33

34

35

41

42

43

44

45

46

Q Quality levelPC Product costDR Defect rateMinCL =Q =MaxCL

Figure 10 3-4-5-6 forward and reverse supply chain network

Table 9 shows ObjPSOA VMM gt ObjGA = ObjPSOA IWM =

ObjPSOA CFM that is GA PSOA IWM and PSOA CFM areall better than PSOA VMM and there are no clear differ-ences in the selection indices of the three algorithms Thecomparative result of system execution is shown in Table 10and 119865119879GA gt 119865119879PSOA IWM = 119865119879PSOA VMM = 119865119879PSOA CFMis the three PSO updating methods that are all superior toGA The convergence times of the algorithms are shownin Table 11 and 119862119879GA gt 119862119879PSOA CFM gt 119862119879PSOA VMM gt

119862119879PSOA IWM that is PSOA IWM has faster convergencespeed than PSOA VMM PSOA VMM and GA The resultsshow that PSOA IWM performs better in objective functionvalue solutions execution times and convergence times

For validating the solving capabilities of the proposedapproaches in cross-stage reverse logistics problems morelarge-scope network structures 6-6-6-6 6-6-6-6-6 3-10-10-60 6-8-8-10-30 and 8-10-20-20-60 were demon-strated The analysis results also show that PSOA IWM has


Table 2 Experimental design results of GA with different groups of parameters

GAGeneration Population Mutation rate Crossover rate Convergence time (S) Execution time (S) Objective function value

1000

10002 06 4565 6522 5858455

095 3691 5272 5864019

005 06 5888 8412 5820524095 6012 8588 5853552

20002 06 9907 14153 5857317

095 5849 8357 5791562

005 06 11126 15894 5788794095 9415 13451 5787604

2000

10002 06 5942 11212 5830374

095 5187 9788 5873883

005 06 9085 17142 5769888095 8987 16958 5802988

20002 06 8823 16649 5769203

095 7251 13681 5793471

005 06 15542 29372 5755047095 13379 25245 5769029

Table 3 Experimental design results of PSOA IWM with different groups of parameters

PSOA IWMGeneration Particle Velocity Weight Convergence time (S) Execution time (S) Objective function value

1000

1020 04 117 249 5816602

09 126 269 5853555

50 04 228 486 588147309 294 562 5935652

2020 04 345 521 5938588

09 271 577 5824685

50 04 576 1012 581133809 617 1121 5899211

2000

1020 04 296 489 6129503

09 238 521 5817566

50 04 469 924 584003409 510 1026 5851926

2020 04 473 931 5912584

09 502 1006 5803912

50 04 756 1888 573972109 1194 2234 5809798

better capabilities for the proposed problems as shown inTable 12 Therefore this study used PSOA IWM to solvecross-stage reverse logistics problems

Tables 13 14 and 15 show the received forward and reversetransportation volume of the three periods since there wereno defective products generated in the first period there is noreturned transportation volume While this study considersthe transportation losses andmanufacturerrsquos losses upstreamsuppliers produced more products than required to ensure

that final demandwasmetThe quantity of defective productsfrom the second stage was acquired through the defectiveproduct rate of all the suppliers The reverse transportationvolume was divided and returned to the upstream supplychain partners respectively according to the splitting ratio ofdefective product quantity For example 30 of the defectiveproducts generated by the fourth stage retailer would bereturned to the third stage 30 to the second stage and therest would be returned to the first stage the third stage would


Table 4 Experimental design results of PSOA CFM with different groups of parameters

PSOA CFMGeneration Particle Velocity 119888

1 1198882

Convergence time (S) Execution time (S) Objective function value

1000

1020 205 205 277 376 5968602

28 13 184 392 5809097

50 205 205 485 818 591679528 13 414 795 5757822

2020 205 205 337 505 604557

28 13 443 729 5880764

50 205 205 901 1916 598957128 13 854 1541 5835304

2000

1020 205 205 645 908 5796706

28 13 620 868 5749695

50 205 205 1153 1922 601022228 13 986 1644 5834792

2020 205 205 834 1557 5945546

28 13 991 1653 5796291

50 205 205 2264 3774 605729628 13 1884 3140 5740339

Table 5 Experimental design results of PSOA VMMwith different groups of parameters

PSOA VMMGeneration Particle Velocity Convergence time (S) Execution time (S) Objective function value

100010 20 197 295 6207676

50 389 581 6263544

20 20 391 583 621080650 874 1304 6164093

200010 20 353 521 6177516

50 727 1212 6140259

20 20 713 1005 614276150 1445 2409 6096037

Table 6 ANOVA verification of objective function

Algorithm Total Average VarianceGA 172442869 5748095 322633934PSOA IWM 172069405 5735646 255882757PSOA VMM 181137384 6037912 1066796023PSOA CFM 172527080 5750902 1571503097

Hypothesis 1198670 ObjGA = ObjPSOA IWM = ObjPSOA VMM = ObjPSOA CFM 119867

1 otherwise

119875 value = 359119864 minus 28rArr 1198670is rejected

Table 7 ANOVA verification of completion time


Hypothesis1198670 119865119879GA = 119865119879PSOA IWM = 119865119879PSOA VMM = 119865119879PSOA CFM 119867

1 otherwise

119875 value = 762119864 minus 71 rArr 1198670is rejected


Table 8 ANOVA verification of convergence time

Algorithm Total Average VarianceGA 46626 1554 967PSO IWM 2269 75 32PSO VMM 4332 144 101PSO CFM 5672 189 120


1 otherwise

119875-value = 325119864 minus 122 rArr 1198670is rejected

Table 9 Multiple comparison on objective function

ObjGA ObjPSOA IWM ObjPSOA VMM

ObjPSOA IWM (minus +)ObjPSOA VMM (minus minus) (minus minus)ObjPSOA CFM (+ minus) (minus +) (+ +)

Table 10 Multiple comparison on execution time

119865119879GA 119865119879PSOA IWM 119865119879PSOA VMM

119865119879PSOA IWM (+ +)119865119879PSOA VMM (+ +) (minus +)119865119879PSOA CFM (+ +) (minus +) (minus +)

Table 11 Multiple comparison on convergence time


119862119879PSOA IWM (+ +)119862119879PSOA VMM (+ +) (minus minus)119862119879PSOA CFM (+ +) (minus minus) (minus minus)

Table 12 Analysis results on different network structures

Network GA PSOA IWM PSOA CFM PSOA VMM

Objective function

3-4-5-6 5748095a1b 57356461 57509621 603791226-6-6-6 64448212 64242681 65047513 72552374

3-10-10-60 97241222 95445731 98021153 1022415646-6-6-6-6 76046012 75865551 76155213 823544446-8-8-10-30 120122532 115325211 124227343 1345758748-10-20-20-60 168544232 163724161 171141253 181127944

Execution time

3-4-5-6 30692 1891 2201 20216-6-6-6 32642 4181 4241 3901

3-10-10-60 62144 7453 6582 61316-6-6-6-6 53313 6102 5131 48416-8-8-10-30 78264 11253 9212 85218-10-20-20-60 99784 18743 13852 10271

Convergence time

3-4-5-6 15544 751 1893 14426-6-6-6 19662 1861 2271 2261

3-10-10-60 41533 2871 3022 31226-6-6-6-6 30293 2361 2652 27226-8-8-10-30 55743 3521 4072 42528-10-20-20-60 63254 3981 4422 4863

aAverage value branking (by multiple comparison)


Table 13 The first period transportation plan by PSOA IWM

From To Stage 1 Stage 2 Stage 3 Stage 411 12 13 21 22 23 24 31 32 33 34 35 41 42 43 44 45 46

Stage 111 0 0 0 3412 5 646 17 013 1615 154 6 15

Stage 2

21 379 392 190 237 32722 38 0 8 261 45923 0 10 10 0 224 0 0 48 0 0

Stage 3

31 6 28 194 163 1 532 0 9 114 13 146 10033 0 0 0 27 168 5634 126 61 1 154 0 13735 291 366 0 8 0 72

Demand 400 450 300 350 300 350

Table 14 The second period transportation plan by PSOA IWM


Stage 111 29 142 72 15812 120 43 150 2413 576 845 194 128

Stage 2

21 12 0 19 177 115 148 90 16422 9 6 8 189 139 51 183 421

23 0 0 0 104 78 130 74 12

24 0 0 0 136 30 15 91 37

Stage 3

31 1 2 1 3 1 0 0 67 95 130 69 126 9532 2 4 0 2 0 3 0 41 54 111 106 27 533 0 0 1 0 1 0 0 11 2 74 73 81 9534 2 0 3 1 1 2 0 36 45 23 148 127 4335 2 1 5 0 1 1 5 162 165 131 24 92 25

Stage 4

41 2 0 2 0 4 0 0 0 1 1 0 242 0 2 0 0 1 0 0 0 1 0 0 043 2 0 0 0 0 0 2 0 0 0 1 144 1 0 0 0 0 1 0 0 0 0 0 145 0 3 0 1 2 0 0 2 1 0 0 046 3 1 0 1 2 0 0 2 0 0 0 1

Demand 300 350 450 400 430 250Bold data are the reverse transportation volumes

return 50 to the second stage the rest would be returned tothe first stage and the second stage supplier would directlyreturn the defective products to the first stage

4 Conclusion and Suggestion

Enterprises should react to market changes to meet con-sumer demands in a timely manner to maintain and enhancecompetitive advantages in this rapidly changing market

The cross-stage reverse logistics course described in thisstudy could help downstream partners return defective prod-ucts to the upstream partners directly for maintaining andrecovering product function which in turn could reducetransportation costs and time With this paper we haveaccomplished three tasks (1) We presented a mathematicalmodel for partner selection and production-distributionplanning in multistage supply chain networks with cross-stage reverse logistics Based on our research a mathematical


Table 15 The third period transportation plan by PSOA IWM


Stage 111 227 24 48 7312 17 47 0 6513 900 738 84 37

Stage 2

21 7 3 3 133 156 180 239 38322 4 2 23 172 121 144 234 9623 2 4 1 45 0 66 27 024 2 1 0 3 0 73 33 71

Stage 3

31 5 0 1 2 2 1 4 0 4 129 11 134 6432 3 2 0 2 0 2 1 4 3 100 53 57 4933 1 0 1 0 1 0 0 0 81 75 50 139 10734 0 1 3 0 0 4 0 80 50 49 174 36 12535 1 5 0 1 3 1 1 180 172 64 27 0 77

Stage 4

41 1 1 1 0 0 2 1 1 1 0 1 042 0 1 0 0 0 1 0 0 1 0 0 043 1 0 2 0 0 0 3 0 0 2 0 144 2 0 0 0 0 1 0 0 0 0 1 045 3 0 2 3 0 0 1 3 0 1 0 046 1 0 2 1 0 1 0 0 1 0 0 1


model for solving multistage supply chain design problemsconsidering the cross-stage reverse logistics has yet to bepresented However cross-stage reverse logistics shouldmeetthe practical logistics operation conditions therefore (2)we applied a GA and three PSO algorithms to efficientlysolve the mathematical model of cross-stage reverse logisticsproblems In this paper we emphasized the suitability ofadopting a GA and three PSOs to find the solution to themathematical model hence (3) we compared four proposedalgorithms to find which one works best with the proposedproblem The comprehensive results show that PSOA IWMhas the qualities and capabilities for dealing with a multi-stage supply chain design problem with cross-stage reverselogistics Further research should be conducted to employother heuristic algorithms such as ant colony and simulatedannealing for solving this problemConsideration should alsobe given to extending this developed approach to encompassmore complex problems such as problems involving resourceconstraints transportation and economic batches

Conflict of Interests

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

Acknowledgments

The authors would like to thank Mr K Hsiao for supportingwriting of programs and the National Science Council of Tai-wan for their partial financial support (Grants no NSC 102-2410-H-027-009 and NSC 101-2410-H-027-006) The authors

would also like to acknowledge the editors and anonymousreviewers for their helpful comments and suggestions whichgreatly improved the presentation of this paper

References

[1] C J Vidal and M Goetschalckx ldquoStrategic production-distri-bution models a critical review with emphasis on global supplychain modelsrdquo European Journal of Operational Research vol98 no 1 pp 1ndash18 1997

[2] B M Beamon ldquoSupply chain design and analysis models andmethodsrdquo International Journal of Production Economics vol55 no 3 pp 281ndash294 1998

[3] S S Erenguc N C Simpson and A J Vakharia ldquoIntegratedproductiondistribution planning in supply chains an invitedreviewrdquo European Journal of Operational Research vol 115 no2 pp 219ndash236 1999

[4] J Xu Q Liu and R Wang ldquoA class of multi-objective supplychain networks optimal model under random fuzzy environ-ment and its application to the industry of Chinese liquorrdquoInformation Sciences vol 178 no 8 pp 2022ndash2043 2008

[5] R A Aliev B Fazlollahi B G Guirimov and R R AlievldquoFuzzy-genetic approach to aggregate production-distributionplanning in supply chain managementrdquo Information Sciencesvol 177 no 20 pp 4241ndash4255 2007

[6] S-W Chiou ldquoA non-smooth optimization model for a two-tiered supply chain networkrdquo Information Sciences vol 177 no24 pp 5754ndash5762 2007

[7] D Y Sha and Z H Che ldquoVirtual integration with a multi-criteria partner selectionmodel for themulti-echelonmanufac-turing systemrdquoThe International Journal of Advanced Manufac-turing Technology vol 25 no 7-8 pp 793ndash802 2005


[8] D Y Sha and Z H Che ldquoSupply chain network design partnerselection and productiondistribution planning using a system-atic modelrdquo Journal of the Operational Research Society vol 57no 1 pp 52ndash62 2006

[9] Z H Che and Z Cui ldquoUnbalanced supply chain design usingthe analytic network process and a hybrid heuristic-based algo-rithm with balance modulating mechanismrdquo The InternationalJournal of Bio-Inspired Computation vol 3 no 1 pp 56ndash662011

[10] J R Stock Reverse Logistics Council of Logistics ManagementOak Brook Ill USA 1992

[11] B Trebilcock ldquoReverse logistics heroesrdquo Modern MaterialsHandling vol 56 no 10 pp 63ndash65 2001

[12] M Cohen ldquoReplace Rebuild or remanufacturerdquo EquipmentManagement vol 16 no 1 pp 22ndash26 1988

[13] C D White E Masanet C M Rosen and S L BeckmanldquoProduct recovery with some byte an overview of manage-ment challenges and environmental consequences in reversemanufacturing for the computer industryrdquo Journal of CleanerProduction vol 11 no 4 pp 445ndash458 2003

[14] J Gattorna Strategic Supply Chain Alignment-Best Practice inSupply Chain Management Ashgate 1998

[15] C R Carter and L M Ellram ldquoReverse logistics a review ofthe literature and framework for future investigationrdquo Journalof Business Logistics vol 19 no 1 pp 85ndash102 1998

[16] S Dowlatshahi ldquoDeveloping a theory of reverse logisticsrdquo Inter-faces vol 30 no 3 pp 143ndash155 2000

[17] M Fleischmann J M Bloemhof-Ruwaard R Dekker E vander Laan J A E E van Nunen and L N van WassenhoveldquoQuantitative models for reverse logistics a reviewrdquo EuropeanJournal of Operational Research vol 103 no 1 pp 1ndash17 1997

[18] D S Rogers andR Tibben-Lembke ldquoAn examination of reverselogistics practicesrdquo Journal of Business Logistics vol 22 no 2pp 129ndash148 2001

[19] T Spengler H Puchert T Penkuhn and O Rentz ldquoEnvi-ronmental integrated production and recycling managementrdquoEuropean Journal of Operational Research vol 97 no 2 pp 308ndash326 1997

[20] V Jayaraman V D R Guide Jr and R Srivastava ldquoA closed-loop logistics model for remanufacturingrdquo Journal of the Oper-ational Research Society vol 50 no 5 pp 497ndash508 1999

[21] A I Barros R Dekker and V Scholten ldquoA two-level networkfor recycling sand a case studyrdquo European Journal of Opera-tional Research vol 110 no 2 pp 199ndash214 1998

[22] L Kroon and G Vrijens ldquoReturnable containers an example ofreverse logisticsrdquo International Journal of Physical Distributionamp Logistics Management vol 25 no 2 pp 56ndash68 1995

[23] M Fleischmann Quantitative Models for Reverse LogisticsSpringer Berlin Germany 2001

[24] M M Amini D Retzlaff-Roberts and C C BienstockldquoDesigning a reverse logistics operation for short cycle timerepair servicesrdquo International Journal of Production Economicsvol 96 no 3 pp 367ndash380 2005

[25] M Fleischmann P Beullens J M Bloemhof-Ruwaard and LN van Wassenhove ldquoThe impact of product recovery on logis-tics network designrdquo Production and Operations Managementvol 10 no 2 pp 156ndash173 2001

[26] R C Savaskan S Bhattacharya and L N V WassenhoveldquoClosed loop supply chain models with product remanufactur-ingrdquoManagement Science vol 50 no 2 pp 239ndash252 2004

[27] M Chouinard S DrsquoAmours and D Aıt-Kadi ldquoIntegration ofreverse logistics activities within a supply chain informationsystemrdquo Computers in Industry vol 56 no 1 pp 105ndash124 2005

[28] Y Kainuma and N Tawara ldquoA multiple attribute utility theoryapproach to lean and green supply chain managementrdquo Inter-national Journal of Production Economics vol 101 no 1 pp 99ndash108 2006

[29] A Nagurney and F Toyasaki ldquoReverse supply chain manage-ment and electronic waste recycling a multitiered networkequilibrium framework for e-cyclingrdquo Transportation ResearchE vol 41 no 1 pp 1ndash28 2005

[30] Y Nikolaidis ldquoA modelling framework for the acquisition andremanufacturing of used productsrdquo International Journal ofSustainable Engineering vol 2 no 3 pp 154ndash170 2009

[31] G Nenes and Y Nikolaidis ldquoA multi-period model for manag-ing used product returns internationalrdquo Journal of ProductionResearch vol 50 pp 1360ndash1376 2012

[32] M Salema A Barbosa-Povoa and A Novais ldquoSimultaneousdesign and planning of supply chains with reverse flows agenericmodelling frameworkrdquo European Journal of OperationalResearch vol 203 no 2 pp 336ndash349 2010

[33] T Pinto-Varela A P Barbosa-Povoa and A Q Novais ldquoBi-objective optimization approach to the design and planning ofsupply chains economic versus environmental performancesrdquoComputers and Chemical Engineering vol 35 no 8 pp 1454ndash1468 2011

[34] S Amin and G Zhang ldquoA proposed mathematical model forclosed-loop network configuration based on product life cyclerdquoInternational Journal of Advanced Manufacturing Technologyvol 58 no 5ndash8 pp 791ndash801 2012

[35] M Huang M Song L H Lee and W K Ching ldquoAnalysisfor strategy of closed-loop supply chain with dual recyclingchannelrdquo International Journal of Production Economics vol144 no 2 pp 510ndash520 2013

[36] P L Meena and S P Sarmah ldquoMultiple sourcing under sup-plier failure risk and quantity discount a genetic algorithmapproachrdquo Transportation Research E vol 50 pp 84ndash97 2013

[37] B Stojanovic M Milivojevic M Ivanovic N Milivojevicand D Divac ldquoAdaptive system for dam behavior modelingbased on linear regression and genetic algorithmsrdquo Advances inEngineering Software vol 65 pp 182ndash190 2013

[38] R Belevicius D Jatulis and D Sesok ldquoOptimization of tallguyed masts using genetic algorithmsrdquo Engineering Structuresvol 56 pp 239ndash245 2013

[39] Z H Che and C J Chiang ldquoA modified Pareto genetic algo-rithm for multi-objective build-to-order supply chain planningwith product assemblyrdquo Advances in Engineering Software vol41 no 7-8 pp 1011ndash1022 2010

[40] S P Nachiappan and N Jawahar ldquoA genetic algorithm foroptimal operating parameters of VMI system in a two-echelonsupply chainrdquo European Journal of Operational Research vol182 no 3 pp 1433ndash1452 2007

[41] H S Wang and Z H Che ldquoAn integrated model for supplierselection decisions in configuration changesrdquo Expert Systemswith Applications vol 32 no 4 pp 1132ndash1140 2007

[42] Z H Che and T A Chiang ldquoDesigning a collaborative supplychain plan using the analytic hierarchy process and geneticalgorithm with cycle time estimationrdquo International Journal ofProduction Research vol 50 no 16 pp 4426ndash4443 2012

[43] J Kennedy and R Eberhart ldquoParticle swarm optimizationrdquoin Proceedings of the IEEE International Conference on NeuralNetworks vol 4 pp 1942ndash1948 December 1995


[44] Z Liao and J Rittscher ldquoA multi-objective supplier selectionmodel under stochastic demand conditionsrdquo International Jour-nal of Production Economics vol 105 no 1 pp 150ndash159 2007

[45] L-P Zhang H-J Yu and S-X Hu ldquoOptimal choice of param-eters for particle swarm optimizationrdquo Journal of ZhejiangUniversity Science A vol 6 no 6 pp 528ndash534 2005

[46] X H Shi Y C Liang C Lu H P Lee andQ XWang ldquoParticleswarm optimization-based algorithms for TSP and generalizedTSPrdquo Information Processing Letters vol 103 no 5 pp 169ndash1762007

[47] Z H Che ldquoPSO-based back-propagation artificial neural net-work for product and mold cost estimation of plastic injectionmoldingrdquo Computers and Industrial Engineering vol 58 no 4pp 625ndash637 2010

[48] Z H Che ldquoA particle swarm optimization algorithm for solvingunbalanced supply chain planning problemsrdquo Applied SoftComputing vol 12 no 4 pp 1279ndash1287 2012

[49] C Priya and P Lakshmi ldquoParticle swarm optimisation appliedto real time control of spherical tank systemrdquo InternationalJournal of Bio-Inspired Computation vol 4 no 4 pp 206ndash2162012

[50] L Ali S L Sabat and S K Udgata ldquoParticle swarm optimi-sation with stochastic ranking for constrained numerical andengineering benchmark problemsrdquo International Journal of Bio-Inspired Computation vol 4 no 3 pp 155ndash166 2012

[51] E Garcıa-Gonzalo and J L Fernandez-Martınez ldquoA brief his-torical review of particle swarm optimization (PSO)rdquo Journal ofBioinformatics and Intelligent Control vol 1 no 1 pp 3ndash16 2012

[52] L Ali and S L Sabat ldquoParticle swarm optimization based uni-versal solver for global optimizationrdquo Journal of Bioinformaticsand Intelligent Control vol 1 no 1 pp 95ndash105 2012

[53] M Salehi Maleh S Soleymani R Rasouli Nezhad and NGhadimi ldquoUsing particle swarm optimization algorithm basedon multi-objective function in reconfigured system for optimalplacement of distributed generationrdquo Journal of Bioinformaticsand Intelligent Control vol 2 no 2 pp 119ndash1124 2013

[54] H M Abdelsalam and A M Mohamed ldquoOptimal sequencingof design projectsrsquo activities using discrete particle swarm opti-misationrdquo International Journal of Bio-Inspired Computationvol 4 no 2 pp 100ndash110 2012

[55] Y Dong J Tang B Xu and DWang ldquoAn application of swarmoptimization to nonlinear programmingrdquo Computers andMathematics with Applications vol 49 no 11-12 pp 1655ndash16682005

[56] P-Y Yin and J-Y Wang ldquoA particle swarm optimizationapproach to the nonlinear resource allocation problemrdquoAppliedMathematics and Computation vol 183 no 1 pp 232ndash2422006

