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1、Chapter5:NetworkDesignintheSupplyChainExerciseSolutions1.(a)Theobjectiveofthismodelistodecideoptimallocationsofhomeoffices,andnumberoftripsfromeachhomeoffice,soastominimizetheoverallnetworkcost.Theoverallnetworkcostisacombinationoffixedcostsofsettinguphomeofficesandthetotaltripcosts.Ther
2、earetwoconstraintsetsinthemodel.Thefirstconstraintsetrequiresthataspecifiednumberoftripsbecompletedtoeachstatejandthesecondconstraintsetpreventstripsfromahomeofficeiunlessitisopen.Also,notethatthereisnocapacityrestrictionateachofthehomeoffices.Whileafeasiblesolutioncanbeachievedbylocatin
3、gasinglehomeofficeforalltripstoallstates,itiseasytoseethatthismightnotsaveontripcosts,sincetripratesvarybetweenhomeofficesandstates.Weneedtoidentifybetterwaystoplantripsfromdifferenthomeofficestodifferentstatessothatthetripcostsareataminimum.Thus,weneedanoptimizationmodeltohandlethis.Opt
4、imizationmodel:n=4:possiblehomeofficelocations.m=16:numberofstates.Dj=AnnualtripsneededtostatejKi=numberoftripsthatcanbehandledfromahomeofficeAsexplained,inthismodelthereisnorestrictionfi=Annualizedfixedcostofsettingupahomeofficecij=Costofatripfromhomeofficeitostatejyi=1ifhomeofficeiisop
5、en,0otherwisexij=Numberoftripsfromhomeofficeitostatej.Itshouldbeintegralandnon-negativePleasenotethat(5.2)isnotactiveinthismodelsinceKisaslargeasneeded.However,itwillbeusedinanswering(b).19SYMBOLINPUTCELLDjAnnualtripsneededtostatejE7:E22cijTransportationcostfromofficeitostatejG7:G22,I7:I
6、22,K7:K22,M7:M22fifixedcostofsettingupofficeiG26,I26,K26,M26xijnumberofconsultantsfromofficeitostatej.F7:F22,H7:H22,J7:J22,L7:L22obj.objectivefunctionM315.1demandconstraintsN7:N22(SheetSCconsultinginworkbookexercise5.1.xls)19Withthiswesolvethemodeltoobtainthefollowingresults:StateTotal#o
7、ftripsTripsfromLACostfromLATripsfromTulsaCostfromTulsaTripsfromDenverCostFromDenverTripsfromSeattleCostfromSeattleWashington40-150-250-2004025Oregon35-150-250-2003575California10010075-200-150-125Idaho25-150-200-12525125Nevada4040100-200-125-150Montana25-175-175-12525125W
