The travelingpurchaserproblemwithbudgetconstraint

Let usconsiderasetofmarketsplusadepotandasetofproductsforeachofwhichapositivedemand is specified.Eachproductismadeavailableinasubsetofmarketsineachofwhichonlyagivenquantity, less thanorequaltotherequiredone,canbepurchasedatagivenunitprice.Thedistancebetweeneach couple ofmarketsandbetweeneachmarketandthedepotisknown.TheTravelingPurchaserProblem with Budgetconstraint(TPP-B)looksforasimplecyclestartingatandendingtothedepotandvisiting a subsetofmarketsataminimumtravelingcostandsuchthatthedemandforeachproductissatisfied and thecostgloballyspentforpurchasingtheproductsdoesnotexceedadefinedbudgetthreshold.As the TPPalsothisproblemarisesinseveralapplicationdomains,butwhiletheformerhasbeenlargely studied, veryfewcontributionsexistintheliteraturefortheTPP-B.Weproposeandcomparetwosolution algorithms, anenhancedlocal-searchheuristicandavariableneighborhoodsearch(VNS)approachalso tested inamulti-startvariant.Theproposedalgorithmshavebeenusedtosolveboththecapacitated and theuncapacitatedversionoftheproblem.Testproblemshavebeenobtainedbyaddingabudget constraint toknownbenchmarkinstancesfortheTPP.