The gravitymultipleserverlocationproblem

Modelsforlocatingfacilitiesandserviceproviderstoserveasetofdemandpointsareproposed.The numberoffacilitiesisunknown,however,thereisagivennumberofserverstobedistributedamong the facilities.EachfacilityactsasanM/M/kqueuingsystem.Theobjectivefunctionistheminimization of thecombinedtraveltimeandthewaitingtimeatthefacilityforallcustomers.Thedistributionof demandamongthefacilitiesisgovernedbythegravityrule.Twomodelsareproposed:astationaryone and aninteractiveone.Inthestationarymodelitisassumedthatcustomersdonotconsiderthewaiting time atthefacilityintheirfacilityselectiondecision.Intheinteractivemodelweassumethat customersknowtheexpectedwaitingtimeatthefacilityandconsideritintheirfacilityselection decision.Theinteractivemodelismorecomplicatedbecausetheallocationofthedemandamongthe facilitiesdependsonthedemanditself.Themodelsareanalyzedandthreeheuristicsolutionalgorithms are proposed.Thealgorithmsweretestedonasetofproblemswithupto1000demandpointsand20 servers.