Title of article :
Models foratravelingpurchaserproblemwithadditionalside-constraints
Author/Authors :
Luis Gouveia، نويسنده , , AnaPaias ، نويسنده , , StefanVo? b، نويسنده ,
Issue Information :
ماهنامه با شماره پیاپی سال 2011
Abstract :
The travelingpurchaserproblem(TPP)istheproblemofdeterminingatourofapurchaserthatneedsto
buy severalitemsindifferentshopssuchthatthetotalamountoftravelandpurchasecostsis
minimized.Motivatedbyanapplicationinmachinescheduling,westudyavariantoftheproblemwith
additionalconstraints,namely,alimitonthemaximumnumberofmarketstobevisited,alimitonthe
numberofitemsboughtpermarketandwhereonlyonecopyperitemneedstobebought.Wepresent
an integer linearprogramming (ILP) modelwhichisadequateforobtainingoptimalintegersolutionsfor
instanceswithupto100markets.WealsopresentandtestseveralvariationsofaLagrangianrelaxation
combinedwithasubgradientoptimizationprocedure.Therelaxedproblemcanbesolvedbydynamic
programmingandcanalsobeviewedasresultingfromapplyingastatespacerelaxationtechniquetoa
dynamicprogrammingformulation.TheLagrangianbasedmethodiscombinedwithaheuristicthat
attemptstotransformrelaxedsolutionsintofeasiblesolutions.Computationalresultsforinstances
with upto300marketsshowthatwiththeexceptionofafewcases,thereporteddifferencesbetween
best upperboundandlowerboundvaluesontheoptimalsolutionsarereasonablysmall.
Keywords :
Traveling purchaser problem , Dynamic programming , State space relaxation , Discretized (time-dependent) formulation
Journal title :
Computers and Operations Research
Journal title :
Computers and Operations Research