[57] A Salman I Ahmad and S Al-Madani ldquoParticle swarm opti-mization for task assignment problemrdquo Microprocessors andMicrosystems vol 26 no 8 pp 363ndash371 2002

[58] W A McCall Measurement Macmillan New York NY USA1939

[59] Z H Che ldquoA genetic algorithm-based model for solving multi-period supplier selection problem with assembly sequencerdquoInternational Journal of Production Research vol 48 no 15 pp4355ndash4377 2010

[60] D E Goldberg Genetic Algorithms in Search Optimization andMachine Learning Addison-Wesley New York NY USA 1988

[61] R C Eberhart and Y Shi ldquoComparison between genetic algo-rithms and particle swarm optimizationrdquo in Proceedings of the

7th Annual Conference on Evolutionary Programming pp 611ndash616 Springer Berlin Germany 1998

[62] M Clerc ldquoThe swarm and the queen towards a deterministicand adaptive particle swarm optimizationrdquo in Proceeding of theIEEE Congress on Evolutionary Computation vol 3 pp 1951ndash1957 1999

[63] R Eberhart and J Kennedy ldquoNew optimizer using particleswarm theoryrdquo in Proceedings of the 6th International Sympo-sium onMicroMachine and Human Science pp 39ndash43 October1995

[64] A E Eiben R Hinterding and Z Michalewicz ldquoParametercontrol in evolutionary algorithmsrdquo IEEE Transactions on Evo-lutionary Computation vol 3 no 2 pp 124ndash141 1999

[65] H A Scheffe ldquoAmethod for judging all contrasts in the analysisof variancerdquo Biometrika vol 40 no 1-2 pp 87ndash104 1953

Submit your manuscripts athttpwwwhindawicom

Computer Games Technology

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Distributed Sensor Networks


Advances in

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ReconfigurableComputing

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014


Applied Computational Intelligence and Soft Computing

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Artificial Intelligence

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Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014


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Hindawi Publishing Corporation

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Biomedical Imaging


ArtificialNeural Systems

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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



SupplierRaw materialsAssembly partsPackaging materialsParts manufactures

Processing programsInitial manufacturesRemanufacturingMaintenanceReutilizationResaleRecycle

Final productProductAlternate parts Distribution centers

RegionalityTerritoriality

Customer

DisposalBurialIncineration

Forward logistics

Reverse logistics

∙∙

∙∙

∙∙

∙∙

∙∙

∙∙

∙∙

∙∙

Figure 1 The reverse logistics flow of the products (Gattorna [14])

implemented The reverse logistics flow of products is shownin Figure 1

Many scholars have defined reverse logistics briefly andclearly [10 15ndash18] and some have studied the reverse logisticsnetwork design for different fields such as the steel industry[19] electronic equipment [20] sand recycling [21] reusablepackaging [22] and general recovery networks [23] Aminiet al [24] demonstrated how an effective and profitablereverse logistics operation for an RSSC was designed foran MDM in which customer operations demanded a quickrepair service Fleischmann et al [25] considered a logisticsnetwork design in a reverse logistics context and presented ageneric facility location model by discussing the differencescompared with traditional logistics settings This model wasthen used to analyze the impact of product return flow onlogistics networks

In addition Savaskan et al [26] developed a detailedunderstanding of the implications that a manufacturerrsquosreverse channel choice has on forward channel decisions andthe used product return rate from customers Chouinardet al [27] addressed problems related to integrating reverselogistics activities within an organization and to coordinat-ing this new system Kainuma and Tawara [28] proposedthe multiple-attribute utility theory method for assessing asupply chain including reusing and recycling throughout thelife cycle of products and services Nagurney and Toyasaki[29] developed a model linking these decisions to prices andmaterial shipments among end-of-life electronics sourcesrecyclers processors and suppliers for deterministic scenar-ios Nikolaidis [30] proposed a single-period mathematicalmodel for determining a reverse supply chain plan that con-siders procurement and returnsrsquo remanufacturing andNenesand Nikolaidis [31] extended Nikolaidisrsquos model to a multi-period model Salema et al [32] developed a multiperiodmultiproduct model for designing supply chain networksregarding reverse flowsMore recently Pinto-Varela et al [33]considered an environmental perspective to develop amixed-integer linear programming model for planning reversesupply chains Amin and Zhang [34] presented a mixed-integer linear programming model for designing a closed-loop supply chain network regarding product life cycles In

additionHuang et al [35] analyzed strategies of a closed-loopsupply chain containing a dual recycling channel Althoughcross-stage logistics in reverse supply chains generally existsin practice our research suggests that it has yet to be ade-quately addressed Hence the motivation of this study is todesign the reverse supply chain with cross-stage logistics

Reverse logistics is more complex than forward logisticsand this study aimed to develop a mathematical foundationfor modeling a cross-stage reverse logistics plan that enablesdefective products with differing degrees of damage to bereturned to upstream partners in the stages of a supply chainfor maintenance replacement or restructuring This cross-stage reverse logisticsmodel can help save time lessen unnec-essary deliveries and more importantly meet the conditionsof reverse logistics operation more efficiently

Recently GAs have been regarded as a novel approachto solving complex large-scale and real-world optimiza-tion problems [6 36ndash42] Moreover the PSO proposed byKennedy and Eberhart [43] was an iteration optimizationinstrument generating a group of initial solutions at thebeginning and then acquiring the optimal value throughiteration Liao and Rittscher [44] applied this instrumentto scheduling problems related to industrial piece workrequiring minimal completion time Zhang et al [45] appliedPSO to solve the minimization problems of the projectduration for resource-constrained scheduling Shi et al [46]applied a PSO to the traveling salesman problem Che [47]developed a PSO-based back-propagation artificial neuralnetwork for estimating the product and mold costs of plasticinjection molding and Che [48] proposed a modified PSOmethod for solving multiechelon unbalanced supply chainplanning problems Priya and Lakshmi [49] applied PSO forperforming the real time control of spherical tank systemand Ali et al [50] used the PSO for solving the constrainednumerical and engineering benchmark problems Otherrelated studies concerning the use of PSO for the optimizationproblems are [51ndash54]

In addition Dong et al [55] compared the improved PSOa combinatorial particle swarm optimization (CPSO) withGA and the results showed that the improved PSO was moreeffective in solving nonlinear problems Yin and Wang [56]



Demand

21

22

23

21

31

32

33

34

41

42

43

44

11

12

13

14












reverse logistics





hellip








ANOVA


reverse logistics


ObjectiveMinimize

Constraints

lowast

lowast

lowast

lowast

lowast

lowast

lowast

lowast

lowast

lowast

lowast

lowast

lowastlowast

lowast

lowast



+


JS

rs = s + 1 j = 1

sum sum


J

j = 1

sum )

Scheff e method








Parameters







Min119862119875(119904119894)


Max119862119875(119904119894)



119875119862(119904119894)


119875119876(119904119894)



119879119878((119904119894)(119904+1119895))


119875119862(119904119894)



stage 119904119879119862((119904119894)(119904+1119895))


119879119878((119904119894)(119904+1119895))


119879

119875119862(119904119894)


119879



119879119862((119904119894)(119904+1119895))


119879

119879119878((119904119894)(119904+1119895))


119878119866119875119862119904119894


119878119866119879119862((119904119894)(119904+1119895))


119878119866119875119876119904119894


119878119866119879119878((119904119894)(119904+1119895))


119865119877(119904119894)


119879119865119877((119904119894)(119904+1119895))


119908119875119862

119908119879119862

119908119879119878

119908119875119876



Decision Variables

119880119899



119877119880119899








119904new119894


Vnew119894







119891119875119862

=

119873

sum

119899=1

119878

sum

119904=1

119868

sum

119894=1

119879

119875119862(119904119894)

times [

[

100381710038171003817100381710038171003817100381710038171003817

119880119899

((119904119894)(119904+11))

1 minus 119865119877(119904119894)

100381710038171003817100381710038171003817100381710038171003817

+

119869

sum

119895=2

10038171003817100381710038171003817119880119899

((119904minus1119895)(119904119894))(1minus119879119865119877

((119904minus1119895)(119904119894)))10038171003817100381710038171003817]

]

(1)


119891119879119862 =

119873

sum

119899=1

119878

sum

119904=1

119868

sum

119894=1

119869

sum

119895=1

119879

119879119862(119904119894)(119904+1119895)

119880119899

((119904119894)(119904+1119895)) (2)



119891119875119876

=

119873

sum

119899=1

119878

sum

119904=1

119868

sum

119894=1

119879

119875119876(119904119894)

times [

[

100381710038171003817100381710038171003817100381710038171003817

119880119899

((119904119894)(119904+11))

1 minus 119865119877(119904119894)

100381710038171003817100381710038171003817100381710038171003817

+

119869

sum

119895=2

10038171003817100381710038171003817119880119899

((119904minus1119895)(119904119894))(1minus119879119865119877

((119904minus1119895)(119904119894)))10038171003817100381710038171003817]

]

(3)


119891119879119878 =

119873

sum

119899=1

119878

sum

119904=1

119868

sum

119894=1

119869

sum

119895=1

119879

119879119878(119904119894)(119904+1119895)

119880119899

((119904119894)(119904+1119895)) (4)


119903119875119862 =

119873

sum

119899=2

119878minus1

sum

119904=1

119868

sum

119894=1

119879

119875119862(119904119894)

119878

sum

119903119904=119904+1

119869

sum

119895=1

119877119880119899

((119903119904119895)(119904119894)) (5)


119903119879119862 =

119873

sum

119899=2

119878

sum

119904=1

119868

sum

119894=1

119879

119879119862((119903119904119895)(119904119894))

119878

sum

119903119904=119904+1

119869

sum

119895=1

119877119880119899

((119903119904119895)(119904119894)) (6)


119903119875119876 =

119873

sum

119899=2

119878minus1

sum

119904=1

119868

sum

119894=1

119879

119875119876(119904119894)

119878

sum

119903119904=119904+1

119869

sum

119895=1

119877119880119899

((119903119904119895)(119904119894)) (7)


119903119879119878 =

119873

sum

119899=2

119878

sum

119904=1

119868

sum

119894=1

119879

119879119878((119903119904119895)(119904119894))

119878

sum

119903119904=119904+1

119869

sum

119895=1

119877119880119899

((119903119904119895)(119904119894)) (8)


Minimize 119885 = 119908119875119862

(119891119875119862 + 119903119875119862)

+ 119908119879119862

(119891119879119862 + 119903119879119862)

minus 119908119875119876

(119891119875119876 + 119903119875119876)

+ 119908119879119878

(119891119879119878 + 119903119879119878)

st

(9)


Min119862119875(119904119894)

le

119869

sum

119895=1

10038171003817100381710038171003817119880119899

((119904minus1119895)(119904119894))(1 minus 119879119865119877

((119904minus1119895)(119904119894)))10038171003817100381710038171003817

+

119878

sum

119903119904=119904+1

119869

sum

119895=1

119877119880119899minus1

((119903119904119895)(119904119894))le Max119862119875

(119904119894)

for 119899 = 1 2 3 119873

119904 = 2 3 119878 119894 = 1 2 3 119868

(10)

Min119862119875(119904119894)

le

119869

sum

119895=1

10038171003817100381710038171003817100381710038171003817100381710038171003817

119880119899

((119904119894)(119904+1119895))

1 minus 119865119877(119904119894)

10038171003817100381710038171003817100381710038171003817100381710038171003817

+

119878

sum

119903119904=119904+1

119869

sum

119895=1

119877119880119899minus1

((119903119904119895)(119904119894))le Max119862119875

(119904119894)

for 119899 = 1 2 3 119873 119904 = 1

119894 = 1 2 3 119868

(11)


119869

sum

119895=1

100381710038171003817100381710038171003817119880119899

((119904minus1119895)(119904119894))(1 minus 119879119865119877

((119904minus1119895)(119904119894)))100381710038171003817100381710038171003817

+

119878

sum

119903119904=119904+1

119869

sum

119895=1

119877119880119899minus1

((119903119904119895)(119904119894))

=

119869

sum

119895=1

119880119899

((119904+1119895)(119904119894))+

119904minus1

sum

119903119904=1

119869

sum

119895=1

119877119880119899

((119904119894)(119903119904119895))

for 119899 = 1 2 3 119873

119904 = 1 2 3 119878 119894 = 1 2 3 119868

(12)

119904

sum

119903119904=1

119869

sum

119895=1

119877119880119899

((119903119904119895)(119904119894))

=

10038171003817100381710038171003817100381710038171003817100381710038171003817

(

119869

sum

119895=1

10038171003817100381710038171003817119880119899

((119904minus1119895)(119904119894))(1 minus 119879119865119877

((119904minus1119895)(119904119894)))10038171003817100381710038171003817

+

119878

sum

119903119904=119904+1

119869

sum

119895=1

119877119880119899minus1

((119903119904119895)(119904119894)))119865119877(119904119894)

10038171003817100381710038171003817100381710038171003817100381710038171003817

for 119899 = 1 2 3 119873

119904 = 1 2 3 119878 119894 = 1 2 3 119868

(13)



119869

sum

119895=1

10038171003817100381710038171003817119880119899

((119904minus1119895)(119904119894))(1 minus 119879119865119877

((119904minus1119895)(119904119894)))10038171003817100381710038171003817

minus

119904minus1

sum

119903119904=1

119869

sum

119895=1

119877119880119899

((119904119894)(119904minus119903119904119895))= 119862119863

119899

(119904119894)

for 119899 = 1 2 3 119873 119904 = 119878

119894 = 1 2 3 119868

(14)


0 le 119908119875119862

119908119879119862

119908119879119878 119908119875119876

le 1

119908119875119862

+ 119908119879119862

+ 119908119879119878

+ 119908119875119876

= 1

(15)


119877119880119899

((119903119904119895)(119904119894))= 0 for 119899 le 0 119904 = 1 2 3 4 119878 minus 1

119903119904 = 119904 + 1 119878 119894 = 1 2 3 119868

119895 = 1 2 3 119869

(16)


119880119899

((119904119894)(119904+1119895))ge 0 and 119880

119899

((119904119894)(119904+1119895))isin Integer

for 119899 = 1 2 3 119873 119904 = 1 2 3 119878

119894 = 1 2 3 119868 119895 = 1 2 3 119869

(17)

119877119880119899

((119903119904119895)(119904119894))ge 0 and 119880

119899

((119904119894)(119904+1119895))isin Integer

for 119904 = 1 2 3 119878 119903119904 = 119878 + 1 119878

119899 = 1 2 3 119873 119894 = 1 2 3 119868 119895 = 1 2 3 119869

(18)


119879

119875119862(119904119894)

=119875119862(119904119894)

minus 119875119862(119904119894)

119878119866119875119862(119904119894)

10+ 50 for 119904 = 1 2 3 119878

119894 = 1 2 3 119868

119879

119879119862((119904119894)(119904+1119895))

=

119879119862((119904119894)(119904+1119895))

minus 119879119862((119904119894)(119904+1119895))

119878119866119879119862((119904119894)(119904+1119895))

10+ 50

for 119904 = 1 2 3 119878 119894 = 1 2 3 119868

119895 = 1 2 3 119869

119879

119875119876(119904119894)

=119875119876(119904119894)

minus 119875119876(119904119894)

119878119866119875119876(119904119894)10

+ 50 for 119904 = 1 2 3 119878

119894 = 1 2 3 119868

119879

119879119878((119904119894)(119904+1119895))

=

119879119878((119904119894)(119904+1119895))

minus 119879119878((119904119894)(119904+1119895))

119878119866119879119878((119904119894)(119904+1119895))

10+ 50

for 119904 = 1 2 3 119878 119894 = 1 2 3 119868

119895 = 1 2 3 119869

(19)


























Mutation point

After mutation






Particle 1 2 3 4 5 6 117 118 119Line

Volume 0 0 42 9 0 0 0 2 0



















Vnew119894

= 119908Vold119894

+ 1198881times rand () times (119904

lowast

119894minus 119904

old119894

) + 1198882


old119894

)

119904new119894

= 119904old119894

+ Vnew119894

(20)


Vnew119894

= Vold119894

+ 1198881times rand () times (119904

lowast

119894minus 119904

old119894

) + 1198882


old119894

)

119904new119894

= 119904old119894

+ Vnew119894

if V119894gt Vmax V

119894= Vmax


119894= minusVmax

(21)



Vnew119894

= 119896 times ⟨Vold119894

+ 1198881times rand () times (119904

lowast

119894minus 119904

old119894

)


119894minus 119904

old119894

)⟩

119904new119894

= 119904old119894

+ Vnew119894

119870 =2


120601 = 1198881+ 1198882 120601 gt 4

(22)








Siliconmaterial



test Customer

Manufacturing unit


Reverse route





1= 205 119888

2= 205 pro-

posed byClerc [62] 1198881= 28 119888



1= 28 119888

2= 13 velocity = 50







1

119899119894

+1

119899119895

)



1

119899119894

+1

119899119895

))

(23)


Table1Datao

ftranspo


Transportatio

nlin

e11ndash21

11ndash22

11ndash23

11ndash24

12ndash21

12ndash22

12ndash23

12ndash24

13ndash21

13ndash22

13ndash23

13ndash24

21ndash31

21ndash32

21ndash33

21ndash34

Transportatio

ndefectrate

001

003

002

002

002

001

004

005

004

003

005

001

003

002

001

004

Transportatio

ncost

56

103

75

64

43

510

45

34

Transportatio

nlin

e21ndash35

22ndash31

22ndash32

22ndash33

22ndash34

22ndash35

23ndash31

23ndash32

23ndash33

23ndash34

23ndash35

24ndash

31

24ndash

32

24ndash

33

24ndash

34

24ndash

35

Transportatio

ndefectrate

002

002

003

004

002

005

003

004

002

003

001

003

004

002

001

002

Transportatio

ncost

54

56

22

58

54

65

65

45

Transportatio

nlin

e31ndash41

31ndash42

31ndash43

31ndash44

31ndash45

31ndash46

32ndash41

32ndash42

32ndash43

32ndash44

32ndash45

32ndash46

33ndash41

33ndash42

33ndash43

33ndash44

Transportatio

ndefectrate

003

002

001

002

001

003

002

003

001

004

002

003

002

003

004

005

Transportatio

ncost

45

46

46

46

35

45

56

48

Transportatio

nlin

e33ndash45

33ndash46

34ndash

41

34ndash

42

34ndash

43

34ndash

44

34ndash

45

34ndash

46

35ndash41

35ndash42

35ndash43

35ndash44

35ndash45

35ndash46

Transportatio

ndefectrate

002

001

002

003

005

004

002

003

003

002

003

004

005

003

Transportatio

ncost

65

44

65

56

25

65

42


Stage 4

Stage 3

Stage 2

Stage 1


Q7PC20

30 = Q = 1700

Q9PC15

10 = Q = 1600

Q10PC12

20 = Q = 1800

Q9PC16

DR00220 = Q = 1550

Q7PC13

DR00310 = Q = 1700

Q8PC15

DR00215 = Q = 1650

Q9PC20

DR00130 = Q = 1700

Q7PC12

DR00220 = Q = 1700

Q6PC13

DR00330 = Q = 1600

Q8PC18

DR00125 = Q = 1350

Q7PC15

DR00230 = Q = 1500

Q8PC13

DR002150 = Q = 1600

Q6PC10

DR00330 = Q = 1350

Q10PC20

DR00120 = Q = 1500

Q8PC12

DR00225 = Q = 1400

Q7PC15

DR00126 = Q = 1250

Q9PC11

DR00320 = Q = 1450

Q7PC12

DR00330 = Q = 1500

Demand

11

12

13

21

22

23

24

31

32

33

34

35

41

42

43

44

45

46










1000

10002 06 4565 6522 5858455

095 3691 5272 5864019

005 06 5888 8412 5820524095 6012 8588 5853552

20002 06 9907 14153 5857317

095 5849 8357 5791562

005 06 11126 15894 5788794095 9415 13451 5787604

2000

10002 06 5942 11212 5830374

095 5187 9788 5873883

005 06 9085 17142 5769888095 8987 16958 5802988

20002 06 8823 16649 5769203

095 7251 13681 5793471

005 06 15542 29372 5755047095 13379 25245 5769029



1000

1020 04 117 249 5816602

09 126 269 5853555

50 04 228 486 588147309 294 562 5935652

2020 04 345 521 5938588

09 271 577 5824685

50 04 576 1012 581133809 617 1121 5899211

2000

1020 04 296 489 6129503

09 238 521 5817566

50 04 469 924 584003409 510 1026 5851926

2020 04 473 931 5912584

09 502 1006 5803912

50 04 756 1888 573972109 1194 2234 5809798







1 1198882


1000

1020 205 205 277 376 5968602

28 13 184 392 5809097

50 205 205 485 818 591679528 13 414 795 5757822

2020 205 205 337 505 604557

28 13 443 729 5880764

50 205 205 901 1916 598957128 13 854 1541 5835304

2000

1020 205 205 645 908 5796706

28 13 620 868 5749695

50 205 205 1153 1922 601022228 13 986 1644 5834792

2020 205 205 834 1557 5945546

28 13 991 1653 5796291

50 205 205 2264 3774 605729628 13 1884 3140 5740339



100010 20 197 295 6207676

50 389 581 6263544

20 20 391 583 621080650 874 1304 6164093

200010 20 353 521 6177516

50 727 1212 6140259

20 20 713 1005 614276150 1445 2409 6096037




1 otherwise





1 otherwise






1 otherwise













Objective function

3-4-5-6 5748095a1b 57356461 57509621 603791226-6-6-6 64448212 64242681 65047513 72552374

3-10-10-60 97241222 95445731 98021153 1022415646-6-6-6-6 76046012 75865551 76155213 823544446-8-8-10-30 120122532 115325211 124227343 1345758748-10-20-20-60 168544232 163724161 171141253 181127944

Execution time

3-4-5-6 30692 1891 2201 20216-6-6-6 32642 4181 4241 3901

3-10-10-60 62144 7453 6582 61316-6-6-6-6 53313 6102 5131 48416-8-8-10-30 78264 11253 9212 85218-10-20-20-60 99784 18743 13852 10271

Convergence time

3-4-5-6 15544 751 1893 14426-6-6-6 19662 1861 2271 2261

3-10-10-60 41533 2871 3022 31226-6-6-6-6 30293 2361 2652 27226-8-8-10-30 55743 3521 4072 42528-10-20-20-60 63254 3981 4422 4863





Stage 111 0 0 0 3412 5 646 17 013 1615 154 6 15

Stage 2

21 379 392 190 237 32722 38 0 8 261 45923 0 10 10 0 224 0 0 48 0 0

Stage 3

31 6 28 194 163 1 532 0 9 114 13 146 10033 0 0 0 27 168 5634 126 61 1 154 0 13735 291 366 0 8 0 72

Demand 400 450 300 350 300 350



Stage 111 29 142 72 15812 120 43 150 2413 576 845 194 128

Stage 2

21 12 0 19 177 115 148 90 16422 9 6 8 189 139 51 183 421

23 0 0 0 104 78 130 74 12

24 0 0 0 136 30 15 91 37

Stage 3

31 1 2 1 3 1 0 0 67 95 130 69 126 9532 2 4 0 2 0 3 0 41 54 111 106 27 533 0 0 1 0 1 0 0 11 2 74 73 81 9534 2 0 3 1 1 2 0 36 45 23 148 127 4335 2 1 5 0 1 1 5 162 165 131 24 92 25

