Heuristic andexactalgorithmsforamin–maxselectivevehicle routing problem

In thiswork,weinvestigateavehicleroutingproblemwherenotallclientsneedtobevisitedandthegoal is tominimizethelongestvehicleroute.Weproposetwoexactsolutionapproachesforsolvingthe problem:aBranch-and-cut(BC)algorithmandaLocalBranching(LB)methodthatusesBCasitsinner solver.Ourcomputationalexperienceindicatesthat,inpractice,theproblemisdifficulttosolve,mainly when thenumberofvehiclesgrows.Inadditiontotheexactmethods,wepresentaheuristicthatrelieson GRASPandontheresolutionofarestrictedintegerprogrambasedonasetcoveringreformulationforthe problem.TheheuristicwascapableofsignificantlyimprovingthebestsolutionsprovidedbyBCandLB,in one tenthofthetimestakenbythemtoachievetheirbestupperbounds.