Lower boundsforthemixedcapacitatedarcroutingproblem

Capacitated arcroutingproblems(CARP)ariseindistributionorcollectingproblemswhereactivitiesare performed byvehicles,withlimitedcapacity,andarecontinuouslydistributedalongsomepre-defined links ofanetwork.TheCARPisdefinedeitherasanundirectedproblemorasadirectedproblemdepend- ing onwhethertherequiredlinksareundirectedordirected.Themixedcapacitatedarcroutingproblem (MCARP) modelsamorerealisticscenariosinceitconsidersdirectedaswellasundirectedrequiredlinks in theassociatednetwork.WepresentacompactflowbasedmodelfortheMCARP.Duetoitslargenum- ber ofvariablesandconstraints,wehavecreatedanaggregatedversionoftheoriginalmodel.Although this modelisnolongervalid,weshowthatitprovidesthesamelinearprogrammingboundthanthe original model.Differentsetsofvalidinequalitiesarealsoderived.Thequalityofthemodelsistestedon benchmark instanceswithquitepromisingresults.