Stage 4

41 2 0 2 0 4 0 0 0 1 1 0 242 0 2 0 0 1 0 0 0 1 0 0 043 2 0 0 0 0 0 2 0 0 0 1 144 1 0 0 0 0 1 0 0 0 0 0 145 0 3 0 1 2 0 0 2 1 0 0 046 3 1 0 1 2 0 0 2 0 0 0 1









Stage 111 227 24 48 7312 17 47 0 6513 900 738 84 37

Stage 2

21 7 3 3 133 156 180 239 38322 4 2 23 172 121 144 234 9623 2 4 1 45 0 66 27 024 2 1 0 3 0 73 33 71

Stage 3

31 5 0 1 2 2 1 4 0 4 129 11 134 6432 3 2 0 2 0 2 1 4 3 100 53 57 4933 1 0 1 0 1 0 0 0 81 75 50 139 10734 0 1 3 0 0 4 0 80 50 49 174 36 12535 1 5 0 1 3 1 1 180 172 64 27 0 77

Stage 4

41 1 1 1 0 0 2 1 1 1 0 1 042 0 1 0 0 0 1 0 0 1 0 0 043 1 0 2 0 0 0 3 0 0 2 0 144 2 0 0 0 0 1 0 0 0 0 1 045 3 0 2 3 0 0 1 3 0 1 0 046 1 0 2 1 0 1 0 0 1 0 0 1





Acknowledgments



References












































































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in





Demand

21

22

23

21

31

32

33

34

41

42

43

44

11

12

13

14












reverse logistics





hellip








ANOVA


reverse logistics


ObjectiveMinimize

Constraints

lowast

lowast

lowast

lowast

lowast

lowast

lowast

lowast

lowast

lowast

lowast

lowast

lowastlowast

lowast

lowast



+


JS

rs = s + 1 j = 1

sum sum


J

j = 1

sum )

Scheff e method








Parameters







Min119862119875(119904119894)


Max119862119875(119904119894)



119875119862(119904119894)


119875119876(119904119894)



119879119878((119904119894)(119904+1119895))


119875119862(119904119894)



stage 119904119879119862((119904119894)(119904+1119895))


119879119878((119904119894)(119904+1119895))


119879

119875119862(119904119894)


119879



119879119862((119904119894)(119904+1119895))


119879

119879119878((119904119894)(119904+1119895))


119878119866119875119862119904119894


119878119866119879119862((119904119894)(119904+1119895))


119878119866119875119876119904119894


119878119866119879119878((119904119894)(119904+1119895))


119865119877(119904119894)


119879119865119877((119904119894)(119904+1119895))


119908119875119862

119908119879119862

119908119879119878

119908119875119876



Decision Variables

119880119899



119877119880119899








119904new119894


Vnew119894







119891119875119862

=

119873

sum

119899=1

119878

sum

119904=1

119868

sum

119894=1

119879

119875119862(119904119894)

times [

[

100381710038171003817100381710038171003817100381710038171003817

119880119899

((119904119894)(119904+11))

1 minus 119865119877(119904119894)

100381710038171003817100381710038171003817100381710038171003817

+

119869

sum

119895=2

10038171003817100381710038171003817119880119899

((119904minus1119895)(119904119894))(1minus119879119865119877

((119904minus1119895)(119904119894)))10038171003817100381710038171003817]

]

(1)


119891119879119862 =

119873

sum

119899=1

119878

sum

119904=1

119868

sum

119894=1

119869

sum

119895=1

119879

119879119862(119904119894)(119904+1119895)

119880119899

((119904119894)(119904+1119895)) (2)



119891119875119876

=

119873

sum

119899=1

119878

sum

119904=1

119868

sum

119894=1

119879

119875119876(119904119894)

times [

[

100381710038171003817100381710038171003817100381710038171003817

119880119899

((119904119894)(119904+11))

1 minus 119865119877(119904119894)

100381710038171003817100381710038171003817100381710038171003817

+

119869

sum

119895=2

10038171003817100381710038171003817119880119899

((119904minus1119895)(119904119894))(1minus119879119865119877

((119904minus1119895)(119904119894)))10038171003817100381710038171003817]

]

(3)


119891119879119878 =

119873

sum

119899=1

119878

sum

119904=1

119868

sum

119894=1

119869

sum

119895=1

119879

119879119878(119904119894)(119904+1119895)

119880119899

((119904119894)(119904+1119895)) (4)


119903119875119862 =

119873

sum

119899=2

119878minus1

sum

119904=1

119868

sum

119894=1

119879

119875119862(119904119894)

119878

sum

119903119904=119904+1

119869

sum

119895=1

119877119880119899

((119903119904119895)(119904119894)) (5)


119903119879119862 =

119873

sum

119899=2

119878

sum

119904=1

119868

sum

119894=1

119879

119879119862((119903119904119895)(119904119894))

119878

sum

119903119904=119904+1

119869

sum

119895=1

119877119880119899

((119903119904119895)(119904119894)) (6)


119903119875119876 =

119873

sum

119899=2

119878minus1

sum

119904=1

119868

sum

119894=1

119879

119875119876(119904119894)

119878

sum

119903119904=119904+1

119869

sum

119895=1

119877119880119899

((119903119904119895)(119904119894)) (7)


119903119879119878 =

119873

sum

119899=2

119878

sum

119904=1

119868

sum

119894=1

119879

119879119878((119903119904119895)(119904119894))

119878

sum

119903119904=119904+1

119869

sum

119895=1

119877119880119899

((119903119904119895)(119904119894)) (8)


Minimize 119885 = 119908119875119862

(119891119875119862 + 119903119875119862)

+ 119908119879119862

(119891119879119862 + 119903119879119862)

minus 119908119875119876

(119891119875119876 + 119903119875119876)

+ 119908119879119878

(119891119879119878 + 119903119879119878)

st

(9)


Min119862119875(119904119894)

le

119869

sum

119895=1

10038171003817100381710038171003817119880119899

((119904minus1119895)(119904119894))(1 minus 119879119865119877

((119904minus1119895)(119904119894)))10038171003817100381710038171003817

+

119878

sum

119903119904=119904+1

119869

sum

119895=1

119877119880119899minus1

((119903119904119895)(119904119894))le Max119862119875

(119904119894)

for 119899 = 1 2 3 119873

119904 = 2 3 119878 119894 = 1 2 3 119868

(10)

Min119862119875(119904119894)

le

119869

sum

119895=1

10038171003817100381710038171003817100381710038171003817100381710038171003817

119880119899

((119904119894)(119904+1119895))

1 minus 119865119877(119904119894)

10038171003817100381710038171003817100381710038171003817100381710038171003817

+

119878

sum

119903119904=119904+1

119869

sum

119895=1

119877119880119899minus1

((119903119904119895)(119904119894))le Max119862119875

(119904119894)

for 119899 = 1 2 3 119873 119904 = 1

119894 = 1 2 3 119868

(11)


119869

sum

119895=1

100381710038171003817100381710038171003817119880119899

((119904minus1119895)(119904119894))(1 minus 119879119865119877

((119904minus1119895)(119904119894)))100381710038171003817100381710038171003817

+

119878

sum

119903119904=119904+1

119869

sum

119895=1

119877119880119899minus1

((119903119904119895)(119904119894))

=

119869

sum

119895=1

119880119899

((119904+1119895)(119904119894))+

119904minus1

sum

119903119904=1

119869

sum

119895=1

119877119880119899

((119904119894)(119903119904119895))

for 119899 = 1 2 3 119873

119904 = 1 2 3 119878 119894 = 1 2 3 119868

(12)

119904

sum

119903119904=1

119869

sum

119895=1

119877119880119899

((119903119904119895)(119904119894))

=

10038171003817100381710038171003817100381710038171003817100381710038171003817

(

119869

sum

119895=1

10038171003817100381710038171003817119880119899

((119904minus1119895)(119904119894))(1 minus 119879119865119877

((119904minus1119895)(119904119894)))10038171003817100381710038171003817

+

119878

sum

119903119904=119904+1

119869

sum

119895=1

119877119880119899minus1

((119903119904119895)(119904119894)))119865119877(119904119894)

10038171003817100381710038171003817100381710038171003817100381710038171003817

for 119899 = 1 2 3 119873

119904 = 1 2 3 119878 119894 = 1 2 3 119868

(13)



119869

sum

119895=1

10038171003817100381710038171003817119880119899

((119904minus1119895)(119904119894))(1 minus 119879119865119877

((119904minus1119895)(119904119894)))10038171003817100381710038171003817

minus

119904minus1

sum

119903119904=1

119869

sum

119895=1

119877119880119899

((119904119894)(119904minus119903119904119895))= 119862119863

119899

(119904119894)

for 119899 = 1 2 3 119873 119904 = 119878

119894 = 1 2 3 119868

(14)


0 le 119908119875119862

119908119879119862

119908119879119878 119908119875119876

le 1

119908119875119862

+ 119908119879119862

+ 119908119879119878

+ 119908119875119876

= 1

(15)


119877119880119899

((119903119904119895)(119904119894))= 0 for 119899 le 0 119904 = 1 2 3 4 119878 minus 1

119903119904 = 119904 + 1 119878 119894 = 1 2 3 119868

119895 = 1 2 3 119869

(16)


119880119899

((119904119894)(119904+1119895))ge 0 and 119880

119899

((119904119894)(119904+1119895))isin Integer

for 119899 = 1 2 3 119873 119904 = 1 2 3 119878

119894 = 1 2 3 119868 119895 = 1 2 3 119869

(17)

119877119880119899

((119903119904119895)(119904119894))ge 0 and 119880

119899

((119904119894)(119904+1119895))isin Integer

for 119904 = 1 2 3 119878 119903119904 = 119878 + 1 119878

119899 = 1 2 3 119873 119894 = 1 2 3 119868 119895 = 1 2 3 119869

(18)


119879

119875119862(119904119894)

=119875119862(119904119894)

minus 119875119862(119904119894)

119878119866119875119862(119904119894)

10+ 50 for 119904 = 1 2 3 119878

119894 = 1 2 3 119868

119879

119879119862((119904119894)(119904+1119895))

=

119879119862((119904119894)(119904+1119895))

minus 119879119862((119904119894)(119904+1119895))

119878119866119879119862((119904119894)(119904+1119895))

10+ 50

for 119904 = 1 2 3 119878 119894 = 1 2 3 119868

119895 = 1 2 3 119869

119879

119875119876(119904119894)

=119875119876(119904119894)

minus 119875119876(119904119894)

119878119866119875119876(119904119894)10

+ 50 for 119904 = 1 2 3 119878

119894 = 1 2 3 119868

119879

119879119878((119904119894)(119904+1119895))

=

119879119878((119904119894)(119904+1119895))

minus 119879119878((119904119894)(119904+1119895))

119878119866119879119878((119904119894)(119904+1119895))

10+ 50

for 119904 = 1 2 3 119878 119894 = 1 2 3 119868

119895 = 1 2 3 119869

(19)


























Mutation point

After mutation






Particle 1 2 3 4 5 6 117 118 119Line

Volume 0 0 42 9 0 0 0 2 0



















Vnew119894

= 119908Vold119894

+ 1198881times rand () times (119904

lowast

119894minus 119904

old119894

) + 1198882


old119894

)

119904new119894

= 119904old119894

+ Vnew119894

(20)


Vnew119894

= Vold119894

+ 1198881times rand () times (119904

lowast

119894minus 119904

old119894

) + 1198882


old119894

)

119904new119894

= 119904old119894

+ Vnew119894

if V119894gt Vmax V

119894= Vmax


119894= minusVmax

(21)



Vnew119894

= 119896 times ⟨Vold119894

+ 1198881times rand () times (119904

lowast

119894minus 119904

old119894

)


119894minus 119904

old119894

)⟩

119904new119894

= 119904old119894

+ Vnew119894

119870 =2


120601 = 1198881+ 1198882 120601 gt 4

(22)








Siliconmaterial



test Customer

Manufacturing unit


Reverse route





1= 205 119888

2= 205 pro-

posed byClerc [62] 1198881= 28 119888



1= 28 119888

2= 13 velocity = 50







1

119899119894

+1

119899119895

)



1

119899119894

+1

119899119895

))

(23)


Table1Datao

ftranspo


Transportatio

nlin

e11ndash21

11ndash22

11ndash23

11ndash24

12ndash21

12ndash22

12ndash23

12ndash24

13ndash21

13ndash22

13ndash23

13ndash24

21ndash31

21ndash32

21ndash33

21ndash34

Transportatio

ndefectrate

001

003

002

002

002

001

004

005

004

003

005

001

003

002

001

004

Transportatio

ncost

56

103

75

64

43

510

45

34

Transportatio

nlin

e21ndash35

22ndash31

22ndash32

22ndash33

22ndash34

22ndash35

23ndash31

23ndash32

23ndash33

23ndash34

23ndash35

24ndash

31

24ndash

32

24ndash

33

24ndash

34

24ndash

35

Transportatio

ndefectrate

002

002

003

004

002

005

003

004

002

003

001

003

004

002

001

002

Transportatio

ncost

54

56

22

58

54

65

65

45

Transportatio

nlin

e31ndash41

31ndash42

31ndash43

31ndash44

31ndash45

31ndash46

32ndash41

32ndash42

32ndash43

32ndash44

32ndash45

32ndash46

33ndash41

33ndash42

33ndash43

33ndash44

Transportatio

ndefectrate

003

002

001

002

001

003

002

003

001

004

002

003

002

003

004

005

Transportatio

ncost

45

46

46

46

35

45

56

48

Transportatio

nlin

e33ndash45

33ndash46

34ndash

41

34ndash

42

34ndash

43

34ndash

44

34ndash

45

34ndash

46

35ndash41

35ndash42

35ndash43

35ndash44

35ndash45

35ndash46

Transportatio

ndefectrate

002

001

002

003

005

004

002

003

003

002

003

004

005

003

Transportatio

ncost

65

44

65

56

25

65

42


Stage 4

Stage 3

Stage 2

Stage 1


Q7PC20

30 = Q = 1700

Q9PC15

10 = Q = 1600

Q10PC12

20 = Q = 1800

Q9PC16

DR00220 = Q = 1550

Q7PC13

DR00310 = Q = 1700

Q8PC15

DR00215 = Q = 1650

Q9PC20

DR00130 = Q = 1700

Q7PC12

DR00220 = Q = 1700

Q6PC13

DR00330 = Q = 1600

Q8PC18

DR00125 = Q = 1350

Q7PC15

DR00230 = Q = 1500

Q8PC13

DR002150 = Q = 1600

Q6PC10

DR00330 = Q = 1350

Q10PC20

DR00120 = Q = 1500

Q8PC12

DR00225 = Q = 1400

Q7PC15

DR00126 = Q = 1250

Q9PC11

DR00320 = Q = 1450

Q7PC12

DR00330 = Q = 1500

Demand

11

12

13

21

22

23

24

31

32

33

34

35

41

42

43

44

45

46










1000

10002 06 4565 6522 5858455

095 3691 5272 5864019

005 06 5888 8412 5820524095 6012 8588 5853552

20002 06 9907 14153 5857317

095 5849 8357 5791562

005 06 11126 15894 5788794095 9415 13451 5787604

2000

10002 06 5942 11212 5830374

095 5187 9788 5873883

005 06 9085 17142 5769888095 8987 16958 5802988

20002 06 8823 16649 5769203

095 7251 13681 5793471

005 06 15542 29372 5755047095 13379 25245 5769029



1000

1020 04 117 249 5816602

09 126 269 5853555

50 04 228 486 588147309 294 562 5935652

2020 04 345 521 5938588

09 271 577 5824685

50 04 576 1012 581133809 617 1121 5899211

2000

1020 04 296 489 6129503

09 238 521 5817566

50 04 469 924 584003409 510 1026 5851926

2020 04 473 931 5912584

09 502 1006 5803912

50 04 756 1888 573972109 1194 2234 5809798







1 1198882


1000

1020 205 205 277 376 5968602

28 13 184 392 5809097

50 205 205 485 818 591679528 13 414 795 5757822

2020 205 205 337 505 604557

28 13 443 729 5880764

50 205 205 901 1916 598957128 13 854 1541 5835304

2000

1020 205 205 645 908 5796706

28 13 620 868 5749695

50 205 205 1153 1922 601022228 13 986 1644 5834792

2020 205 205 834 1557 5945546

28 13 991 1653 5796291

50 205 205 2264 3774 605729628 13 1884 3140 5740339



100010 20 197 295 6207676

50 389 581 6263544

20 20 391 583 621080650 874 1304 6164093

200010 20 353 521 6177516

50 727 1212 6140259

20 20 713 1005 614276150 1445 2409 6096037




1 otherwise





1 otherwise






1 otherwise













Objective function

3-4-5-6 5748095a1b 57356461 57509621 603791226-6-6-6 64448212 64242681 65047513 72552374

3-10-10-60 97241222 95445731 98021153 1022415646-6-6-6-6 76046012 75865551 76155213 823544446-8-8-10-30 120122532 115325211 124227343 1345758748-10-20-20-60 168544232 163724161 171141253 181127944

Execution time

3-4-5-6 30692 1891 2201 20216-6-6-6 32642 4181 4241 3901

3-10-10-60 62144 7453 6582 61316-6-6-6-6 53313 6102 5131 48416-8-8-10-30 78264 11253 9212 85218-10-20-20-60 99784 18743 13852 10271

Convergence time

3-4-5-6 15544 751 1893 14426-6-6-6 19662 1861 2271 2261

3-10-10-60 41533 2871 3022 31226-6-6-6-6 30293 2361 2652 27226-8-8-10-30 55743 3521 4072 42528-10-20-20-60 63254 3981 4422 4863





Stage 111 0 0 0 3412 5 646 17 013 1615 154 6 15

Stage 2

21 379 392 190 237 32722 38 0 8 261 45923 0 10 10 0 224 0 0 48 0 0

Stage 3

31 6 28 194 163 1 532 0 9 114 13 146 10033 0 0 0 27 168 5634 126 61 1 154 0 13735 291 366 0 8 0 72

Demand 400 450 300 350 300 350



Stage 111 29 142 72 15812 120 43 150 2413 576 845 194 128

Stage 2

21 12 0 19 177 115 148 90 16422 9 6 8 189 139 51 183 421

23 0 0 0 104 78 130 74 12

24 0 0 0 136 30 15 91 37

Stage 3

31 1 2 1 3 1 0 0 67 95 130 69 126 9532 2 4 0 2 0 3 0 41 54 111 106 27 533 0 0 1 0 1 0 0 11 2 74 73 81 9534 2 0 3 1 1 2 0 36 45 23 148 127 4335 2 1 5 0 1 1 5 162 165 131 24 92 25

Stage 4

41 2 0 2 0 4 0 0 0 1 1 0 242 0 2 0 0 1 0 0 0 1 0 0 043 2 0 0 0 0 0 2 0 0 0 1 144 1 0 0 0 0 1 0 0 0 0 0 145 0 3 0 1 2 0 0 2 1 0 0 046 3 1 0 1 2 0 0 2 0 0 0 1









Stage 111 227 24 48 7312 17 47 0 6513 900 738 84 37

Stage 2

21 7 3 3 133 156 180 239 38322 4 2 23 172 121 144 234 9623 2 4 1 45 0 66 27 024 2 1 0 3 0 73 33 71

Stage 3

31 5 0 1 2 2 1 4 0 4 129 11 134 6432 3 2 0 2 0 2 1 4 3 100 53 57 4933 1 0 1 0 1 0 0 0 81 75 50 139 10734 0 1 3 0 0 4 0 80 50 49 174 36 12535 1 5 0 1 3 1 1 180 172 64 27 0 77

Stage 4

41 1 1 1 0 0 2 1 1 1 0 1 042 0 1 0 0 0 1 0 0 1 0 0 043 1 0 2 0 0 0 3 0 0 2 0 144 2 0 0 0 0 1 0 0 0 0 1 045 3 0 2 3 0 0 1 3 0 1 0 046 1 0 2 1 0 1 0 0 1 0 0 1





Acknowledgments



References












































































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in





reverse logistics





hellip








ANOVA


reverse logistics


ObjectiveMinimize

Constraints

lowast

lowast

lowast

lowast

lowast

lowast

lowast

lowast

lowast

lowast

lowast

lowast

lowastlowast

lowast

lowast



+


JS

rs = s + 1 j = 1

sum sum


J

j = 1

sum )

Scheff e method








Parameters







Min119862119875(119904119894)


Max119862119875(119904119894)



119875119862(119904119894)


119875119876(119904119894)



119879119878((119904119894)(119904+1119895))


119875119862(119904119894)



stage 119904119879119862((119904119894)(119904+1119895))


119879119878((119904119894)(119904+1119895))


119879

119875119862(119904119894)


119879



119879119862((119904119894)(119904+1119895))


119879

119879119878((119904119894)(119904+1119895))


119878119866119875119862119904119894


119878119866119879119862((119904119894)(119904+1119895))


119878119866119875119876119904119894


119878119866119879119878((119904119894)(119904+1119895))


119865119877(119904119894)


119879119865119877((119904119894)(119904+1119895))


119908119875119862

119908119879119862

119908119879119878

119908119875119876



Decision Variables

119880119899



119877119880119899








119904new119894


Vnew119894







119891119875119862

=

119873

sum

119899=1

119878

sum

119904=1

119868

sum

119894=1

119879

119875119862(119904119894)

times [

[

100381710038171003817100381710038171003817100381710038171003817

119880119899

((119904119894)(119904+11))

1 minus 119865119877(119904119894)

100381710038171003817100381710038171003817100381710038171003817

+

119869

sum

119895=2

10038171003817100381710038171003817119880119899

((119904minus1119895)(119904119894))(1minus119879119865119877

((119904minus1119895)(119904119894)))10038171003817100381710038171003817]

]

(1)


119891119879119862 =

119873

sum

119899=1

119878

sum

119904=1

119868

sum

119894=1

119869

sum

119895=1

119879

119879119862(119904119894)(119904+1119895)

119880119899

((119904119894)(119904+1119895)) (2)



119891119875119876

=

119873

sum

119899=1

119878

sum

119904=1

119868

sum

119894=1

119879

119875119876(119904119894)

times [

[

100381710038171003817100381710038171003817100381710038171003817

119880119899

((119904119894)(119904+11))

1 minus 119865119877(119904119894)

100381710038171003817100381710038171003817100381710038171003817

+

119869

sum

119895=2

10038171003817100381710038171003817119880119899

((119904minus1119895)(119904119894))(1minus119879119865119877

((119904minus1119895)(119904119894)))10038171003817100381710038171003817]

]

(3)


119891119879119878 =

119873

sum

119899=1

119878

sum

119904=1

119868

sum

119894=1

119869

sum

119895=1

119879

119879119878(119904119894)(119904+1119895)

119880119899

((119904119894)(119904+1119895)) (4)


119903119875119862 =

119873

sum

119899=2

119878minus1

sum

119904=1

119868

sum

119894=1

119879

119875119862(119904119894)

119878

sum

119903119904=119904+1

119869

sum

119895=1

119877119880119899

((119903119904119895)(119904119894)) (5)


119903119879119862 =

119873

sum

119899=2

119878

sum

119904=1

119868

sum

119894=1

119879

119879119862((119903119904119895)(119904119894))

119878

sum

119903119904=119904+1

119869

sum

119895=1

119877119880119899

((119903119904119895)(119904119894)) (6)


119903119875119876 =

119873

sum

119899=2

119878minus1

sum

119904=1

119868

sum

119894=1

119879

119875119876(119904119894)

119878

sum

119903119904=119904+1

119869

sum

119895=1

119877119880119899

((119903119904119895)(119904119894)) (7)


119903119879119878 =

119873

sum

119899=2

119878

sum

119904=1

119868

sum

119894=1

119879

119879119878((119903119904119895)(119904119894))

