Acontinuousanalysisframeworkforthesolutionoflocation–allocationproblemswith dense demand

Location–allocation problemsariseinseveralcontexts,includingsupplychainanddatamining.Inits most commoninterpretation,thebasicproblemconsistsofoptimallylocatingfacilitiesandallocatingcus- tomers tofacilitiessoastominimizethetotalcost.Thestandardapproachtosolvinglocation–allocation problems istomodelalternativelocationsitesandcustomersasdiscreteentities.Manyprobleminstances in practiceinvolvedensedemanddataanduncertaintiesaboutthecostandlocationsofthepotential sites. Theuseofdiscretemodelsisofteninappropriateinsuchcases.Thispaperpresentsanalternative methodology wherethemarketdemandismodeledasacontinuousdensityfunctionandtheresulting formulation issolvedbymeansofcalculustechniques.Themethodologyprioritizestheallocationdeci- sions ratherthanlocationdecisions,whichisthecommonpracticeinthelocationliterature.Thesolution algorithm proposedinthisframeworkisalocalsearchheuristic(steepest-descentalgorithm)andis applicable toproblemswheretheallocationdecisionsareintheformofpolygons,e.g.,withEuclidean distances. Extensivecomputationalexperimentsconfirmtheefficiencyoftheproposedmethodology.