Logistic Modelling - MyEssayDoc

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. 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]

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]

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
Distribution centre	25	51

Last Updated on January 22, 2018