119878

sum

119903119904=119904+1

119869

sum

119895=1

119877119880119899

((119903119904119895)(119904119894)) (8)


Minimize 119885 = 119908119875119862

(119891119875119862 + 119903119875119862)

+ 119908119879119862

(119891119879119862 + 119903119879119862)

minus 119908119875119876

(119891119875119876 + 119903119875119876)

+ 119908119879119878

(119891119879119878 + 119903119879119878)

st

(9)


Min119862119875(119904119894)

le

119869

sum

119895=1

10038171003817100381710038171003817119880119899

((119904minus1119895)(119904119894))(1 minus 119879119865119877

((119904minus1119895)(119904119894)))10038171003817100381710038171003817

+

119878

sum

119903119904=119904+1

119869

sum

119895=1

119877119880119899minus1

((119903119904119895)(119904119894))le Max119862119875

(119904119894)

for 119899 = 1 2 3 119873

119904 = 2 3 119878 119894 = 1 2 3 119868

(10)

Min119862119875(119904119894)

le

119869

sum

119895=1

10038171003817100381710038171003817100381710038171003817100381710038171003817

119880119899

((119904119894)(119904+1119895))

1 minus 119865119877(119904119894)

10038171003817100381710038171003817100381710038171003817100381710038171003817

+

119878

sum

119903119904=119904+1

119869

sum

119895=1

119877119880119899minus1

((119903119904119895)(119904119894))le Max119862119875

(119904119894)

for 119899 = 1 2 3 119873 119904 = 1

119894 = 1 2 3 119868

(11)


119869

sum

119895=1

100381710038171003817100381710038171003817119880119899

((119904minus1119895)(119904119894))(1 minus 119879119865119877

((119904minus1119895)(119904119894)))100381710038171003817100381710038171003817

+

119878

sum

119903119904=119904+1

119869

sum

119895=1

119877119880119899minus1

((119903119904119895)(119904119894))

=

119869

sum

119895=1

119880119899

((119904+1119895)(119904119894))+

119904minus1

sum

119903119904=1

119869

sum

119895=1

119877119880119899

((119904119894)(119903119904119895))

for 119899 = 1 2 3 119873

119904 = 1 2 3 119878 119894 = 1 2 3 119868

(12)

119904

sum

119903119904=1

119869

sum

119895=1

119877119880119899

((119903119904119895)(119904119894))

=

10038171003817100381710038171003817100381710038171003817100381710038171003817

(

119869

sum

119895=1

10038171003817100381710038171003817119880119899

((119904minus1119895)(119904119894))(1 minus 119879119865119877

((119904minus1119895)(119904119894)))10038171003817100381710038171003817

+

119878

sum

119903119904=119904+1

119869

sum

119895=1

119877119880119899minus1

((119903119904119895)(119904119894)))119865119877(119904119894)

10038171003817100381710038171003817100381710038171003817100381710038171003817

for 119899 = 1 2 3 119873

119904 = 1 2 3 119878 119894 = 1 2 3 119868

(13)



119869

sum

119895=1

10038171003817100381710038171003817119880119899

((119904minus1119895)(119904119894))(1 minus 119879119865119877

((119904minus1119895)(119904119894)))10038171003817100381710038171003817

minus

119904minus1

sum

119903119904=1

119869

sum

119895=1

119877119880119899

((119904119894)(119904minus119903119904119895))= 119862119863

119899

(119904119894)

for 119899 = 1 2 3 119873 119904 = 119878

119894 = 1 2 3 119868

(14)


0 le 119908119875119862

119908119879119862

119908119879119878 119908119875119876

le 1

119908119875119862

+ 119908119879119862

+ 119908119879119878

+ 119908119875119876

= 1

(15)


119877119880119899

((119903119904119895)(119904119894))= 0 for 119899 le 0 119904 = 1 2 3 4 119878 minus 1

119903119904 = 119904 + 1 119878 119894 = 1 2 3 119868

119895 = 1 2 3 119869

(16)


119880119899

((119904119894)(119904+1119895))ge 0 and 119880

119899

((119904119894)(119904+1119895))isin Integer

for 119899 = 1 2 3 119873 119904 = 1 2 3 119878

119894 = 1 2 3 119868 119895 = 1 2 3 119869

(17)

119877119880119899

((119903119904119895)(119904119894))ge 0 and 119880

119899

((119904119894)(119904+1119895))isin Integer

for 119904 = 1 2 3 119878 119903119904 = 119878 + 1 119878

119899 = 1 2 3 119873 119894 = 1 2 3 119868 119895 = 1 2 3 119869

(18)


119879

119875119862(119904119894)

=119875119862(119904119894)

minus 119875119862(119904119894)

119878119866119875119862(119904119894)

10+ 50 for 119904 = 1 2 3 119878

119894 = 1 2 3 119868

119879

119879119862((119904119894)(119904+1119895))

=

119879119862((119904119894)(119904+1119895))

minus 119879119862((119904119894)(119904+1119895))

119878119866119879119862((119904119894)(119904+1119895))

10+ 50

for 119904 = 1 2 3 119878 119894 = 1 2 3 119868

119895 = 1 2 3 119869

119879

119875119876(119904119894)

=119875119876(119904119894)

minus 119875119876(119904119894)

119878119866119875119876(119904119894)10

+ 50 for 119904 = 1 2 3 119878

119894 = 1 2 3 119868

119879

119879119878((119904119894)(119904+1119895))

=

119879119878((119904119894)(119904+1119895))

minus 119879119878((119904119894)(119904+1119895))

119878119866119879119878((119904119894)(119904+1119895))

10+ 50

for 119904 = 1 2 3 119878 119894 = 1 2 3 119868

119895 = 1 2 3 119869

(19)


























Mutation point

After mutation






Particle 1 2 3 4 5 6 117 118 119Line

Volume 0 0 42 9 0 0 0 2 0



















Vnew119894

= 119908Vold119894

+ 1198881times rand () times (119904

lowast

119894minus 119904

old119894

) + 1198882


old119894

)

119904new119894

= 119904old119894

+ Vnew119894

(20)


Vnew119894

= Vold119894

+ 1198881times rand () times (119904

lowast

119894minus 119904

old119894

) + 1198882


old119894

)

119904new119894

= 119904old119894

+ Vnew119894

if V119894gt Vmax V

119894= Vmax


119894= minusVmax

(21)



Vnew119894

= 119896 times ⟨Vold119894

+ 1198881times rand () times (119904

lowast

119894minus 119904

old119894

)


119894minus 119904

old119894

)⟩

119904new119894

= 119904old119894

+ Vnew119894

119870 =2


120601 = 1198881+ 1198882 120601 gt 4

(22)








Siliconmaterial



test Customer

Manufacturing unit


Reverse route





1= 205 119888

2= 205 pro-

posed byClerc [62] 1198881= 28 119888



1= 28 119888

2= 13 velocity = 50







1

119899119894

+1

119899119895

)



1

119899119894

+1

119899119895

))

(23)


Table1Datao

ftranspo


Transportatio

nlin

e11ndash21

11ndash22

11ndash23

11ndash24

12ndash21

12ndash22

12ndash23

12ndash24

13ndash21

13ndash22

13ndash23

13ndash24

21ndash31

21ndash32

21ndash33

21ndash34

Transportatio

ndefectrate

001

003

002

002

002

001

004

005

004

003

005

001

003

002

001

004

Transportatio

ncost

56

103

75

64

43

510

45

34

Transportatio

nlin

e21ndash35

22ndash31

22ndash32

22ndash33

22ndash34

22ndash35

23ndash31

23ndash32

23ndash33

23ndash34

23ndash35

24ndash

31

24ndash

32

24ndash

33

24ndash

34

24ndash

35

Transportatio

ndefectrate

002

002

003

004

002

005

003

004

002

003

001

003

004

002

001

002

Transportatio

ncost

54

56

22

58

54

65

65

45

Transportatio

nlin

e31ndash41

31ndash42

31ndash43

31ndash44

31ndash45

31ndash46

32ndash41

32ndash42

32ndash43

32ndash44

32ndash45

32ndash46

33ndash41

33ndash42

33ndash43

33ndash44

Transportatio

ndefectrate

003

002

001

002

001

003

002

003

001

004

002

003

002

003

004

005

Transportatio

ncost

45

46

46

46

35

45

56

48

Transportatio

nlin

e33ndash45

33ndash46

34ndash

41

34ndash

42

34ndash

43

34ndash

44

34ndash

45

34ndash

46

35ndash41

35ndash42

35ndash43

35ndash44

35ndash45

35ndash46

Transportatio

ndefectrate

002

001

002

003

005

004

002

003

003

002

003

004

005

003

Transportatio

ncost

65

44

65

56

25

65

42


Stage 4

Stage 3

Stage 2

Stage 1


Q7PC20

30 = Q = 1700

Q9PC15

10 = Q = 1600

Q10PC12

20 = Q = 1800

Q9PC16

DR00220 = Q = 1550

Q7PC13

DR00310 = Q = 1700

Q8PC15

DR00215 = Q = 1650

Q9PC20

DR00130 = Q = 1700

Q7PC12

DR00220 = Q = 1700

Q6PC13

DR00330 = Q = 1600

Q8PC18

DR00125 = Q = 1350

Q7PC15

DR00230 = Q = 1500

Q8PC13

DR002150 = Q = 1600

Q6PC10

DR00330 = Q = 1350

Q10PC20

DR00120 = Q = 1500

Q8PC12

DR00225 = Q = 1400

Q7PC15

DR00126 = Q = 1250

Q9PC11

DR00320 = Q = 1450

Q7PC12

DR00330 = Q = 1500

Demand

11

12

13

21

22

23

24

31

32

33

34

35

41

42

43

44

45

46










1000

10002 06 4565 6522 5858455

095 3691 5272 5864019

005 06 5888 8412 5820524095 6012 8588 5853552

20002 06 9907 14153 5857317

095 5849 8357 5791562

005 06 11126 15894 5788794095 9415 13451 5787604

2000

10002 06 5942 11212 5830374

095 5187 9788 5873883

005 06 9085 17142 5769888095 8987 16958 5802988

20002 06 8823 16649 5769203

095 7251 13681 5793471

005 06 15542 29372 5755047095 13379 25245 5769029



1000

1020 04 117 249 5816602

09 126 269 5853555

50 04 228 486 588147309 294 562 5935652

2020 04 345 521 5938588

09 271 577 5824685

50 04 576 1012 581133809 617 1121 5899211

2000

1020 04 296 489 6129503

09 238 521 5817566

50 04 469 924 584003409 510 1026 5851926

2020 04 473 931 5912584

09 502 1006 5803912

50 04 756 1888 573972109 1194 2234 5809798







1 1198882


1000

1020 205 205 277 376 5968602

28 13 184 392 5809097

50 205 205 485 818 591679528 13 414 795 5757822

2020 205 205 337 505 604557

28 13 443 729 5880764

50 205 205 901 1916 598957128 13 854 1541 5835304

2000

1020 205 205 645 908 5796706

28 13 620 868 5749695

50 205 205 1153 1922 601022228 13 986 1644 5834792

2020 205 205 834 1557 5945546

28 13 991 1653 5796291

50 205 205 2264 3774 605729628 13 1884 3140 5740339



100010 20 197 295 6207676

50 389 581 6263544

20 20 391 583 621080650 874 1304 6164093

200010 20 353 521 6177516

50 727 1212 6140259

20 20 713 1005 614276150 1445 2409 6096037




1 otherwise





1 otherwise






1 otherwise













Objective function

3-4-5-6 5748095a1b 57356461 57509621 603791226-6-6-6 64448212 64242681 65047513 72552374

3-10-10-60 97241222 95445731 98021153 1022415646-6-6-6-6 76046012 75865551 76155213 823544446-8-8-10-30 120122532 115325211 124227343 1345758748-10-20-20-60 168544232 163724161 171141253 181127944

Execution time

3-4-5-6 30692 1891 2201 20216-6-6-6 32642 4181 4241 3901

3-10-10-60 62144 7453 6582 61316-6-6-6-6 53313 6102 5131 48416-8-8-10-30 78264 11253 9212 85218-10-20-20-60 99784 18743 13852 10271

Convergence time

3-4-5-6 15544 751 1893 14426-6-6-6 19662 1861 2271 2261

3-10-10-60 41533 2871 3022 31226-6-6-6-6 30293 2361 2652 27226-8-8-10-30 55743 3521 4072 42528-10-20-20-60 63254 3981 4422 4863





Stage 111 0 0 0 3412 5 646 17 013 1615 154 6 15

Stage 2

21 379 392 190 237 32722 38 0 8 261 45923 0 10 10 0 224 0 0 48 0 0

Stage 3

31 6 28 194 163 1 532 0 9 114 13 146 10033 0 0 0 27 168 5634 126 61 1 154 0 13735 291 366 0 8 0 72

Demand 400 450 300 350 300 350



Stage 111 29 142 72 15812 120 43 150 2413 576 845 194 128

Stage 2

21 12 0 19 177 115 148 90 16422 9 6 8 189 139 51 183 421

23 0 0 0 104 78 130 74 12

24 0 0 0 136 30 15 91 37

Stage 3

31 1 2 1 3 1 0 0 67 95 130 69 126 9532 2 4 0 2 0 3 0 41 54 111 106 27 533 0 0 1 0 1 0 0 11 2 74 73 81 9534 2 0 3 1 1 2 0 36 45 23 148 127 4335 2 1 5 0 1 1 5 162 165 131 24 92 25

Stage 4

41 2 0 2 0 4 0 0 0 1 1 0 242 0 2 0 0 1 0 0 0 1 0 0 043 2 0 0 0 0 0 2 0 0 0 1 144 1 0 0 0 0 1 0 0 0 0 0 145 0 3 0 1 2 0 0 2 1 0 0 046 3 1 0 1 2 0 0 2 0 0 0 1









Stage 111 227 24 48 7312 17 47 0 6513 900 738 84 37

Stage 2

21 7 3 3 133 156 180 239 38322 4 2 23 172 121 144 234 9623 2 4 1 45 0 66 27 024 2 1 0 3 0 73 33 71

Stage 3

31 5 0 1 2 2 1 4 0 4 129 11 134 6432 3 2 0 2 0 2 1 4 3 100 53 57 4933 1 0 1 0 1 0 0 0 81 75 50 139 10734 0 1 3 0 0 4 0 80 50 49 174 36 12535 1 5 0 1 3 1 1 180 172 64 27 0 77

Stage 4

41 1 1 1 0 0 2 1 1 1 0 1 042 0 1 0 0 0 1 0 0 1 0 0 043 1 0 2 0 0 0 3 0 0 2 0 144 2 0 0 0 0 1 0 0 0 0 1 045 3 0 2 3 0 0 1 3 0 1 0 046 1 0 2 1 0 1 0 0 1 0 0 1





Acknowledgments



References












































































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




119875119862(119904119894)


119875119876(119904119894)



119879119878((119904119894)(119904+1119895))


119875119862(119904119894)



stage 119904119879119862((119904119894)(119904+1119895))


119879119878((119904119894)(119904+1119895))


119879

119875119862(119904119894)


119879



119879119862((119904119894)(119904+1119895))


119879

119879119878((119904119894)(119904+1119895))


119878119866119875119862119904119894


119878119866119879119862((119904119894)(119904+1119895))


119878119866119875119876119904119894


119878119866119879119878((119904119894)(119904+1119895))


119865119877(119904119894)


119879119865119877((119904119894)(119904+1119895))


119908119875119862

119908119879119862

119908119879119878

119908119875119876



Decision Variables

119880119899



119877119880119899








119904new119894


Vnew119894







119891119875119862

=

119873

sum

119899=1

119878

sum

119904=1

119868

sum

119894=1

119879

119875119862(119904119894)

times [

[

100381710038171003817100381710038171003817100381710038171003817

119880119899

((119904119894)(119904+11))

1 minus 119865119877(119904119894)

100381710038171003817100381710038171003817100381710038171003817

+

119869

sum

119895=2

10038171003817100381710038171003817119880119899

((119904minus1119895)(119904119894))(1minus119879119865119877

((119904minus1119895)(119904119894)))10038171003817100381710038171003817]

]

(1)


119891119879119862 =

119873

sum

119899=1

119878

sum

119904=1

119868

sum

119894=1

119869

sum

119895=1

119879

119879119862(119904119894)(119904+1119895)

119880119899

((119904119894)(119904+1119895)) (2)



119891119875119876

=

119873

sum

119899=1

119878

sum

119904=1

119868

sum

119894=1

119879

119875119876(119904119894)

times [

[

100381710038171003817100381710038171003817100381710038171003817

119880119899

((119904119894)(119904+11))

1 minus 119865119877(119904119894)

100381710038171003817100381710038171003817100381710038171003817

+

119869

sum

119895=2

10038171003817100381710038171003817119880119899

((119904minus1119895)(119904119894))(1minus119879119865119877

((119904minus1119895)(119904119894)))10038171003817100381710038171003817]

]

(3)


119891119879119878 =

119873

sum

119899=1

119878

sum

119904=1

119868

sum

119894=1

119869

sum

119895=1

119879

119879119878(119904119894)(119904+1119895)

119880119899

((119904119894)(119904+1119895)) (4)


119903119875119862 =

119873

sum

119899=2

119878minus1

sum

119904=1

119868

sum

119894=1

119879

119875119862(119904119894)

119878

sum

119903119904=119904+1

119869

sum

119895=1

119877119880119899

((119903119904119895)(119904119894)) (5)


119903119879119862 =

119873

sum

119899=2

119878

sum

119904=1

119868

sum

119894=1

119879

119879119862((119903119904119895)(119904119894))

119878

sum

119903119904=119904+1

119869

sum

119895=1

119877119880119899

((119903119904119895)(119904119894)) (6)


119903119875119876 =

119873

sum

119899=2

119878minus1

sum

119904=1

119868

sum

119894=1

119879

119875119876(119904119894)

119878

sum

119903119904=119904+1

119869

sum

119895=1

119877119880119899

((119903119904119895)(119904119894)) (7)


119903119879119878 =

119873

sum

119899=2

119878

sum

119904=1

119868

sum

119894=1

119879

119879119878((119903119904119895)(119904119894))

119878

sum

119903119904=119904+1

119869

sum

119895=1

119877119880119899

((119903119904119895)(119904119894)) (8)


Minimize 119885 = 119908119875119862

(119891119875119862 + 119903119875119862)

+ 119908119879119862

(119891119879119862 + 119903119879119862)

minus 119908119875119876

(119891119875119876 + 119903119875119876)

+ 119908119879119878

(119891119879119878 + 119903119879119878)

st

(9)


Min119862119875(119904119894)

le

119869

sum

119895=1

10038171003817100381710038171003817119880119899

((119904minus1119895)(119904119894))(1 minus 119879119865119877

((119904minus1119895)(119904119894)))10038171003817100381710038171003817

+

119878

sum

119903119904=119904+1

119869

sum

119895=1

119877119880119899minus1

((119903119904119895)(119904119894))le Max119862119875

(119904119894)

for 119899 = 1 2 3 119873

119904 = 2 3 119878 119894 = 1 2 3 119868

(10)

Min119862119875(119904119894)

le

119869

sum

119895=1

10038171003817100381710038171003817100381710038171003817100381710038171003817

119880119899

((119904119894)(119904+1119895))

1 minus 119865119877(119904119894)

10038171003817100381710038171003817100381710038171003817100381710038171003817

+

119878

sum

119903119904=119904+1

119869

sum

119895=1

119877119880119899minus1

((119903119904119895)(119904119894))le Max119862119875

(119904119894)

for 119899 = 1 2 3 119873 119904 = 1

119894 = 1 2 3 119868

(11)


119869

sum

119895=1

100381710038171003817100381710038171003817119880119899

((119904minus1119895)(119904119894))(1 minus 119879119865119877

((119904minus1119895)(119904119894)))100381710038171003817100381710038171003817

+

119878

sum

119903119904=119904+1

119869

sum

119895=1

119877119880119899minus1

((119903119904119895)(119904119894))

=

119869

sum

119895=1

119880119899

((119904+1119895)(119904119894))+

119904minus1

sum

119903119904=1

119869

sum

119895=1

119877119880119899

((119904119894)(119903119904119895))

for 119899 = 1 2 3 119873

119904 = 1 2 3 119878 119894 = 1 2 3 119868

(12)

119904

sum

119903119904=1

119869

sum

119895=1

119877119880119899

((119903119904119895)(119904119894))

=

10038171003817100381710038171003817100381710038171003817100381710038171003817

(

119869

sum

119895=1

10038171003817100381710038171003817119880119899

((119904minus1119895)(119904119894))(1 minus 119879119865119877

((119904minus1119895)(119904119894)))10038171003817100381710038171003817

+

119878

sum

119903119904=119904+1

119869

sum

119895=1

119877119880119899minus1

((119903119904119895)(119904119894)))119865119877(119904119894)

10038171003817100381710038171003817100381710038171003817100381710038171003817

for 119899 = 1 2 3 119873

119904 = 1 2 3 119878 119894 = 1 2 3 119868

(13)



119869

sum

119895=1

10038171003817100381710038171003817119880119899

((119904minus1119895)(119904119894))(1 minus 119879119865119877

((119904minus1119895)(119904119894)))10038171003817100381710038171003817

minus

119904minus1

sum

119903119904=1

119869

sum

119895=1

119877119880119899

((119904119894)(119904minus119903119904119895))= 119862119863

119899

(119904119894)

for 119899 = 1 2 3 119873 119904 = 119878

119894 = 1 2 3 119868

(14)


0 le 119908119875119862

119908119879119862

119908119879119878 119908119875119876

le 1

119908119875119862

+ 119908119879119862

+ 119908119879119878

+ 119908119875119876

= 1

(15)


119877119880119899

((119903119904119895)(119904119894))= 0 for 119899 le 0 119904 = 1 2 3 4 119878 minus 1

119903119904 = 119904 + 1 119878 119894 = 1 2 3 119868

119895 = 1 2 3 119869

(16)


119880119899

((119904119894)(119904+1119895))ge 0 and 119880

119899

((119904119894)(119904+1119895))isin Integer

for 119899 = 1 2 3 119873 119904 = 1 2 3 119878

119894 = 1 2 3 119868 119895 = 1 2 3 119869

(17)

119877119880119899

((119903119904119895)(119904119894))ge 0 and 119880

119899

((119904119894)(119904+1119895))isin Integer

for 119904 = 1 2 3 119878 119903119904 = 119878 + 1 119878

119899 = 1 2 3 119873 119894 = 1 2 3 119868 119895 = 1 2 3 119869

(18)


119879

119875119862(119904119894)

=119875119862(119904119894)

minus 119875119862(119904119894)

119878119866119875119862(119904119894)

10+ 50 for 119904 = 1 2 3 119878

119894 = 1 2 3 119868

119879

119879119862((119904119894)(119904+1119895))

=

119879119862((119904119894)(119904+1119895))

minus 119879119862((119904119894)(119904+1119895))

119878119866119879119862((119904119894)(119904+1119895))

10+ 50

for 119904 = 1 2 3 119878 119894 = 1 2 3 119868

119895 = 1 2 3 119869

119879

119875119876(119904119894)

=119875119876(119904119894)

minus 119875119876(119904119894)

119878119866119875119876(119904119894)10

+ 50 for 119904 = 1 2 3 119878

119894 = 1 2 3 119868

119879

119879119878((119904119894)(119904+1119895))

=

119879119878((119904119894)(119904+1119895))

minus 119879119878((119904119894)(119904+1119895))

119878119866119879119878((119904119894)(119904+1119895))

