MIP modelsforconnectedfacilitylocation:Atheoreticaland computationalstudy

This articlecomprisesthefirsttheoreticalandcomputationalstudyonmixedintegerprogramming (MIP)modelsfortheconnectedfacilitylocationproblem(ConFL).ConFLcombinesfacilitylocationand Steiner trees:givenasetofcustomers,asetofpotentialfacilitylocationsandsomeinter-connection nodes, ConFLsearchesfortheminimum-costwayofassigningeachcustomertoexactlyoneopen facility,andconnectingtheopenfacilitiesviaaSteinertree.ThecostsneededforbuildingtheSteiner tree,facilityopeningcostsandtheassignmentcostsneedtobeminimized. We modelConFLusingsevencompactandthreemixedintegerprogrammingformulationsof exponentialsize.WealsoshowhowtotransformConFLintotheSteinerarborescenceproblem.Afull hierarchybetweenthemodelsisprovided.Fortwoexponentialsizemodelswedevelopabranch-and- cut algorithm.Anextensivecomputationalstudyisbasedontwobenchmarksetsofrandomly generatedinstanceswithupto1300nodesand115,000edges.Weempiricallycomparethepresented modelswithrespecttothequalityofobtainedboundsandthecorrespondingrunningtime.Wereport optimalvaluesforallbut16instancesforwhichtheobtainedgapsarebelow0.6%.