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 ID x coordinate y coordinate Demand
1 35 7 12
2 93 75 24
3 53 95 16
4 51 81 7
5 51 55 9
6 1 67 20
7 9 23 10
8 75 7 18
9 15 97 26
10 79 5 17
11 9 19 2
12 39 1 11
13 47 1 9
14 33 97 12
15 27 83 11
16 83 79 12
17 17 59 23
18 47 19 7
19 57 9 1
20 87 41 26
21 55 25 10
22 21 91 9
23 21 13 22
24 67 1 21
25 59 21 17
26 1 75 2
27 33 85 15
28 25 21 16
29 45 29 14
30 63 77 23
31 1 77 24
32 77 41 2
33 35 11 12
34 9 77 18
35 61 87 5
36 59 91 19
37 63 79 15
38 97 67 8
39 9 45 6
40 93 21 14
41 83 71 13
42 95 57 5
43 31 69 24
44 77 17 25
45 63 57 2
46 3 63 8
47 11 69 14
48 7 9 2
49 37 65 13
50 75 83 10
51 15 53 6
52 69 5 6
53 69 27 24
54 5 19 21
55 49 31 20
56 77 17 24
57 15 7 4
58 91 39 19
59 79 17 14
60 67 75 23
61 93 51 2
62 25 33 16
63 9 19 23
64 3 65 14
Distribution centre
25 51

 

Last Updated on January 22, 2018 by Essay Pro