10+ 50

for 119904 = 1 2 3 119878 119894 = 1 2 3 119868

119895 = 1 2 3 119869

(19)


























Mutation point

After mutation






Particle 1 2 3 4 5 6 117 118 119Line

Volume 0 0 42 9 0 0 0 2 0



















Vnew119894

= 119908Vold119894

+ 1198881times rand () times (119904

lowast

119894minus 119904

old119894

) + 1198882


old119894

)

119904new119894

= 119904old119894

+ Vnew119894

(20)


Vnew119894

= Vold119894

+ 1198881times rand () times (119904

lowast

119894minus 119904

old119894

) + 1198882


old119894

)

119904new119894

= 119904old119894

+ Vnew119894

if V119894gt Vmax V

119894= Vmax


119894= minusVmax

(21)



Vnew119894

= 119896 times ⟨Vold119894

+ 1198881times rand () times (119904

lowast

119894minus 119904

old119894

)


119894minus 119904

old119894

)⟩

119904new119894

= 119904old119894

+ Vnew119894

119870 =2


120601 = 1198881+ 1198882 120601 gt 4

(22)








Siliconmaterial



test Customer

Manufacturing unit


Reverse route





1= 205 119888

2= 205 pro-

posed byClerc [62] 1198881= 28 119888



1= 28 119888

2= 13 velocity = 50







1

119899119894

+1

119899119895

)



1

119899119894

+1

119899119895

))

(23)


Table1Datao

ftranspo


Transportatio

nlin

e11ndash21

11ndash22

11ndash23

11ndash24

12ndash21

12ndash22

12ndash23

12ndash24

13ndash21

13ndash22

13ndash23

13ndash24

21ndash31

21ndash32

21ndash33

21ndash34

Transportatio

ndefectrate

001

003

002

002

002

001

004

005

004

003

005

001

003

002

001

004

Transportatio

ncost

56

103

75

64

43

510

45

34

Transportatio

nlin

e21ndash35

22ndash31

22ndash32

22ndash33

22ndash34

22ndash35

23ndash31

23ndash32

23ndash33

23ndash34

23ndash35

24ndash

31

24ndash

32

24ndash

33

24ndash

34

24ndash

35

Transportatio

ndefectrate

002

002

003

004

002

005

003

004

002

003

001

003

004

002

001

002

Transportatio

ncost

54

56

22

58

54

65

65

45

Transportatio

nlin

e31ndash41

31ndash42

31ndash43

31ndash44

31ndash45

31ndash46

32ndash41

32ndash42

32ndash43

32ndash44

32ndash45

32ndash46

33ndash41

33ndash42

33ndash43

33ndash44

Transportatio

ndefectrate

003

002

001

002

001

003

002

003

001

004

002

003

002

003

004

005

Transportatio

ncost

45

46

46

46

35

45

56

48

Transportatio

nlin

e33ndash45

33ndash46

34ndash

41

34ndash

42

34ndash

43

34ndash

44

34ndash

45

34ndash

46

35ndash41

35ndash42

35ndash43

35ndash44

35ndash45

35ndash46

Transportatio

ndefectrate

002

001

002

003

005

004

002

003

003

002

003

004

005

003

Transportatio

ncost

65

44

65

56

25

65

42


Stage 4

Stage 3

Stage 2

Stage 1


Q7PC20

30 = Q = 1700

Q9PC15

10 = Q = 1600

Q10PC12

20 = Q = 1800

Q9PC16

DR00220 = Q = 1550

Q7PC13

DR00310 = Q = 1700

Q8PC15

DR00215 = Q = 1650

Q9PC20

DR00130 = Q = 1700

Q7PC12

DR00220 = Q = 1700

Q6PC13

DR00330 = Q = 1600

Q8PC18

DR00125 = Q = 1350

Q7PC15

DR00230 = Q = 1500

Q8PC13

DR002150 = Q = 1600

Q6PC10

DR00330 = Q = 1350

Q10PC20

DR00120 = Q = 1500

Q8PC12

DR00225 = Q = 1400

Q7PC15

DR00126 = Q = 1250

Q9PC11

DR00320 = Q = 1450

Q7PC12

DR00330 = Q = 1500

Demand

11

12

13

21

22

23

24

31

32

33

34

35

41

42

43

44

45

46










1000

10002 06 4565 6522 5858455

095 3691 5272 5864019

005 06 5888 8412 5820524095 6012 8588 5853552

20002 06 9907 14153 5857317

095 5849 8357 5791562

005 06 11126 15894 5788794095 9415 13451 5787604

2000

10002 06 5942 11212 5830374

095 5187 9788 5873883

005 06 9085 17142 5769888095 8987 16958 5802988

20002 06 8823 16649 5769203

095 7251 13681 5793471

005 06 15542 29372 5755047095 13379 25245 5769029



1000

1020 04 117 249 5816602

09 126 269 5853555

50 04 228 486 588147309 294 562 5935652

2020 04 345 521 5938588

09 271 577 5824685

50 04 576 1012 581133809 617 1121 5899211

2000

1020 04 296 489 6129503

09 238 521 5817566

50 04 469 924 584003409 510 1026 5851926

2020 04 473 931 5912584

09 502 1006 5803912

50 04 756 1888 573972109 1194 2234 5809798







1 1198882


1000

1020 205 205 277 376 5968602

28 13 184 392 5809097

50 205 205 485 818 591679528 13 414 795 5757822

2020 205 205 337 505 604557

28 13 443 729 5880764

50 205 205 901 1916 598957128 13 854 1541 5835304

2000

1020 205 205 645 908 5796706

28 13 620 868 5749695

50 205 205 1153 1922 601022228 13 986 1644 5834792

2020 205 205 834 1557 5945546

28 13 991 1653 5796291

50 205 205 2264 3774 605729628 13 1884 3140 5740339



100010 20 197 295 6207676

50 389 581 6263544

20 20 391 583 621080650 874 1304 6164093

200010 20 353 521 6177516

50 727 1212 6140259

20 20 713 1005 614276150 1445 2409 6096037




1 otherwise





1 otherwise






1 otherwise













Objective function

3-4-5-6 5748095a1b 57356461 57509621 603791226-6-6-6 64448212 64242681 65047513 72552374

3-10-10-60 97241222 95445731 98021153 1022415646-6-6-6-6 76046012 75865551 76155213 823544446-8-8-10-30 120122532 115325211 124227343 1345758748-10-20-20-60 168544232 163724161 171141253 181127944

Execution time

3-4-5-6 30692 1891 2201 20216-6-6-6 32642 4181 4241 3901

3-10-10-60 62144 7453 6582 61316-6-6-6-6 53313 6102 5131 48416-8-8-10-30 78264 11253 9212 85218-10-20-20-60 99784 18743 13852 10271

Convergence time

3-4-5-6 15544 751 1893 14426-6-6-6 19662 1861 2271 2261

3-10-10-60 41533 2871 3022 31226-6-6-6-6 30293 2361 2652 27226-8-8-10-30 55743 3521 4072 42528-10-20-20-60 63254 3981 4422 4863





Stage 111 0 0 0 3412 5 646 17 013 1615 154 6 15

Stage 2

21 379 392 190 237 32722 38 0 8 261 45923 0 10 10 0 224 0 0 48 0 0

Stage 3

31 6 28 194 163 1 532 0 9 114 13 146 10033 0 0 0 27 168 5634 126 61 1 154 0 13735 291 366 0 8 0 72

Demand 400 450 300 350 300 350



Stage 111 29 142 72 15812 120 43 150 2413 576 845 194 128

Stage 2

21 12 0 19 177 115 148 90 16422 9 6 8 189 139 51 183 421

23 0 0 0 104 78 130 74 12

24 0 0 0 136 30 15 91 37

Stage 3

31 1 2 1 3 1 0 0 67 95 130 69 126 9532 2 4 0 2 0 3 0 41 54 111 106 27 533 0 0 1 0 1 0 0 11 2 74 73 81 9534 2 0 3 1 1 2 0 36 45 23 148 127 4335 2 1 5 0 1 1 5 162 165 131 24 92 25

Stage 4

41 2 0 2 0 4 0 0 0 1 1 0 242 0 2 0 0 1 0 0 0 1 0 0 043 2 0 0 0 0 0 2 0 0 0 1 144 1 0 0 0 0 1 0 0 0 0 0 145 0 3 0 1 2 0 0 2 1 0 0 046 3 1 0 1 2 0 0 2 0 0 0 1









Stage 111 227 24 48 7312 17 47 0 6513 900 738 84 37

Stage 2

21 7 3 3 133 156 180 239 38322 4 2 23 172 121 144 234 9623 2 4 1 45 0 66 27 024 2 1 0 3 0 73 33 71

Stage 3

31 5 0 1 2 2 1 4 0 4 129 11 134 6432 3 2 0 2 0 2 1 4 3 100 53 57 4933 1 0 1 0 1 0 0 0 81 75 50 139 10734 0 1 3 0 0 4 0 80 50 49 174 36 12535 1 5 0 1 3 1 1 180 172 64 27 0 77

Stage 4

41 1 1 1 0 0 2 1 1 1 0 1 042 0 1 0 0 0 1 0 0 1 0 0 043 1 0 2 0 0 0 3 0 0 2 0 144 2 0 0 0 0 1 0 0 0 0 1 045 3 0 2 3 0 0 1 3 0 1 0 046 1 0 2 1 0 1 0 0 1 0 0 1





Acknowledgments



References












































































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in





119891119875119876

=

119873

sum

119899=1

119878

sum

119904=1

119868

sum

119894=1

119879

119875119876(119904119894)

times [

[

100381710038171003817100381710038171003817100381710038171003817

119880119899

((119904119894)(119904+11))

1 minus 119865119877(119904119894)

100381710038171003817100381710038171003817100381710038171003817

+

119869

sum

119895=2

10038171003817100381710038171003817119880119899

((119904minus1119895)(119904119894))(1minus119879119865119877

((119904minus1119895)(119904119894)))10038171003817100381710038171003817]

]

(3)


119891119879119878 =

119873

sum

119899=1

119878

sum

119904=1

119868

sum

119894=1

119869

sum

119895=1

119879

119879119878(119904119894)(119904+1119895)

119880119899

((119904119894)(119904+1119895)) (4)


119903119875119862 =

119873

sum

119899=2

119878minus1

sum

119904=1

119868

sum

119894=1

119879

119875119862(119904119894)

119878

sum

119903119904=119904+1

119869

sum

119895=1

119877119880119899

((119903119904119895)(119904119894)) (5)


119903119879119862 =

119873

sum

119899=2

119878

sum

119904=1

119868

sum

119894=1

119879

119879119862((119903119904119895)(119904119894))

119878

sum

119903119904=119904+1

119869

sum

119895=1

119877119880119899

((119903119904119895)(119904119894)) (6)


119903119875119876 =

119873

sum

119899=2

119878minus1

sum

119904=1

119868

sum

119894=1

119879

119875119876(119904119894)

119878

sum

119903119904=119904+1

119869

sum

119895=1

119877119880119899

((119903119904119895)(119904119894)) (7)


119903119879119878 =

119873

sum

119899=2

119878

sum

119904=1

119868

sum

119894=1

119879

119879119878((119903119904119895)(119904119894))

119878

sum

119903119904=119904+1

119869

sum

119895=1

119877119880119899

((119903119904119895)(119904119894)) (8)


Minimize 119885 = 119908119875119862

(119891119875119862 + 119903119875119862)

+ 119908119879119862

(119891119879119862 + 119903119879119862)

minus 119908119875119876

(119891119875119876 + 119903119875119876)

+ 119908119879119878

(119891119879119878 + 119903119879119878)

st

(9)


Min119862119875(119904119894)

le

119869

sum

119895=1

10038171003817100381710038171003817119880119899

((119904minus1119895)(119904119894))(1 minus 119879119865119877

((119904minus1119895)(119904119894)))10038171003817100381710038171003817

+

119878

sum

119903119904=119904+1

119869

sum

119895=1

119877119880119899minus1

((119903119904119895)(119904119894))le Max119862119875

(119904119894)

for 119899 = 1 2 3 119873

119904 = 2 3 119878 119894 = 1 2 3 119868

(10)

Min119862119875(119904119894)

le

119869

sum

119895=1

10038171003817100381710038171003817100381710038171003817100381710038171003817

119880119899

((119904119894)(119904+1119895))

1 minus 119865119877(119904119894)

10038171003817100381710038171003817100381710038171003817100381710038171003817

+

119878

sum

119903119904=119904+1

119869

sum

119895=1

119877119880119899minus1

((119903119904119895)(119904119894))le Max119862119875

(119904119894)

for 119899 = 1 2 3 119873 119904 = 1

119894 = 1 2 3 119868

(11)


119869

sum

119895=1

100381710038171003817100381710038171003817119880119899

((119904minus1119895)(119904119894))(1 minus 119879119865119877

((119904minus1119895)(119904119894)))100381710038171003817100381710038171003817

+

119878

sum

119903119904=119904+1

119869

sum

119895=1

119877119880119899minus1

((119903119904119895)(119904119894))

=

119869

sum

119895=1

119880119899

((119904+1119895)(119904119894))+

119904minus1

sum

119903119904=1

119869

sum

119895=1

119877119880119899

((119904119894)(119903119904119895))

for 119899 = 1 2 3 119873

119904 = 1 2 3 119878 119894 = 1 2 3 119868

(12)

119904

sum

119903119904=1

119869

sum

119895=1

119877119880119899

((119903119904119895)(119904119894))

=

10038171003817100381710038171003817100381710038171003817100381710038171003817

(

119869

sum

119895=1

10038171003817100381710038171003817119880119899

((119904minus1119895)(119904119894))(1 minus 119879119865119877

((119904minus1119895)(119904119894)))10038171003817100381710038171003817

+

119878

sum

119903119904=119904+1

119869

sum

119895=1

119877119880119899minus1

((119903119904119895)(119904119894)))119865119877(119904119894)

10038171003817100381710038171003817100381710038171003817100381710038171003817

for 119899 = 1 2 3 119873

119904 = 1 2 3 119878 119894 = 1 2 3 119868

(13)



119869

sum

119895=1

10038171003817100381710038171003817119880119899

((119904minus1119895)(119904119894))(1 minus 119879119865119877

((119904minus1119895)(119904119894)))10038171003817100381710038171003817

minus

119904minus1

sum

119903119904=1

119869

sum

119895=1

119877119880119899

((119904119894)(119904minus119903119904119895))= 119862119863

119899

(119904119894)

for 119899 = 1 2 3 119873 119904 = 119878

119894 = 1 2 3 119868

(14)


0 le 119908119875119862

119908119879119862

119908119879119878 119908119875119876

le 1

119908119875119862

+ 119908119879119862

+ 119908119879119878

+ 119908119875119876

= 1

(15)


119877119880119899

((119903119904119895)(119904119894))= 0 for 119899 le 0 119904 = 1 2 3 4 119878 minus 1

119903119904 = 119904 + 1 119878 119894 = 1 2 3 119868

119895 = 1 2 3 119869

(16)


119880119899

((119904119894)(119904+1119895))ge 0 and 119880

119899

((119904119894)(119904+1119895))isin Integer

for 119899 = 1 2 3 119873 119904 = 1 2 3 119878

119894 = 1 2 3 119868 119895 = 1 2 3 119869

(17)

119877119880119899

((119903119904119895)(119904119894))ge 0 and 119880

119899

((119904119894)(119904+1119895))isin Integer

for 119904 = 1 2 3 119878 119903119904 = 119878 + 1 119878

119899 = 1 2 3 119873 119894 = 1 2 3 119868 119895 = 1 2 3 119869

(18)


119879

119875119862(119904119894)

=119875119862(119904119894)

minus 119875119862(119904119894)

119878119866119875119862(119904119894)

10+ 50 for 119904 = 1 2 3 119878

119894 = 1 2 3 119868

119879

119879119862((119904119894)(119904+1119895))

=

119879119862((119904119894)(119904+1119895))

minus 119879119862((119904119894)(119904+1119895))

119878119866119879119862((119904119894)(119904+1119895))

10+ 50

for 119904 = 1 2 3 119878 119894 = 1 2 3 119868

119895 = 1 2 3 119869

119879

119875119876(119904119894)

=119875119876(119904119894)

minus 119875119876(119904119894)

119878119866119875119876(119904119894)10

+ 50 for 119904 = 1 2 3 119878

119894 = 1 2 3 119868

119879

119879119878((119904119894)(119904+1119895))

=

119879119878((119904119894)(119904+1119895))

minus 119879119878((119904119894)(119904+1119895))

119878119866119879119878((119904119894)(119904+1119895))

10+ 50

for 119904 = 1 2 3 119878 119894 = 1 2 3 119868

119895 = 1 2 3 119869

(19)


























Mutation point

After mutation






Particle 1 2 3 4 5 6 117 118 119Line

Volume 0 0 42 9 0 0 0 2 0



















Vnew119894

= 119908Vold119894

+ 1198881times rand () times (119904

lowast

119894minus 119904

old119894

) + 1198882


old119894

)

119904new119894

= 119904old119894

+ Vnew119894

(20)


Vnew119894

= Vold119894

+ 1198881times rand () times (119904

lowast

119894minus 119904

old119894

) + 1198882


old119894

)

119904new119894

= 119904old119894

+ Vnew119894

if V119894gt Vmax V

119894= Vmax


119894= minusVmax

(21)



Vnew119894

= 119896 times ⟨Vold119894

+ 1198881times rand () times (119904

lowast

119894minus 119904

old119894

)


119894minus 119904

old119894

)⟩

119904new119894

= 119904old119894

+ Vnew119894

119870 =2


120601 = 1198881+ 1198882 120601 gt 4

(22)








Siliconmaterial



test Customer

Manufacturing unit


Reverse route





1= 205 119888

2= 205 pro-

posed byClerc [62] 1198881= 28 119888



1= 28 119888

2= 13 velocity = 50







1

119899119894

+1

119899119895

)



1

119899119894

+1

119899119895

))

(23)


Table1Datao

ftranspo


Transportatio

nlin

e11ndash21

11ndash22

11ndash23

11ndash24

12ndash21

12ndash22

12ndash23

12ndash24

13ndash21

13ndash22

13ndash23

13ndash24

21ndash31

21ndash32

21ndash33

21ndash34

Transportatio

ndefectrate

001

003

002

002

002

001

004

005

004

003

005

001

003

002

001

004

Transportatio

ncost

56

103

75

64

43

510

45

34

Transportatio

nlin

e21ndash35

22ndash31

22ndash32

22ndash33

22ndash34

22ndash35

23ndash31

23ndash32

23ndash33

23ndash34

23ndash35

24ndash

31

24ndash

32

24ndash

33

24ndash

34

24ndash

35

Transportatio

ndefectrate

002

002

003

004

002

005

003

004

002

003

001

003

004

002

001

002

Transportatio

ncost

54

56

22

58

54

65

65

45

Transportatio

nlin

e31ndash41

31ndash42

31ndash43

31ndash44

31ndash45

31ndash46

32ndash41

32ndash42

32ndash43

32ndash44

32ndash45

32ndash46

33ndash41

33ndash42

33ndash43

33ndash44

Transportatio

ndefectrate

003

002

001

002

001

003

002

003

001

004

002

003

002

003

004

005

Transportatio

ncost

45

46

46

46

35

45

56

48

Transportatio

nlin

e33ndash45

33ndash46

34ndash

41

34ndash

42

34ndash

43

34ndash

44

34ndash

45

34ndash

46

35ndash41

35ndash42

35ndash43

35ndash44

35ndash45

35ndash46

Transportatio

ndefectrate

002

001

002

003

005

004

002

003

003

002

003

004

005

003

Transportatio

ncost

65

44

65

56

25

65

42


Stage 4

Stage 3

Stage 2

Stage 1


Q7PC20

30 = Q = 1700

Q9PC15

10 = Q = 1600

Q10PC12

20 = Q = 1800

Q9PC16

DR00220 = Q = 1550

Q7PC13

DR00310 = Q = 1700

Q8PC15

DR00215 = Q = 1650

Q9PC20

DR00130 = Q = 1700

Q7PC12

DR00220 = Q = 1700

Q6PC13

DR00330 = Q = 1600

Q8PC18

DR00125 = Q = 1350

Q7PC15

DR00230 = Q = 1500

Q8PC13

DR002150 = Q = 1600

Q6PC10

DR00330 = Q = 1350

Q10PC20

DR00120 = Q = 1500

Q8PC12

DR00225 = Q = 1400

Q7PC15

DR00126 = Q = 1250

Q9PC11

DR00320 = Q = 1450

Q7PC12

DR00330 = Q = 1500

Demand

11

12

13

21

22

23

24

31

32

33

34

35

41

42

43

44

45

46










1000

10002 06 4565 6522 5858455

095 3691 5272 5864019

005 06 5888 8412 5820524095 6012 8588 5853552

20002 06 9907 14153 5857317

095 5849 8357 5791562

005 06 11126 15894 5788794095 9415 13451 5787604

2000

10002 06 5942 11212 5830374

095 5187 9788 5873883

005 06 9085 17142 5769888095 8987 16958 5802988

20002 06 8823 16649 5769203

095 7251 13681 5793471

005 06 15542 29372 5755047095 13379 25245 5769029



1000

1020 04 117 249 5816602

09 126 269 5853555

50 04 228 486 588147309 294 562 5935652

2020 04 345 521 5938588

09 271 577 5824685

50 04 576 1012 581133809 617 1121 5899211

2000

1020 04 296 489 6129503

09 238 521 5817566

50 04 469 924 584003409 510 1026 5851926

2020 04 473 931 5912584

09 502 1006 5803912

50 04 756 1888 573972109 1194 2234 5809798







1 1198882


1000

1020 205 205 277 376 5968602

28 13 184 392 5809097

50 205 205 485 818 591679528 13 414 795 5757822

2020 205 205 337 505 604557

28 13 443 729 5880764

50 205 205 901 1916 598957128 13 854 1541 5835304

2000

1020 205 205 645 908 5796706

28 13 620 868 5749695

50 205 205 1153 1922 601022228 13 986 1644 5834792

2020 205 205 834 1557 5945546

28 13 991 1653 5796291

50 205 205 2264 3774 605729628 13 1884 3140 5740339



100010 20 197 295 6207676

50 389 581 6263544

20 20 391 583 621080650 874 1304 6164093

200010 20 353 521 6177516

50 727 1212 6140259

20 20 713 1005 614276150 1445 2409 6096037




1 otherwise





1 otherwise






1 otherwise













Objective function

3-4-5-6 5748095a1b 57356461 57509621 603791226-6-6-6 64448212 64242681 65047513 72552374

3-10-10-60 97241222 95445731 98021153 1022415646-6-6-6-6 76046012 75865551 76155213 823544446-8-8-10-30 120122532 115325211 124227343 1345758748-10-20-20-60 168544232 163724161 171141253 181127944

Execution time

3-4-5-6 30692 1891 2201 20216-6-6-6 32642 4181 4241 3901

3-10-10-60 62144 7453 6582 61316-6-6-6-6 53313 6102 5131 48416-8-8-10-30 78264 11253 9212 85218-10-20-20-60 99784 18743 13852 10271

Convergence time

3-4-5-6 15544 751 1893 14426-6-6-6 19662 1861 2271 2261

3-10-10-60 41533 2871 3022 31226-6-6-6-6 30293 2361 2652 27226-8-8-10-30 55743 3521 4072 42528-10-20-20-60 63254 3981 4422 4863





