Logistic Modelling

Problem:RoutingofFruitandVegetableDistribution

 

Afruitandvegetable wholesalerdistributesfruits andvegetables toretailers primarily locatedin the SouthEastofEngland.Thefruitsandvegetablesarepackagedinto handerecttrays.Ahomogeneous fleetof9vansdeliverthetraysoffruitsand vegetablesto64retailers.Eachretailerhasaspecificquantityofdemandforthefruits andvegetables,andeachvanhas alimitedcapacityfor carrying100trays. Thevans depart fromthedistributioncentretoservicetheretailerswithknownlocationsand demands, andthenreturntothedistributioncentre. Thelocations oftheretailersare expressedusing(x,y)coordinatesontheEuclideanplane. Thecoordinatesofthe locationsandthedemandsaredescribedinthefile“fruit-vegetable-distribution.xls”on Moodle.

Themainobjectiveistoassignthevanstoroutesto deliverthe fruits andvegetables totheretailerssoastominimisethetotaldistancetravelledbythevans,subjecttothe followinghardconstraints:

 

Eachvandepartsfrom andreturnstothedistributioncentre.

Eachretailer is visitedexactlyonce byasingle van.

Eachvanhasalimitedcapacityof 100trays.

Thetotalloadonanyvanassociatedwithagivenroutemustnotexceedthe capacityofthevan.

Thenumber ofvansavailableatthe distributioncentreis 9.

 

 

  1. 1. Formulate mathematicallythe optimisationmodel of the fruit and vegetable distributionroutingproblemtominimisethetotaldistancetravelledby thevan Describeclearlyindetailyouroptimisationmodel:fitness function,decision variables, andconstraints.Provide anyreferences intheliterature youhave used.

[Maximum 300words excluding references] [10 marks]

 

 

 

2.Consider thedata described inthefile“fruit-vegetable-distributiong.xls”onMoodle.

The datadescribes thecoordinates ofthelocations andthe demands ofretailers, coordinatesofthelocationofthedistribution centre,capacityofthevans,andthe numberofvansavailable atthedistributioncentre.

 

SetuptheExcel spreadsheetandoptimisationmodelsonEvolverandexplain clearlytheimplementationofthedecisionvariables,theconstraints,andthefitness function.IndicatewhichEvolversolvingmethodyouhaveusedtosolvetheproblem andtheinitial solution you have used.

Solvetheproblemtofindthe best minimum distancetravelledby experimenting with thefollowingparameters:

(a) Populationsize:30and 50

(b) Foreachpopulationsize,considerthefollowingcrossoverandmutation rates:

(i)  Crossover rate=0.8,mutationrate= 0.01. (ii) Crossover rate= 0.9,mutationrate= 0.02. (iii)Crossover rate= 0.6,mutationrate= 0.35. (iv)Crossoverrate= 0.4,mutationrate= 0.8.

(c)Thestoppingcriterionfor alltheexperimentsshouldbesetto20000 generations.

 

Foreachcombinationprovideadetaileddescriptionofthebestsolution:totaldistance travelled,set ofroutesto betravelledby thevans,computationtimerequiredto generatethebestsolution.For eachvan,specify theretailerstovisitandtheorderin whichtheyhave tobevisited.

Provideagraphicalillustrationoftheroutesofthevans fortheinitialsolutionandthe overall bestsolutionfor eachpopulationsize.

[Maximum 1200words] [35marks]

 

 

  1. 3. Thebestsolution,b-best,foundintheliteratureforthedataprovidedis1174.

Analyseyourresultsanddiscussthe effectofthepopulation size,crossover and mutationrates onthe qualityofthebestsolutionsforthedifferentcombinations and how thesesolutionscomparetob-best. Provideagraphicalillustrationto comparethequalityofthebestsolutions foundforthe differentpopulationsize, crossover andmutationratecombinationsand howtheycomparetob-best.

                                    [Maximum 500words]

[15marks]

 

 

 

  1. 4. SolvetheproblemusingtheTabusearch(TS)methodwithOptQuestand thesamestoppingconditionasGA, 20000iterations.Comparethesolution qualityandthecomputationtimeofthebestsolutionfoundwithGAandTS. Discussandargumentthedifferenceinthesolutionqualityandcomputationtime ofbothmethods,andhowthesolutionofTScomparestob-best.

[Maximum 500words] [15marks]

 

 

 

 

 

5.GA,TS,andSimulatedAnnealing(SA)havebeenwidelyusedintheliterature to        solve  the  capacitated  vehicle  routing  problem  with  wide-ranging applications inthefields oflogistics and transportation.Discussandcompare theperformance ofGA,TS, andSAinterms solutionqualityandcomputation time insolving thecapacitatedvehiclerouting problem.  Illustratethe performanceanalysisofthesemethodsandthecomparativestudywithsome experimental resultsoncasestudies fromtheliterature.

 

Your essaysshoulddemonstrateliterature research,readingand understanding withalist ofreferences.

[Maximum1000wordsexcludingreferences] [25marks]

 

Routing of Fruit and Vegetable Distribution
Retailer IDx coordinatey coordinateDemand
135712
2937524
3539516
451817
551559
616720
792310
875718
9159726
1079517
119192
1239111
134719
14339712
15278311
16837912
17175923
1847197
195791
20874126
21552510
2221919
23211322
2467121
25592117
261752
27338515
28252116
29452914
30637723
3117724
3277412
33351112
3497718
3561875
36599119
37637915
3897678
399456
40932114
41837113
4295575
43316924
44771725
4563572
463638
47116914
48792
49376513
50758310
5115536
526956
53692724
5451921
55493120
56771724
571574
58913919
59791714
60677523
6193512
62253316
6391923
6436514
Distribution centre
2551

 

Last Updated on January 22, 2018