Stage 111 0 0 0 3412 5 646 17 013 1615 154 6 15

Stage 2

21 379 392 190 237 32722 38 0 8 261 45923 0 10 10 0 224 0 0 48 0 0

Stage 3

31 6 28 194 163 1 532 0 9 114 13 146 10033 0 0 0 27 168 5634 126 61 1 154 0 13735 291 366 0 8 0 72

Demand 400 450 300 350 300 350



Stage 111 29 142 72 15812 120 43 150 2413 576 845 194 128

Stage 2

21 12 0 19 177 115 148 90 16422 9 6 8 189 139 51 183 421

23 0 0 0 104 78 130 74 12

24 0 0 0 136 30 15 91 37

Stage 3

31 1 2 1 3 1 0 0 67 95 130 69 126 9532 2 4 0 2 0 3 0 41 54 111 106 27 533 0 0 1 0 1 0 0 11 2 74 73 81 9534 2 0 3 1 1 2 0 36 45 23 148 127 4335 2 1 5 0 1 1 5 162 165 131 24 92 25

Stage 4

41 2 0 2 0 4 0 0 0 1 1 0 242 0 2 0 0 1 0 0 0 1 0 0 043 2 0 0 0 0 0 2 0 0 0 1 144 1 0 0 0 0 1 0 0 0 0 0 145 0 3 0 1 2 0 0 2 1 0 0 046 3 1 0 1 2 0 0 2 0 0 0 1









Stage 111 227 24 48 7312 17 47 0 6513 900 738 84 37

Stage 2

21 7 3 3 133 156 180 239 38322 4 2 23 172 121 144 234 9623 2 4 1 45 0 66 27 024 2 1 0 3 0 73 33 71

Stage 3

31 5 0 1 2 2 1 4 0 4 129 11 134 6432 3 2 0 2 0 2 1 4 3 100 53 57 4933 1 0 1 0 1 0 0 0 81 75 50 139 10734 0 1 3 0 0 4 0 80 50 49 174 36 12535 1 5 0 1 3 1 1 180 172 64 27 0 77

Stage 4

41 1 1 1 0 0 2 1 1 1 0 1 042 0 1 0 0 0 1 0 0 1 0 0 043 1 0 2 0 0 0 3 0 0 2 0 144 2 0 0 0 0 1 0 0 0 0 1 045 3 0 2 3 0 0 1 3 0 1 0 046 1 0 2 1 0 1 0 0 1 0 0 1





Acknowledgments



References












































































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in





119869

sum

119895=1

10038171003817100381710038171003817119880119899

((119904minus1119895)(119904119894))(1 minus 119879119865119877

((119904minus1119895)(119904119894)))10038171003817100381710038171003817

minus

119904minus1

sum

119903119904=1

119869

sum

119895=1

119877119880119899

((119904119894)(119904minus119903119904119895))= 119862119863

119899

(119904119894)

for 119899 = 1 2 3 119873 119904 = 119878

119894 = 1 2 3 119868

(14)


0 le 119908119875119862

119908119879119862

119908119879119878 119908119875119876

le 1

119908119875119862

+ 119908119879119862

+ 119908119879119878

+ 119908119875119876

= 1

(15)


119877119880119899

((119903119904119895)(119904119894))= 0 for 119899 le 0 119904 = 1 2 3 4 119878 minus 1

119903119904 = 119904 + 1 119878 119894 = 1 2 3 119868

119895 = 1 2 3 119869

(16)


119880119899

((119904119894)(119904+1119895))ge 0 and 119880

119899

((119904119894)(119904+1119895))isin Integer

for 119899 = 1 2 3 119873 119904 = 1 2 3 119878

119894 = 1 2 3 119868 119895 = 1 2 3 119869

(17)

119877119880119899

((119903119904119895)(119904119894))ge 0 and 119880

119899

((119904119894)(119904+1119895))isin Integer

for 119904 = 1 2 3 119878 119903119904 = 119878 + 1 119878

119899 = 1 2 3 119873 119894 = 1 2 3 119868 119895 = 1 2 3 119869

(18)


119879

119875119862(119904119894)

=119875119862(119904119894)

minus 119875119862(119904119894)

119878119866119875119862(119904119894)

10+ 50 for 119904 = 1 2 3 119878

119894 = 1 2 3 119868

119879

119879119862((119904119894)(119904+1119895))

=

119879119862((119904119894)(119904+1119895))

minus 119879119862((119904119894)(119904+1119895))

119878119866119879119862((119904119894)(119904+1119895))

10+ 50

for 119904 = 1 2 3 119878 119894 = 1 2 3 119868

119895 = 1 2 3 119869

119879

119875119876(119904119894)

=119875119876(119904119894)

minus 119875119876(119904119894)

119878119866119875119876(119904119894)10

+ 50 for 119904 = 1 2 3 119878

119894 = 1 2 3 119868

119879

119879119878((119904119894)(119904+1119895))

=

119879119878((119904119894)(119904+1119895))

minus 119879119878((119904119894)(119904+1119895))

119878119866119879119878((119904119894)(119904+1119895))

10+ 50

for 119904 = 1 2 3 119878 119894 = 1 2 3 119868

119895 = 1 2 3 119869

(19)


























Mutation point

After mutation






Particle 1 2 3 4 5 6 117 118 119Line

Volume 0 0 42 9 0 0 0 2 0



















Vnew119894

= 119908Vold119894

+ 1198881times rand () times (119904

lowast

119894minus 119904

old119894

) + 1198882


old119894

)

119904new119894

= 119904old119894

+ Vnew119894

(20)


Vnew119894

= Vold119894

+ 1198881times rand () times (119904

lowast

119894minus 119904

old119894

) + 1198882


old119894

)

119904new119894

= 119904old119894

+ Vnew119894

if V119894gt Vmax V

119894= Vmax


119894= minusVmax

(21)



Vnew119894

= 119896 times ⟨Vold119894

+ 1198881times rand () times (119904

lowast

119894minus 119904

old119894

)


119894minus 119904

old119894

)⟩

119904new119894

= 119904old119894

+ Vnew119894

119870 =2


120601 = 1198881+ 1198882 120601 gt 4

(22)








Siliconmaterial



test Customer

Manufacturing unit


Reverse route





1= 205 119888

2= 205 pro-

posed byClerc [62] 1198881= 28 119888



1= 28 119888

2= 13 velocity = 50







1

119899119894

+1

119899119895

)



1

119899119894

+1

119899119895

))

(23)


Table1Datao

ftranspo


Transportatio

nlin

e11ndash21

11ndash22

11ndash23

11ndash24

12ndash21

12ndash22

12ndash23

12ndash24

13ndash21

13ndash22

13ndash23

13ndash24

21ndash31

21ndash32

21ndash33

21ndash34

Transportatio

ndefectrate

001

003

002

002

002

001

004

005

004

003

005

001

003

002

001

004

Transportatio

ncost

56

103

75

64

43

510

45

34

Transportatio

nlin

e21ndash35

22ndash31

22ndash32

22ndash33

22ndash34

22ndash35

23ndash31

23ndash32

23ndash33

23ndash34

23ndash35

24ndash

31

24ndash

32

24ndash

33

24ndash

34

24ndash

35

Transportatio

ndefectrate

002

002

003

004

002

005

003

004

002

003

001

003

004

002

001

002

Transportatio

ncost

54

56

22

58

54

65

65

45

Transportatio

nlin

e31ndash41

31ndash42

31ndash43

31ndash44

31ndash45

31ndash46

32ndash41

32ndash42

32ndash43

32ndash44

32ndash45

32ndash46

33ndash41

33ndash42

33ndash43

33ndash44

Transportatio

ndefectrate

003

002

001

002

001

003

002

003

001

004

002

003

002

003

004

005

Transportatio

ncost

45

46

46

46

35

45

56

48

Transportatio

nlin

e33ndash45

33ndash46

34ndash

41

34ndash

42

34ndash

43

34ndash

44

34ndash

45

34ndash

46

35ndash41

35ndash42

35ndash43

35ndash44

35ndash45

35ndash46

Transportatio

ndefectrate

002

001

002

003

005

004

002

003

003

002

003

004

005

003

Transportatio

ncost

65

44

65

56

25

65

42


Stage 4

Stage 3

Stage 2

Stage 1


Q7PC20

30 = Q = 1700

Q9PC15

10 = Q = 1600

Q10PC12

20 = Q = 1800

Q9PC16

DR00220 = Q = 1550

Q7PC13

DR00310 = Q = 1700

Q8PC15

DR00215 = Q = 1650

Q9PC20

DR00130 = Q = 1700

Q7PC12

DR00220 = Q = 1700

Q6PC13

DR00330 = Q = 1600

Q8PC18

DR00125 = Q = 1350

Q7PC15

DR00230 = Q = 1500

Q8PC13

DR002150 = Q = 1600

Q6PC10

DR00330 = Q = 1350

Q10PC20

DR00120 = Q = 1500

Q8PC12

DR00225 = Q = 1400

Q7PC15

DR00126 = Q = 1250

Q9PC11

DR00320 = Q = 1450

Q7PC12

DR00330 = Q = 1500

Demand

11

12

13

21

22

23

24

31

32

33

34

35

41

42

43

44

45

46










1000

10002 06 4565 6522 5858455

095 3691 5272 5864019

005 06 5888 8412 5820524095 6012 8588 5853552

20002 06 9907 14153 5857317

095 5849 8357 5791562

005 06 11126 15894 5788794095 9415 13451 5787604

2000

10002 06 5942 11212 5830374

095 5187 9788 5873883

005 06 9085 17142 5769888095 8987 16958 5802988

20002 06 8823 16649 5769203

095 7251 13681 5793471

005 06 15542 29372 5755047095 13379 25245 5769029



1000

1020 04 117 249 5816602

09 126 269 5853555

50 04 228 486 588147309 294 562 5935652

2020 04 345 521 5938588

09 271 577 5824685

50 04 576 1012 581133809 617 1121 5899211

2000

1020 04 296 489 6129503

09 238 521 5817566

50 04 469 924 584003409 510 1026 5851926

2020 04 473 931 5912584

09 502 1006 5803912

50 04 756 1888 573972109 1194 2234 5809798







1 1198882


1000

1020 205 205 277 376 5968602

28 13 184 392 5809097

50 205 205 485 818 591679528 13 414 795 5757822

2020 205 205 337 505 604557

28 13 443 729 5880764

50 205 205 901 1916 598957128 13 854 1541 5835304

2000

1020 205 205 645 908 5796706

28 13 620 868 5749695

50 205 205 1153 1922 601022228 13 986 1644 5834792

2020 205 205 834 1557 5945546

28 13 991 1653 5796291

50 205 205 2264 3774 605729628 13 1884 3140 5740339



100010 20 197 295 6207676

50 389 581 6263544

20 20 391 583 621080650 874 1304 6164093

200010 20 353 521 6177516

50 727 1212 6140259

20 20 713 1005 614276150 1445 2409 6096037




1 otherwise





1 otherwise






1 otherwise













Objective function

3-4-5-6 5748095a1b 57356461 57509621 603791226-6-6-6 64448212 64242681 65047513 72552374

3-10-10-60 97241222 95445731 98021153 1022415646-6-6-6-6 76046012 75865551 76155213 823544446-8-8-10-30 120122532 115325211 124227343 1345758748-10-20-20-60 168544232 163724161 171141253 181127944

Execution time

3-4-5-6 30692 1891 2201 20216-6-6-6 32642 4181 4241 3901

3-10-10-60 62144 7453 6582 61316-6-6-6-6 53313 6102 5131 48416-8-8-10-30 78264 11253 9212 85218-10-20-20-60 99784 18743 13852 10271

Convergence time

3-4-5-6 15544 751 1893 14426-6-6-6 19662 1861 2271 2261

3-10-10-60 41533 2871 3022 31226-6-6-6-6 30293 2361 2652 27226-8-8-10-30 55743 3521 4072 42528-10-20-20-60 63254 3981 4422 4863





Stage 111 0 0 0 3412 5 646 17 013 1615 154 6 15

Stage 2

21 379 392 190 237 32722 38 0 8 261 45923 0 10 10 0 224 0 0 48 0 0

Stage 3

31 6 28 194 163 1 532 0 9 114 13 146 10033 0 0 0 27 168 5634 126 61 1 154 0 13735 291 366 0 8 0 72

Demand 400 450 300 350 300 350



Stage 111 29 142 72 15812 120 43 150 2413 576 845 194 128

Stage 2

21 12 0 19 177 115 148 90 16422 9 6 8 189 139 51 183 421

23 0 0 0 104 78 130 74 12

24 0 0 0 136 30 15 91 37

Stage 3

31 1 2 1 3 1 0 0 67 95 130 69 126 9532 2 4 0 2 0 3 0 41 54 111 106 27 533 0 0 1 0 1 0 0 11 2 74 73 81 9534 2 0 3 1 1 2 0 36 45 23 148 127 4335 2 1 5 0 1 1 5 162 165 131 24 92 25

Stage 4

41 2 0 2 0 4 0 0 0 1 1 0 242 0 2 0 0 1 0 0 0 1 0 0 043 2 0 0 0 0 0 2 0 0 0 1 144 1 0 0 0 0 1 0 0 0 0 0 145 0 3 0 1 2 0 0 2 1 0 0 046 3 1 0 1 2 0 0 2 0 0 0 1









Stage 111 227 24 48 7312 17 47 0 6513 900 738 84 37

Stage 2

21 7 3 3 133 156 180 239 38322 4 2 23 172 121 144 234 9623 2 4 1 45 0 66 27 024 2 1 0 3 0 73 33 71

Stage 3

31 5 0 1 2 2 1 4 0 4 129 11 134 6432 3 2 0 2 0 2 1 4 3 100 53 57 4933 1 0 1 0 1 0 0 0 81 75 50 139 10734 0 1 3 0 0 4 0 80 50 49 174 36 12535 1 5 0 1 3 1 1 180 172 64 27 0 77

Stage 4

41 1 1 1 0 0 2 1 1 1 0 1 042 0 1 0 0 0 1 0 0 1 0 0 043 1 0 2 0 0 0 3 0 0 2 0 144 2 0 0 0 0 1 0 0 0 0 1 045 3 0 2 3 0 0 1 3 0 1 0 046 1 0 2 1 0 1 0 0 1 0 0 1





Acknowledgments



References












































































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




















Mutation point

After mutation






Particle 1 2 3 4 5 6 117 118 119Line

Volume 0 0 42 9 0 0 0 2 0



















Vnew119894

= 119908Vold119894

+ 1198881times rand () times (119904

lowast

119894minus 119904

old119894

) + 1198882


old119894

)

119904new119894

= 119904old119894

+ Vnew119894

(20)


Vnew119894

= Vold119894

+ 1198881times rand () times (119904

lowast

119894minus 119904

old119894

) + 1198882


old119894

)

119904new119894

= 119904old119894

+ Vnew119894

if V119894gt Vmax V

119894= Vmax


119894= minusVmax

(21)



Vnew119894

= 119896 times ⟨Vold119894

+ 1198881times rand () times (119904

lowast

119894minus 119904

old119894

)


119894minus 119904

old119894

)⟩

119904new119894

= 119904old119894

+ Vnew119894

119870 =2


120601 = 1198881+ 1198882 120601 gt 4

(22)








Siliconmaterial



test Customer

Manufacturing unit


Reverse route





1= 205 119888

2= 205 pro-

posed byClerc [62] 1198881= 28 119888



1= 28 119888

2= 13 velocity = 50







1

119899119894

+1

119899119895

)



1

119899119894

+1

119899119895

))

(23)


Table1Datao

ftranspo


Transportatio

nlin

e11ndash21

11ndash22

11ndash23

11ndash24

12ndash21

12ndash22

12ndash23

12ndash24

13ndash21

13ndash22

13ndash23

13ndash24

21ndash31

21ndash32

21ndash33

21ndash34

Transportatio

ndefectrate

001

003

002

002

002

001

004

005

004

003

005

001

003

002

001

004

Transportatio

ncost

56

103

75

64

43

510

45

34

Transportatio

nlin

e21ndash35

22ndash31

22ndash32

22ndash33

22ndash34

22ndash35

23ndash31

23ndash32

23ndash33

23ndash34

23ndash35

24ndash

31

24ndash

32

24ndash

33

24ndash

34

24ndash

35

Transportatio

ndefectrate

002

002

003

004

002

005

003

004

002

003

001

003

004

002

001

002

Transportatio

ncost

54

56

22

58

54

65

65

45

Transportatio

nlin

e31ndash41

31ndash42

31ndash43

31ndash44

31ndash45

31ndash46

32ndash41

32ndash42

32ndash43

32ndash44

32ndash45

32ndash46

33ndash41

33ndash42

33ndash43

33ndash44

Transportatio

ndefectrate

003

002

001

002

001

003

002

003

001

004

002

003

002

003

004

005

Transportatio

ncost

45

46

46

46

35

45

56

48

Transportatio

nlin

e33ndash45

33ndash46

34ndash

41

34ndash

42

34ndash

43

34ndash

44

34ndash

45

34ndash

46

35ndash41

35ndash42

35ndash43

35ndash44

35ndash45

35ndash46

Transportatio

ndefectrate

002

001

002

003

005

004

002

003

003

002

003

004

005

003

Transportatio

ncost

65

44

65

56

25

65

42


Stage 4

Stage 3

Stage 2

Stage 1


Q7PC20

30 = Q = 1700

Q9PC15

10 = Q = 1600

Q10PC12

20 = Q = 1800

Q9PC16

DR00220 = Q = 1550

Q7PC13

DR00310 = Q = 1700

Q8PC15

DR00215 = Q = 1650

Q9PC20

DR00130 = Q = 1700

Q7PC12

DR00220 = Q = 1700

Q6PC13

DR00330 = Q = 1600

Q8PC18

DR00125 = Q = 1350

Q7PC15

DR00230 = Q = 1500

Q8PC13

DR002150 = Q = 1600

Q6PC10

DR00330 = Q = 1350

Q10PC20

DR00120 = Q = 1500

Q8PC12

DR00225 = Q = 1400

Q7PC15

DR00126 = Q = 1250

Q9PC11

DR00320 = Q = 1450

Q7PC12

DR00330 = Q = 1500

Demand

11

12

13

21

22

23

24

31

32

33

34

35

41

42

43

44

45

46










1000

10002 06 4565 6522 5858455

095 3691 5272 5864019

005 06 5888 8412 5820524095 6012 8588 5853552

20002 06 9907 14153 5857317

095 5849 8357 5791562

005 06 11126 15894 5788794095 9415 13451 5787604

2000

10002 06 5942 11212 5830374

095 5187 9788 5873883

005 06 9085 17142 5769888095 8987 16958 5802988

20002 06 8823 16649 5769203

095 7251 13681 5793471

005 06 15542 29372 5755047095 13379 25245 5769029



1000

1020 04 117 249 5816602

09 126 269 5853555

50 04 228 486 588147309 294 562 5935652

2020 04 345 521 5938588

09 271 577 5824685

50 04 576 1012 581133809 617 1121 5899211

2000

1020 04 296 489 6129503

09 238 521 5817566

50 04 469 924 584003409 510 1026 5851926

2020 04 473 931 5912584

09 502 1006 5803912

50 04 756 1888 573972109 1194 2234 5809798







1 1198882


1000

1020 205 205 277 376 5968602

28 13 184 392 5809097

50 205 205 485 818 591679528 13 414 795 5757822

2020 205 205 337 505 604557

28 13 443 729 5880764

50 205 205 901 1916 598957128 13 854 1541 5835304

2000

1020 205 205 645 908 5796706

28 13 620 868 5749695

50 205 205 1153 1922 601022228 13 986 1644 5834792

2020 205 205 834 1557 5945546

28 13 991 1653 5796291

50 205 205 2264 3774 605729628 13 1884 3140 5740339



100010 20 197 295 6207676

50 389 581 6263544

20 20 391 583 621080650 874 1304 6164093

200010 20 353 521 6177516

50 727 1212 6140259

20 20 713 1005 614276150 1445 2409 6096037




1 otherwise





1 otherwise






1 otherwise













Objective function

3-4-5-6 5748095a1b 57356461 57509621 603791226-6-6-6 64448212 64242681 65047513 72552374

3-10-10-60 97241222 95445731 98021153 1022415646-6-6-6-6 76046012 75865551 76155213 823544446-8-8-10-30 120122532 115325211 124227343 1345758748-10-20-20-60 168544232 163724161 171141253 181127944

Execution time

3-4-5-6 30692 1891 2201 20216-6-6-6 32642 4181 4241 3901

3-10-10-60 62144 7453 6582 61316-6-6-6-6 53313 6102 5131 48416-8-8-10-30 78264 11253 9212 85218-10-20-20-60 99784 18743 13852 10271

Convergence time

3-4-5-6 15544 751 1893 14426-6-6-6 19662 1861 2271 2261

3-10-10-60 41533 2871 3022 31226-6-6-6-6 30293 2361 2652 27226-8-8-10-30 55743 3521 4072 42528-10-20-20-60 63254 3981 4422 4863





Stage 111 0 0 0 3412 5 646 17 013 1615 154 6 15

Stage 2

21 379 392 190 237 32722 38 0 8 261 45923 0 10 10 0 224 0 0 48 0 0

Stage 3

31 6 28 194 163 1 532 0 9 114 13 146 10033 0 0 0 27 168 5634 126 61 1 154 0 13735 291 366 0 8 0 72

Demand 400 450 300 350 300 350



Stage 111 29 142 72 15812 120 43 150 2413 576 845 194 128

Stage 2

21 12 0 19 177 115 148 90 16422 9 6 8 189 139 51 183 421

23 0 0 0 104 78 130 74 12

24 0 0 0 136 30 15 91 37

Stage 3

31 1 2 1 3 1 0 0 67 95 130 69 126 9532 2 4 0 2 0 3 0 41 54 111 106 27 533 0 0 1 0 1 0 0 11 2 74 73 81 9534 2 0 3 1 1 2 0 36 45 23 148 127 4335 2 1 5 0 1 1 5 162 165 131 24 92 25

Stage 4

41 2 0 2 0 4 0 0 0 1 1 0 242 0 2 0 0 1 0 0 0 1 0 0 043 2 0 0 0 0 0 2 0 0 0 1 144 1 0 0 0 0 1 0 0 0 0 0 145 0 3 0 1 2 0 0 2 1 0 0 046 3 1 0 1 2 0 0 2 0 0 0 1









Stage 111 227 24 48 7312 17 47 0 6513 900 738 84 37

Stage 2

21 7 3 3 133 156 180 239 38322 4 2 23 172 121 144 234 9623 2 4 1 45 0 66 27 024 2 1 0 3 0 73 33 71

Stage 3

31 5 0 1 2 2 1 4 0 4 129 11 134 6432 3 2 0 2 0 2 1 4 3 100 53 57 4933 1 0 1 0 1 0 0 0 81 75 50 139 10734 0 1 3 0 0 4 0 80 50 49 174 36 12535 1 5 0 1 3 1 1 180 172 64 27 0 77

Stage 4

41 1 1 1 0 0 2 1 1 1 0 1 042 0 1 0 0 0 1 0 0 1 0 0 043 1 0 2 0 0 0 3 0 0 2 0 144 2 0 0 0 0 1 0 0 0 0 1 045 3 0 2 3 0 0 1 3 0 1 0 046 1 0 2 1 0 1 0 0 1 0 0 1





Acknowledgments



References












































































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in










Vnew119894

= 119908Vold119894

+ 1198881times rand () times (119904

lowast

119894minus 119904

old119894

) + 1198882


old119894

)

119904new119894

= 119904old119894

+ Vnew119894

(20)


Vnew119894

= Vold119894

+ 1198881times rand () times (119904

lowast

119894minus 119904

old119894

) + 1198882


old119894

)

119904new119894

= 119904old119894

+ Vnew119894

if V119894gt Vmax V

119894= Vmax


119894= minusVmax

(21)



Vnew119894

= 119896 times ⟨Vold119894

+ 1198881times rand () times (119904

lowast

119894minus 119904

old119894

)


119894minus 119904

old119894

)⟩

119904new119894

= 119904old119894

+ Vnew119894

119870 =2


120601 = 1198881+ 1198882 120601 gt 4

(22)








Siliconmaterial



test Customer

Manufacturing unit


Reverse route





1= 205 119888

2= 205 pro-

posed byClerc [62] 1198881= 28 119888



1= 28 119888

2= 13 velocity = 50







1

119899119894

+1

119899119895

)



1

119899119894

+1

119899119895

))

(23)


Table1Datao

ftranspo


Transportatio

nlin

e11ndash21

11ndash22

11ndash23

11ndash24

12ndash21

12ndash22

12ndash23

12ndash24

13ndash21

13ndash22

13ndash23

13ndash24

21ndash31

21ndash32

21ndash33

21ndash34

Transportatio

ndefectrate

001

003

002

002

002

001

004

005

004

003

005

001

003

002

001

004

Transportatio

ncost

56

103

75

64

43

510

45

34

Transportatio

nlin

e21ndash35

22ndash31

22ndash32

22ndash33

22ndash34

22ndash35

23ndash31

23ndash32

23ndash33

23ndash34

23ndash35

24ndash

31

24ndash

32

24ndash

33

24ndash

34

24ndash

35

Transportatio

ndefectrate

002

002

003

004

002

005

003

004

002

003

001

003

004

002

001

002

Transportatio

ncost

54

56

22

58

54

65

65

45

Transportatio

nlin

e31ndash41

31ndash42

31ndash43

31ndash44

31ndash45

31ndash46

32ndash41

32ndash42

32ndash43

32ndash44

32ndash45

32ndash46

33ndash41

33ndash42

33ndash43

33ndash44

Transportatio

ndefectrate

003

002

001

002

001

003

002

003

001

004

002

003

002

003

004

005

Transportatio

ncost

45

46

46

46

35

45

56

48

Transportatio

nlin

e33ndash45

33ndash46

34ndash

41

34ndash

42

34ndash

43

34ndash

44

34ndash

45

34ndash

46

35ndash41

35ndash42

35ndash43

35ndash44

35ndash45

35ndash46

Transportatio

ndefectrate

002

001

002

003

005

004

002

003

003

002

003

004

005

003

Transportatio

ncost

65

44

65

56

25

65

42


Stage 4

Stage 3

Stage 2

Stage 1


Q7PC20

30 = Q = 1700

Q9PC15

10 = Q = 1600

Q10PC12

20 = Q = 1800

Q9PC16

DR00220 = Q = 1550

Q7PC13

DR00310 = Q = 1700

Q8PC15

DR00215 = Q = 1650

Q9PC20

DR00130 = Q = 1700

Q7PC12

DR00220 = Q = 1700

Q6PC13

DR00330 = Q = 1600

Q8PC18

DR00125 = Q = 1350

Q7PC15

DR00230 = Q = 1500

Q8PC13

DR002150 = Q = 1600

Q6PC10

DR00330 = Q = 1350

Q10PC20

DR00120 = Q = 1500

Q8PC12

DR00225 = Q = 1400

Q7PC15

DR00126 = Q = 1250

Q9PC11

DR00320 = Q = 1450

Q7PC12

DR00330 = Q = 1500

Demand

11

12

13

21

22

23

24

31

32

33

34

35

41

42

43

44

45

46










1000

10002 06 4565 6522 5858455

095 3691 5272 5864019

005 06 5888 8412 5820524095 6012 8588 5853552

20002 06 9907 14153 5857317

095 5849 8357 5791562

005 06 11126 15894 5788794095 9415 13451 5787604

2000

10002 06 5942 11212 5830374

095 5187 9788 5873883

005 06 9085 17142 5769888095 8987 16958 5802988

20002 06 8823 16649 5769203

095 7251 13681 5793471

005 06 15542 29372 5755047095 13379 25245 5769029



1000

1020 04 117 249 5816602

09 126 269 5853555

50 04 228 486 588147309 294 562 5935652

2020 04 345 521 5938588

09 271 577 5824685

50 04 576 1012 581133809 617 1121 5899211

2000

1020 04 296 489 6129503

09 238 521 5817566

50 04 469 924 584003409 510 1026 5851926

2020 04 473 931 5912584

09 502 1006 5803912

50 04 756 1888 573972109 1194 2234 5809798







1 1198882


1000

1020 205 205 277 376 5968602

28 13 184 392 5809097

50 205 205 485 818 591679528 13 414 795 5757822

2020 205 205 337 505 604557

28 13 443 729 5880764

50 205 205 901 1916 598957128 13 854 1541 5835304

2000

1020 205 205 645 908 5796706

28 13 620 868 5749695

50 205 205 1153 1922 601022228 13 986 1644 5834792

2020 205 205 834 1557 5945546

28 13 991 1653 5796291

50 205 205 2264 3774 605729628 13 1884 3140 5740339



100010 20 197 295 6207676

50 389 581 6263544

20 20 391 583 621080650 874 1304 6164093

200010 20 353 521 6177516

50 727 1212 6140259

20 20 713 1005 614276150 1445 2409 6096037




1 otherwise





1 otherwise






1 otherwise













Objective function

3-4-5-6 5748095a1b 57356461 57509621 603791226-6-6-6 64448212 64242681 65047513 72552374

3-10-10-60 97241222 95445731 98021153 1022415646-6-6-6-6 76046012 75865551 76155213 823544446-8-8-10-30 120122532 115325211 124227343 1345758748-10-20-20-60 168544232 163724161 171141253 181127944

Execution time

3-4-5-6 30692 1891 2201 20216-6-6-6 32642 4181 4241 3901

3-10-10-60 62144 7453 6582 61316-6-6-6-6 53313 6102 5131 48416-8-8-10-30 78264 11253 9212 85218-10-20-20-60 99784 18743 13852 10271

Convergence time

3-4-5-6 15544 751 1893 14426-6-6-6 19662 1861 2271 2261

3-10-10-60 41533 2871 3022 31226-6-6-6-6 30293 2361 2652 27226-8-8-10-30 55743 3521 4072 42528-10-20-20-60 63254 3981 4422 4863





Stage 111 0 0 0 3412 5 646 17 013 1615 154 6 15

Stage 2

21 379 392 190 237 32722 38 0 8 261 45923 0 10 10 0 224 0 0 48 0 0

Stage 3

31 6 28 194 163 1 532 0 9 114 13 146 10033 0 0 0 27 168 5634 126 61 1 154 0 13735 291 366 0 8 0 72

Demand 400 450 300 350 300 350



Stage 111 29 142 72 15812 120 43 150 2413 576 845 194 128

Stage 2

21 12 0 19 177 115 148 90 16422 9 6 8 189 139 51 183 421

23 0 0 0 104 78 130 74 12

24 0 0 0 136 30 15 91 37

Stage 3

31 1 2 1 3 1 0 0 67 95 130 69 126 9532 2 4 0 2 0 3 0 41 54 111 106 27 533 0 0 1 0 1 0 0 11 2 74 73 81 9534 2 0 3 1 1 2 0 36 45 23 148 127 4335 2 1 5 0 1 1 5 162 165 131 24 92 25

Stage 4

41 2 0 2 0 4 0 0 0 1 1 0 242 0 2 0 0 1 0 0 0 1 0 0 043 2 0 0 0 0 0 2 0 0 0 1 144 1 0 0 0 0 1 0 0 0 0 0 145 0 3 0 1 2 0 0 2 1 0 0 046 3 1 0 1 2 0 0 2 0 0 0 1









Stage 111 227 24 48 7312 17 47 0 6513 900 738 84 37

Stage 2

21 7 3 3 133 156 180 239 38322 4 2 23 172 121 144 234 9623 2 4 1 45 0 66 27 024 2 1 0 3 0 73 33 71

Stage 3

31 5 0 1 2 2 1 4 0 4 129 11 134 6432 3 2 0 2 0 2 1 4 3 100 53 57 4933 1 0 1 0 1 0 0 0 81 75 50 139 10734 0 1 3 0 0 4 0 80 50 49 174 36 12535 1 5 0 1 3 1 1 180 172 64 27 0 77

Stage 4

41 1 1 1 0 0 2 1 1 1 0 1 042 0 1 0 0 0 1 0 0 1 0 0 043 1 0 2 0 0 0 3 0 0 2 0 144 2 0 0 0 0 1 0 0 0 0 1 045 3 0 2 3 0 0 1 3 0 1 0 046 1 0 2 1 0 1 0 0 1 0 0 1





Acknowledgments



References












































































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




Siliconmaterial



test Customer

Manufacturing unit


Reverse route





1= 205 119888

2= 205 pro-

posed byClerc [62] 1198881= 28 119888



1= 28 119888

2= 13 velocity = 50







1

119899119894

+1

119899119895

)



1

119899119894

+1

119899119895

))

(23)


Table1Datao

ftranspo


Transportatio

nlin

e11ndash21

11ndash22

11ndash23

11ndash24

12ndash21

12ndash22

12ndash23

12ndash24

13ndash21

13ndash22

13ndash23

13ndash24

21ndash31

21ndash32

21ndash33

21ndash34

Transportatio

ndefectrate

001

003

002

002

002

001

004

005

004

003

005

001

003

002

001

004

Transportatio

ncost

56

103

75

64

43

510

45

34

Transportatio

nlin

e21ndash35

22ndash31

22ndash32

22ndash33

22ndash34

22ndash35

23ndash31

23ndash32

23ndash33

23ndash34

23ndash35

24ndash

31

24ndash

32

24ndash

33

24ndash

34

24ndash

35

Transportatio

ndefectrate

002

002

003

004

002

005

003

004

002

003

001

003

004

002

001

002

Transportatio

ncost

54

56

22

58

54

65

65

45

Transportatio

nlin

e31ndash41

31ndash42

31ndash43

31ndash44

31ndash45

31ndash46

32ndash41

32ndash42

32ndash43

32ndash44

32ndash45

32ndash46

33ndash41

33ndash42

33ndash43

33ndash44

Transportatio

ndefectrate

003

002

001

002

001

003

002

003

001

004

002

003

002

003

004

005

Transportatio

ncost

45

46

46

46

35

45

56

48

Transportatio

nlin

e33ndash45

33ndash46

34ndash

41

34ndash

42

34ndash

43

34ndash

44

34ndash

45

34ndash

46

35ndash41

35ndash42

35ndash43

35ndash44

35ndash45

35ndash46

Transportatio

ndefectrate

002

001

002

003

005

004

002

003

003

002

003

004

005

003

Transportatio

ncost

65

44

65

56

25

65

42


Stage 4

Stage 3

Stage 2

Stage 1


Q7PC20

30 = Q = 1700

Q9PC15

10 = Q = 1600

Q10PC12

20 = Q = 1800

Q9PC16

DR00220 = Q = 1550

Q7PC13

DR00310 = Q = 1700

Q8PC15

DR00215 = Q = 1650

Q9PC20

DR00130 = Q = 1700

Q7PC12

DR00220 = Q = 1700

Q6PC13

DR00330 = Q = 1600

Q8PC18

DR00125 = Q = 1350

Q7PC15

DR00230 = Q = 1500

Q8PC13

DR002150 = Q = 1600

Q6PC10

DR00330 = Q = 1350

Q10PC20

DR00120 = Q = 1500

Q8PC12

DR00225 = Q = 1400

Q7PC15

DR00126 = Q = 1250

Q9PC11

DR00320 = Q = 1450

Q7PC12

DR00330 = Q = 1500

Demand

11

12

13

21

22

23

24

31

32

33

34

35

41

42

43

44

45

46










1000

10002 06 4565 6522 5858455

095 3691 5272 5864019

005 06 5888 8412 5820524095 6012 8588 5853552

20002 06 9907 14153 5857317

095 5849 8357 5791562

005 06 11126 15894 5788794095 9415 13451 5787604

2000

10002 06 5942 11212 5830374

095 5187 9788 5873883

005 06 9085 17142 5769888095 8987 16958 5802988

20002 06 8823 16649 5769203

095 7251 13681 5793471

005 06 15542 29372 5755047095 13379 25245 5769029



1000

1020 04 117 249 5816602

09 126 269 5853555

50 04 228 486 588147309 294 562 5935652

2020 04 345 521 5938588

09 271 577 5824685

50 04 576 1012 581133809 617 1121 5899211

2000

1020 04 296 489 6129503

09 238 521 5817566

50 04 469 924 584003409 510 1026 5851926

2020 04 473 931 5912584

09 502 1006 5803912

50 04 756 1888 573972109 1194 2234 5809798







1 1198882


1000

1020 205 205 277 376 5968602

28 13 184 392 5809097

50 205 205 485 818 591679528 13 414 795 5757822

2020 205 205 337 505 604557

28 13 443 729 5880764

50 205 205 901 1916 598957128 13 854 1541 5835304

2000

1020 205 205 645 908 5796706

28 13 620 868 5749695

50 205 205 1153 1922 601022228 13 986 1644 5834792

2020 205 205 834 1557 5945546

28 13 991 1653 5796291

50 205 205 2264 3774 605729628 13 1884 3140 5740339



100010 20 197 295 6207676

50 389 581 6263544

20 20 391 583 621080650 874 1304 6164093

200010 20 353 521 6177516

50 727 1212 6140259

20 20 713 1005 614276150 1445 2409 6096037




1 otherwise





1 otherwise






1 otherwise













Objective function

3-4-5-6 5748095a1b 57356461 57509621 603791226-6-6-6 64448212 64242681 65047513 72552374

3-10-10-60 97241222 95445731 98021153 1022415646-6-6-6-6 76046012 75865551 76155213 823544446-8-8-10-30 120122532 115325211 124227343 1345758748-10-20-20-60 168544232 163724161 171141253 181127944

Execution time

3-4-5-6 30692 1891 2201 20216-6-6-6 32642 4181 4241 3901

3-10-10-60 62144 7453 6582 61316-6-6-6-6 53313 6102 5131 48416-8-8-10-30 78264 11253 9212 85218-10-20-20-60 99784 18743 13852 10271

Convergence time

3-4-5-6 15544 751 1893 14426-6-6-6 19662 1861 2271 2261

3-10-10-60 41533 2871 3022 31226-6-6-6-6 30293 2361 2652 27226-8-8-10-30 55743 3521 4072 42528-10-20-20-60 63254 3981 4422 4863





Stage 111 0 0 0 3412 5 646 17 013 1615 154 6 15

Stage 2

21 379 392 190 237 32722 38 0 8 261 45923 0 10 10 0 224 0 0 48 0 0

Stage 3

31 6 28 194 163 1 532 0 9 114 13 146 10033 0 0 0 27 168 5634 126 61 1 154 0 13735 291 366 0 8 0 72

Demand 400 450 300 350 300 350



Stage 111 29 142 72 15812 120 43 150 2413 576 845 194 128

Stage 2

21 12 0 19 177 115 148 90 16422 9 6 8 189 139 51 183 421

23 0 0 0 104 78 130 74 12

24 0 0 0 136 30 15 91 37

Stage 3

31 1 2 1 3 1 0 0 67 95 130 69 126 9532 2 4 0 2 0 3 0 41 54 111 106 27 533 0 0 1 0 1 0 0 11 2 74 73 81 9534 2 0 3 1 1 2 0 36 45 23 148 127 4335 2 1 5 0 1 1 5 162 165 131 24 92 25

Stage 4

41 2 0 2 0 4 0 0 0 1 1 0 242 0 2 0 0 1 0 0 0 1 0 0 043 2 0 0 0 0 0 2 0 0 0 1 144 1 0 0 0 0 1 0 0 0 0 0 145 0 3 0 1 2 0 0 2 1 0 0 046 3 1 0 1 2 0 0 2 0 0 0 1









Stage 111 227 24 48 7312 17 47 0 6513 900 738 84 37

Stage 2

21 7 3 3 133 156 180 239 38322 4 2 23 172 121 144 234 9623 2 4 1 45 0 66 27 024 2 1 0 3 0 73 33 71

Stage 3

31 5 0 1 2 2 1 4 0 4 129 11 134 6432 3 2 0 2 0 2 1 4 3 100 53 57 4933 1 0 1 0 1 0 0 0 81 75 50 139 10734 0 1 3 0 0 4 0 80 50 49 174 36 12535 1 5 0 1 3 1 1 180 172 64 27 0 77

Stage 4

41 1 1 1 0 0 2 1 1 1 0 1 042 0 1 0 0 0 1 0 0 1 0 0 043 1 0 2 0 0 0 3 0 0 2 0 144 2 0 0 0 0 1 0 0 0 0 1 045 3 0 2 3 0 0 1 3 0 1 0 046 1 0 2 1 0 1 0 0 1 0 0 1





Acknowledgments



References












































































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




Table1Datao

ftranspo


Transportatio

nlin

e11ndash21

11ndash22

11ndash23

11ndash24

12ndash21

12ndash22

12ndash23

12ndash24

13ndash21

13ndash22

13ndash23

13ndash24

21ndash31

21ndash32

21ndash33

21ndash34

Transportatio

ndefectrate

001

003

002

002

002

001

004

005

004

003

005

001

003

002

001

004

Transportatio

ncost

56

103

75

64

43

510

45

34

Transportatio

nlin

e21ndash35

22ndash31

22ndash32

22ndash33

22ndash34

22ndash35

23ndash31

23ndash32

23ndash33

23ndash34

23ndash35

24ndash

31

24ndash

32

24ndash

33

24ndash

34

24ndash

35

Transportatio

ndefectrate

002

002

003

004

002

005

003

004

002

003

001

003

004

002

001

002

Transportatio

ncost

54

56

22

58

54

65

65

45

Transportatio

nlin

e31ndash41

31ndash42

31ndash43

31ndash44

31ndash45

31ndash46

32ndash41

32ndash42

32ndash43

32ndash44

32ndash45

32ndash46

33ndash41

33ndash42

33ndash43

33ndash44

Transportatio

ndefectrate

003

002

001

002

001

003

002

003

001

004

002

003

002

003

004

005

Transportatio

ncost

45

46

46

46

35

45

56

48

Transportatio

nlin

e33ndash45

33ndash46

34ndash

41

34ndash

42

34ndash

43

34ndash

44

34ndash

45

34ndash

46

35ndash41

35ndash42

35ndash43

35ndash44

35ndash45

35ndash46

Transportatio

ndefectrate

002

001

002

003

005

004

002

003

003

002

003

004

005

003

Transportatio

ncost

65

44

65

56

25

65

42


Stage 4

Stage 3

Stage 2

Stage 1


Q7PC20

30 = Q = 1700

Q9PC15

10 = Q = 1600

Q10PC12

20 = Q = 1800

Q9PC16

DR00220 = Q = 1550

Q7PC13

DR00310 = Q = 1700

Q8PC15

DR00215 = Q = 1650

Q9PC20

DR00130 = Q = 1700

Q7PC12

DR00220 = Q = 1700

Q6PC13

DR00330 = Q = 1600

Q8PC18

DR00125 = Q = 1350

Q7PC15

DR00230 = Q = 1500

Q8PC13

DR002150 = Q = 1600

Q6PC10

DR00330 = Q = 1350

Q10PC20

DR00120 = Q = 1500

Q8PC12

DR00225 = Q = 1400

Q7PC15

DR00126 = Q = 1250

Q9PC11

DR00320 = Q = 1450

Q7PC12

DR00330 = Q = 1500

Demand

11

12

13

21

22

23

24

31

32

33

34

35

41

42

43

44

45

46










1000

10002 06 4565 6522 5858455

095 3691 5272 5864019

005 06 5888 8412 5820524095 6012 8588 5853552

20002 06 9907 14153 5857317

095 5849 8357 5791562

005 06 11126 15894 5788794095 9415 13451 5787604

2000

10002 06 5942 11212 5830374

095 5187 9788 5873883

005 06 9085 17142 5769888095 8987 16958 5802988

20002 06 8823 16649 5769203

095 7251 13681 5793471

005 06 15542 29372 5755047095 13379 25245 5769029



1000

1020 04 117 249 5816602

09 126 269 5853555

50 04 228 486 588147309 294 562 5935652

2020 04 345 521 5938588

09 271 577 5824685

50 04 576 1012 581133809 617 1121 5899211

2000

1020 04 296 489 6129503

09 238 521 5817566

50 04 469 924 584003409 510 1026 5851926

2020 04 473 931 5912584

09 502 1006 5803912

50 04 756 1888 573972109 1194 2234 5809798







1 1198882


1000

1020 205 205 277 376 5968602

28 13 184 392 5809097

50 205 205 485 818 591679528 13 414 795 5757822

2020 205 205 337 505 604557

28 13 443 729 5880764

50 205 205 901 1916 598957128 13 854 1541 5835304

2000

1020 205 205 645 908 5796706

28 13 620 868 5749695

50 205 205 1153 1922 601022228 13 986 1644 5834792

2020 205 205 834 1557 5945546

28 13 991 1653 5796291

50 205 205 2264 3774 605729628 13 1884 3140 5740339



100010 20 197 295 6207676

50 389 581 6263544

20 20 391 583 621080650 874 1304 6164093

200010 20 353 521 6177516

50 727 1212 6140259

20 20 713 1005 614276150 1445 2409 6096037




1 otherwise





1 otherwise






1 otherwise













Objective function

3-4-5-6 5748095a1b 57356461 57509621 603791226-6-6-6 64448212 64242681 65047513 72552374

3-10-10-60 97241222 95445731 98021153 1022415646-6-6-6-6 76046012 75865551 76155213 823544446-8-8-10-30 120122532 115325211 124227343 1345758748-10-20-20-60 168544232 163724161 171141253 181127944

Execution time

3-4-5-6 30692 1891 2201 20216-6-6-6 32642 4181 4241 3901

3-10-10-60 62144 7453 6582 61316-6-6-6-6 53313 6102 5131 48416-8-8-10-30 78264 11253 9212 85218-10-20-20-60 99784 18743 13852 10271

Convergence time

3-4-5-6 15544 751 1893 14426-6-6-6 19662 1861 2271 2261

3-10-10-60 41533 2871 3022 31226-6-6-6-6 30293 2361 2652 27226-8-8-10-30 55743 3521 4072 42528-10-20-20-60 63254 3981 4422 4863





Stage 111 0 0 0 3412 5 646 17 013 1615 154 6 15

Stage 2

21 379 392 190 237 32722 38 0 8 261 45923 0 10 10 0 224 0 0 48 0 0

Stage 3

31 6 28 194 163 1 532 0 9 114 13 146 10033 0 0 0 27 168 5634 126 61 1 154 0 13735 291 366 0 8 0 72

Demand 400 450 300 350 300 350



Stage 111 29 142 72 15812 120 43 150 2413 576 845 194 128

Stage 2

21 12 0 19 177 115 148 90 16422 9 6 8 189 139 51 183 421

23 0 0 0 104 78 130 74 12

24 0 0 0 136 30 15 91 37

Stage 3

31 1 2 1 3 1 0 0 67 95 130 69 126 9532 2 4 0 2 0 3 0 41 54 111 106 27 533 0 0 1 0 1 0 0 11 2 74 73 81 9534 2 0 3 1 1 2 0 36 45 23 148 127 4335 2 1 5 0 1 1 5 162 165 131 24 92 25

Stage 4

41 2 0 2 0 4 0 0 0 1 1 0 242 0 2 0 0 1 0 0 0 1 0 0 043 2 0 0 0 0 0 2 0 0 0 1 144 1 0 0 0 0 1 0 0 0 0 0 145 0 3 0 1 2 0 0 2 1 0 0 046 3 1 0 1 2 0 0 2 0 0 0 1









Stage 111 227 24 48 7312 17 47 0 6513 900 738 84 37

Stage 2

21 7 3 3 133 156 180 239 38322 4 2 23 172 121 144 234 9623 2 4 1 45 0 66 27 024 2 1 0 3 0 73 33 71

Stage 3

31 5 0 1 2 2 1 4 0 4 129 11 134 6432 3 2 0 2 0 2 1 4 3 100 53 57 4933 1 0 1 0 1 0 0 0 81 75 50 139 10734 0 1 3 0 0 4 0 80 50 49 174 36 12535 1 5 0 1 3 1 1 180 172 64 27 0 77

Stage 4

41 1 1 1 0 0 2 1 1 1 0 1 042 0 1 0 0 0 1 0 0 1 0 0 043 1 0 2 0 0 0 3 0 0 2 0 144 2 0 0 0 0 1 0 0 0 0 1 045 3 0 2 3 0 0 1 3 0 1 0 046 1 0 2 1 0 1 0 0 1 0 0 1





Acknowledgments



References












































































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




Stage 4

Stage 3

Stage 2

Stage 1


Q7PC20

30 = Q = 1700

Q9PC15

10 = Q = 1600

Q10PC12

20 = Q = 1800

Q9PC16

DR00220 = Q = 1550

Q7PC13

DR00310 = Q = 1700

Q8PC15

DR00215 = Q = 1650

Q9PC20

DR00130 = Q = 1700

Q7PC12

DR00220 = Q = 1700

Q6PC13

DR00330 = Q = 1600

Q8PC18

DR00125 = Q = 1350

Q7PC15

DR00230 = Q = 1500

Q8PC13

DR002150 = Q = 1600

Q6PC10

DR00330 = Q = 1350

Q10PC20

DR00120 = Q = 1500

Q8PC12

DR00225 = Q = 1400

Q7PC15

DR00126 = Q = 1250

Q9PC11

DR00320 = Q = 1450

Q7PC12

DR00330 = Q = 1500

Demand

11

12

13

21

22

23

24

31

32

33

34

35

41

42

43

44

45

46










1000

10002 06 4565 6522 5858455

095 3691 5272 5864019

005 06 5888 8412 5820524095 6012 8588 5853552

20002 06 9907 14153 5857317

095 5849 8357 5791562

005 06 11126 15894 5788794095 9415 13451 5787604

2000

10002 06 5942 11212 5830374

095 5187 9788 5873883

005 06 9085 17142 5769888095 8987 16958 5802988

20002 06 8823 16649 5769203

095 7251 13681 5793471

005 06 15542 29372 5755047095 13379 25245 5769029



1000

1020 04 117 249 5816602

09 126 269 5853555

50 04 228 486 588147309 294 562 5935652

2020 04 345 521 5938588

09 271 577 5824685

50 04 576 1012 581133809 617 1121 5899211

2000

1020 04 296 489 6129503

09 238 521 5817566

50 04 469 924 584003409 510 1026 5851926

2020 04 473 931 5912584

09 502 1006 5803912

50 04 756 1888 573972109 1194 2234 5809798







1 1198882


1000

1020 205 205 277 376 5968602

28 13 184 392 5809097

50 205 205 485 818 591679528 13 414 795 5757822

2020 205 205 337 505 604557

28 13 443 729 5880764

50 205 205 901 1916 598957128 13 854 1541 5835304

2000

1020 205 205 645 908 5796706

28 13 620 868 5749695

50 205 205 1153 1922 601022228 13 986 1644 5834792

2020 205 205 834 1557 5945546

28 13 991 1653 5796291

50 205 205 2264 3774 605729628 13 1884 3140 5740339



100010 20 197 295 6207676

50 389 581 6263544

20 20 391 583 621080650 874 1304 6164093

200010 20 353 521 6177516

50 727 1212 6140259

20 20 713 1005 614276150 1445 2409 6096037




1 otherwise





1 otherwise






1 otherwise













Objective function

3-4-5-6 5748095a1b 57356461 57509621 603791226-6-6-6 64448212 64242681 65047513 72552374

3-10-10-60 97241222 95445731 98021153 1022415646-6-6-6-6 76046012 75865551 76155213 823544446-8-8-10-30 120122532 115325211 124227343 1345758748-10-20-20-60 168544232 163724161 171141253 181127944

Execution time

3-4-5-6 30692 1891 2201 20216-6-6-6 32642 4181 4241 3901

3-10-10-60 62144 7453 6582 61316-6-6-6-6 53313 6102 5131 48416-8-8-10-30 78264 11253 9212 85218-10-20-20-60 99784 18743 13852 10271

Convergence time

3-4-5-6 15544 751 1893 14426-6-6-6 19662 1861 2271 2261

3-10-10-60 41533 2871 3022 31226-6-6-6-6 30293 2361 2652 27226-8-8-10-30 55743 3521 4072 42528-10-20-20-60 63254 3981 4422 4863





Stage 111 0 0 0 3412 5 646 17 013 1615 154 6 15

Stage 2

21 379 392 190 237 32722 38 0 8 261 45923 0 10 10 0 224 0 0 48 0 0

Stage 3

31 6 28 194 163 1 532 0 9 114 13 146 10033 0 0 0 27 168 5634 126 61 1 154 0 13735 291 366 0 8 0 72

Demand 400 450 300 350 300 350



Stage 111 29 142 72 15812 120 43 150 2413 576 845 194 128

Stage 2

21 12 0 19 177 115 148 90 16422 9 6 8 189 139 51 183 421

23 0 0 0 104 78 130 74 12

24 0 0 0 136 30 15 91 37

Stage 3

31 1 2 1 3 1 0 0 67 95 130 69 126 9532 2 4 0 2 0 3 0 41 54 111 106 27 533 0 0 1 0 1 0 0 11 2 74 73 81 9534 2 0 3 1 1 2 0 36 45 23 148 127 4335 2 1 5 0 1 1 5 162 165 131 24 92 25

Stage 4

41 2 0 2 0 4 0 0 0 1 1 0 242 0 2 0 0 1 0 0 0 1 0 0 043 2 0 0 0 0 0 2 0 0 0 1 144 1 0 0 0 0 1 0 0 0 0 0 145 0 3 0 1 2 0 0 2 1 0 0 046 3 1 0 1 2 0 0 2 0 0 0 1









Stage 111 227 24 48 7312 17 47 0 6513 900 738 84 37

Stage 2

21 7 3 3 133 156 180 239 38322 4 2 23 172 121 144 234 9623 2 4 1 45 0 66 27 024 2 1 0 3 0 73 33 71

Stage 3

31 5 0 1 2 2 1 4 0 4 129 11 134 6432 3 2 0 2 0 2 1 4 3 100 53 57 4933 1 0 1 0 1 0 0 0 81 75 50 139 10734 0 1 3 0 0 4 0 80 50 49 174 36 12535 1 5 0 1 3 1 1 180 172 64 27 0 77

Stage 4

41 1 1 1 0 0 2 1 1 1 0 1 042 0 1 0 0 0 1 0 0 1 0 0 043 1 0 2 0 0 0 3 0 0 2 0 144 2 0 0 0 0 1 0 0 0 0 1 045 3 0 2 3 0 0 1 3 0 1 0 046 1 0 2 1 0 1 0 0 1 0 0 1





Acknowledgments



References












































































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in






1000

10002 06 4565 6522 5858455

095 3691 5272 5864019

005 06 5888 8412 5820524095 6012 8588 5853552

20002 06 9907 14153 5857317

095 5849 8357 5791562

005 06 11126 15894 5788794095 9415 13451 5787604

2000

10002 06 5942 11212 5830374

095 5187 9788 5873883

005 06 9085 17142 5769888095 8987 16958 5802988

20002 06 8823 16649 5769203

095 7251 13681 5793471

005 06 15542 29372 5755047095 13379 25245 5769029



1000

1020 04 117 249 5816602

09 126 269 5853555

50 04 228 486 588147309 294 562 5935652

2020 04 345 521 5938588

09 271 577 5824685

50 04 576 1012 581133809 617 1121 5899211

2000

1020 04 296 489 6129503

09 238 521 5817566

50 04 469 924 584003409 510 1026 5851926

2020 04 473 931 5912584

09 502 1006 5803912

50 04 756 1888 573972109 1194 2234 5809798







1 1198882


1000

1020 205 205 277 376 5968602

28 13 184 392 5809097

50 205 205 485 818 591679528 13 414 795 5757822

2020 205 205 337 505 604557

28 13 443 729 5880764

50 205 205 901 1916 598957128 13 854 1541 5835304

2000

1020 205 205 645 908 5796706

28 13 620 868 5749695

50 205 205 1153 1922 601022228 13 986 1644 5834792

2020 205 205 834 1557 5945546

28 13 991 1653 5796291

50 205 205 2264 3774 605729628 13 1884 3140 5740339



100010 20 197 295 6207676

50 389 581 6263544

20 20 391 583 621080650 874 1304 6164093

200010 20 353 521 6177516

50 727 1212 6140259

20 20 713 1005 614276150 1445 2409 6096037




1 otherwise





1 otherwise






1 otherwise













Objective function

3-4-5-6 5748095a1b 57356461 57509621 603791226-6-6-6 64448212 64242681 65047513 72552374

3-10-10-60 97241222 95445731 98021153 1022415646-6-6-6-6 76046012 75865551 76155213 823544446-8-8-10-30 120122532 115325211 124227343 1345758748-10-20-20-60 168544232 163724161 171141253 181127944

Execution time

3-4-5-6 30692 1891 2201 20216-6-6-6 32642 4181 4241 3901

3-10-10-60 62144 7453 6582 61316-6-6-6-6 53313 6102 5131 48416-8-8-10-30 78264 11253 9212 85218-10-20-20-60 99784 18743 13852 10271

Convergence time

3-4-5-6 15544 751 1893 14426-6-6-6 19662 1861 2271 2261

3-10-10-60 41533 2871 3022 31226-6-6-6-6 30293 2361 2652 27226-8-8-10-30 55743 3521 4072 42528-10-20-20-60 63254 3981 4422 4863





Stage 111 0 0 0 3412 5 646 17 013 1615 154 6 15

Stage 2

21 379 392 190 237 32722 38 0 8 261 45923 0 10 10 0 224 0 0 48 0 0

Stage 3

31 6 28 194 163 1 532 0 9 114 13 146 10033 0 0 0 27 168 5634 126 61 1 154 0 13735 291 366 0 8 0 72

Demand 400 450 300 350 300 350



Stage 111 29 142 72 15812 120 43 150 2413 576 845 194 128

Stage 2

21 12 0 19 177 115 148 90 16422 9 6 8 189 139 51 183 421

23 0 0 0 104 78 130 74 12

24 0 0 0 136 30 15 91 37

Stage 3

31 1 2 1 3 1 0 0 67 95 130 69 126 9532 2 4 0 2 0 3 0 41 54 111 106 27 533 0 0 1 0 1 0 0 11 2 74 73 81 9534 2 0 3 1 1 2 0 36 45 23 148 127 4335 2 1 5 0 1 1 5 162 165 131 24 92 25

Stage 4

41 2 0 2 0 4 0 0 0 1 1 0 242 0 2 0 0 1 0 0 0 1 0 0 043 2 0 0 0 0 0 2 0 0 0 1 144 1 0 0 0 0 1 0 0 0 0 0 145 0 3 0 1 2 0 0 2 1 0 0 046 3 1 0 1 2 0 0 2 0 0 0 1









Stage 111 227 24 48 7312 17 47 0 6513 900 738 84 37

Stage 2

21 7 3 3 133 156 180 239 38322 4 2 23 172 121 144 234 9623 2 4 1 45 0 66 27 024 2 1 0 3 0 73 33 71

Stage 3

31 5 0 1 2 2 1 4 0 4 129 11 134 6432 3 2 0 2 0 2 1 4 3 100 53 57 4933 1 0 1 0 1 0 0 0 81 75 50 139 10734 0 1 3 0 0 4 0 80 50 49 174 36 12535 1 5 0 1 3 1 1 180 172 64 27 0 77

Stage 4

41 1 1 1 0 0 2 1 1 1 0 1 042 0 1 0 0 0 1 0 0 1 0 0 043 1 0 2 0 0 0 3 0 0 2 0 144 2 0 0 0 0 1 0 0 0 0 1 045 3 0 2 3 0 0 1 3 0 1 0 046 1 0 2 1 0 1 0 0 1 0 0 1





Acknowledgments



References












































































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in






1 1198882


1000

1020 205 205 277 376 5968602

28 13 184 392 5809097

50 205 205 485 818 591679528 13 414 795 5757822

2020 205 205 337 505 604557

28 13 443 729 5880764

50 205 205 901 1916 598957128 13 854 1541 5835304

2000

1020 205 205 645 908 5796706

28 13 620 868 5749695

50 205 205 1153 1922 601022228 13 986 1644 5834792

2020 205 205 834 1557 5945546

28 13 991 1653 5796291

50 205 205 2264 3774 605729628 13 1884 3140 5740339



100010 20 197 295 6207676

50 389 581 6263544

20 20 391 583 621080650 874 1304 6164093

200010 20 353 521 6177516

50 727 1212 6140259

20 20 713 1005 614276150 1445 2409 6096037




1 otherwise





1 otherwise






1 otherwise













Objective function

3-4-5-6 5748095a1b 57356461 57509621 603791226-6-6-6 64448212 64242681 65047513 72552374

3-10-10-60 97241222 95445731 98021153 1022415646-6-6-6-6 76046012 75865551 76155213 823544446-8-8-10-30 120122532 115325211 124227343 1345758748-10-20-20-60 168544232 163724161 171141253 181127944

Execution time

3-4-5-6 30692 1891 2201 20216-6-6-6 32642 4181 4241 3901

3-10-10-60 62144 7453 6582 61316-6-6-6-6 53313 6102 5131 48416-8-8-10-30 78264 11253 9212 85218-10-20-20-60 99784 18743 13852 10271

Convergence time

3-4-5-6 15544 751 1893 14426-6-6-6 19662 1861 2271 2261

3-10-10-60 41533 2871 3022 31226-6-6-6-6 30293 2361 2652 27226-8-8-10-30 55743 3521 4072 42528-10-20-20-60 63254 3981 4422 4863





Stage 111 0 0 0 3412 5 646 17 013 1615 154 6 15

Stage 2

21 379 392 190 237 32722 38 0 8 261 45923 0 10 10 0 224 0 0 48 0 0

Stage 3

31 6 28 194 163 1 532 0 9 114 13 146 10033 0 0 0 27 168 5634 126 61 1 154 0 13735 291 366 0 8 0 72

Demand 400 450 300 350 300 350



Stage 111 29 142 72 15812 120 43 150 2413 576 845 194 128

Stage 2

21 12 0 19 177 115 148 90 16422 9 6 8 189 139 51 183 421

23 0 0 0 104 78 130 74 12

24 0 0 0 136 30 15 91 37

Stage 3

31 1 2 1 3 1 0 0 67 95 130 69 126 9532 2 4 0 2 0 3 0 41 54 111 106 27 533 0 0 1 0 1 0 0 11 2 74 73 81 9534 2 0 3 1 1 2 0 36 45 23 148 127 4335 2 1 5 0 1 1 5 162 165 131 24 92 25

Stage 4

41 2 0 2 0 4 0 0 0 1 1 0 242 0 2 0 0 1 0 0 0 1 0 0 043 2 0 0 0 0 0 2 0 0 0 1 144 1 0 0 0 0 1 0 0 0 0 0 145 0 3 0 1 2 0 0 2 1 0 0 046 3 1 0 1 2 0 0 2 0 0 0 1









Stage 111 227 24 48 7312 17 47 0 6513 900 738 84 37

Stage 2

21 7 3 3 133 156 180 239 38322 4 2 23 172 121 144 234 9623 2 4 1 45 0 66 27 024 2 1 0 3 0 73 33 71

Stage 3

31 5 0 1 2 2 1 4 0 4 129 11 134 6432 3 2 0 2 0 2 1 4 3 100 53 57 4933 1 0 1 0 1 0 0 0 81 75 50 139 10734 0 1 3 0 0 4 0 80 50 49 174 36 12535 1 5 0 1 3 1 1 180 172 64 27 0 77

Stage 4

41 1 1 1 0 0 2 1 1 1 0 1 042 0 1 0 0 0 1 0 0 1 0 0 043 1 0 2 0 0 0 3 0 0 2 0 144 2 0 0 0 0 1 0 0 0 0 1 045 3 0 2 3 0 0 1 3 0 1 0 046 1 0 2 1 0 1 0 0 1 0 0 1





Acknowledgments



References












































































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in







1 otherwise













Objective function

3-4-5-6 5748095a1b 57356461 57509621 603791226-6-6-6 64448212 64242681 65047513 72552374

3-10-10-60 97241222 95445731 98021153 1022415646-6-6-6-6 76046012 75865551 76155213 823544446-8-8-10-30 120122532 115325211 124227343 1345758748-10-20-20-60 168544232 163724161 171141253 181127944

Execution time

3-4-5-6 30692 1891 2201 20216-6-6-6 32642 4181 4241 3901

3-10-10-60 62144 7453 6582 61316-6-6-6-6 53313 6102 5131 48416-8-8-10-30 78264 11253 9212 85218-10-20-20-60 99784 18743 13852 10271

Convergence time

3-4-5-6 15544 751 1893 14426-6-6-6 19662 1861 2271 2261

3-10-10-60 41533 2871 3022 31226-6-6-6-6 30293 2361 2652 27226-8-8-10-30 55743 3521 4072 42528-10-20-20-60 63254 3981 4422 4863





Stage 111 0 0 0 3412 5 646 17 013 1615 154 6 15

Stage 2

21 379 392 190 237 32722 38 0 8 261 45923 0 10 10 0 224 0 0 48 0 0

Stage 3

31 6 28 194 163 1 532 0 9 114 13 146 10033 0 0 0 27 168 5634 126 61 1 154 0 13735 291 366 0 8 0 72

Demand 400 450 300 350 300 350



Stage 111 29 142 72 15812 120 43 150 2413 576 845 194 128

Stage 2

21 12 0 19 177 115 148 90 16422 9 6 8 189 139 51 183 421

23 0 0 0 104 78 130 74 12

24 0 0 0 136 30 15 91 37

Stage 3

31 1 2 1 3 1 0 0 67 95 130 69 126 9532 2 4 0 2 0 3 0 41 54 111 106 27 533 0 0 1 0 1 0 0 11 2 74 73 81 9534 2 0 3 1 1 2 0 36 45 23 148 127 4335 2 1 5 0 1 1 5 162 165 131 24 92 25

Stage 4

41 2 0 2 0 4 0 0 0 1 1 0 242 0 2 0 0 1 0 0 0 1 0 0 043 2 0 0 0 0 0 2 0 0 0 1 144 1 0 0 0 0 1 0 0 0 0 0 145 0 3 0 1 2 0 0 2 1 0 0 046 3 1 0 1 2 0 0 2 0 0 0 1









Stage 111 227 24 48 7312 17 47 0 6513 900 738 84 37

Stage 2

21 7 3 3 133 156 180 239 38322 4 2 23 172 121 144 234 9623 2 4 1 45 0 66 27 024 2 1 0 3 0 73 33 71

Stage 3

31 5 0 1 2 2 1 4 0 4 129 11 134 6432 3 2 0 2 0 2 1 4 3 100 53 57 4933 1 0 1 0 1 0 0 0 81 75 50 139 10734 0 1 3 0 0 4 0 80 50 49 174 36 12535 1 5 0 1 3 1 1 180 172 64 27 0 77

Stage 4

41 1 1 1 0 0 2 1 1 1 0 1 042 0 1 0 0 0 1 0 0 1 0 0 043 1 0 2 0 0 0 3 0 0 2 0 144 2 0 0 0 0 1 0 0 0 0 1 045 3 0 2 3 0 0 1 3 0 1 0 046 1 0 2 1 0 1 0 0 1 0 0 1





Acknowledgments



References












































































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in






Stage 111 0 0 0 3412 5 646 17 013 1615 154 6 15

Stage 2

21 379 392 190 237 32722 38 0 8 261 45923 0 10 10 0 224 0 0 48 0 0

Stage 3

31 6 28 194 163 1 532 0 9 114 13 146 10033 0 0 0 27 168 5634 126 61 1 154 0 13735 291 366 0 8 0 72

Demand 400 450 300 350 300 350



Stage 111 29 142 72 15812 120 43 150 2413 576 845 194 128

Stage 2

21 12 0 19 177 115 148 90 16422 9 6 8 189 139 51 183 421

23 0 0 0 104 78 130 74 12

24 0 0 0 136 30 15 91 37

Stage 3

31 1 2 1 3 1 0 0 67 95 130 69 126 9532 2 4 0 2 0 3 0 41 54 111 106 27 533 0 0 1 0 1 0 0 11 2 74 73 81 9534 2 0 3 1 1 2 0 36 45 23 148 127 4335 2 1 5 0 1 1 5 162 165 131 24 92 25

Stage 4

41 2 0 2 0 4 0 0 0 1 1 0 242 0 2 0 0 1 0 0 0 1 0 0 043 2 0 0 0 0 0 2 0 0 0 1 144 1 0 0 0 0 1 0 0 0 0 0 145 0 3 0 1 2 0 0 2 1 0 0 046 3 1 0 1 2 0 0 2 0 0 0 1









Stage 111 227 24 48 7312 17 47 0 6513 900 738 84 37

Stage 2

21 7 3 3 133 156 180 239 38322 4 2 23 172 121 144 234 9623 2 4 1 45 0 66 27 024 2 1 0 3 0 73 33 71

Stage 3

31 5 0 1 2 2 1 4 0 4 129 11 134 6432 3 2 0 2 0 2 1 4 3 100 53 57 4933 1 0 1 0 1 0 0 0 81 75 50 139 10734 0 1 3 0 0 4 0 80 50 49 174 36 12535 1 5 0 1 3 1 1 180 172 64 27 0 77

Stage 4

41 1 1 1 0 0 2 1 1 1 0 1 042 0 1 0 0 0 1 0 0 1 0 0 043 1 0 2 0 0 0 3 0 0 2 0 144 2 0 0 0 0 1 0 0 0 0 1 045 3 0 2 3 0 0 1 3 0 1 0 046 1 0 2 1 0 1 0 0 1 0 0 1





Acknowledgments



References












































































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in






Stage 111 227 24 48 7312 17 47 0 6513 900 738 84 37

Stage 2

21 7 3 3 133 156 180 239 38322 4 2 23 172 121 144 234 9623 2 4 1 45 0 66 27 024 2 1 0 3 0 73 33 71

Stage 3

31 5 0 1 2 2 1 4 0 4 129 11 134 6432 3 2 0 2 0 2 1 4 3 100 53 57 4933 1 0 1 0 1 0 0 0 81 75 50 139 10734 0 1 3 0 0 4 0 80 50 49 174 36 12535 1 5 0 1 3 1 1 180 172 64 27 0 77

Stage 4

41 1 1 1 0 0 2 1 1 1 0 1 042 0 1 0 0 0 1 0 0 1 0 0 043 1 0 2 0 0 0 3 0 0 2 0 144 2 0 0 0 0 1 0 0 0 0 1 045 3 0 2 3 0 0 1 3 0 1 0 046 1 0 2 1 0 1 0 0 1 0 0 1





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



research article designing a multistage supply chain...

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