Thisstudy is afacilitylocationandtask allocationproblem ofathree-levelsupplychainunderstochasticdemandforonesuchproduct inaperiodof time withlead time andinventory costsat thestrategic andtacticallevels, Consistingofplants, distributors (wholesalers) and retailers and three-levelsupplychainisselectedbecausethe literatureinthis areaisweak.Decisionsincludelocatinganumberofproductionfacilitiesand distribution centersamong afinite setofpotentialsitesand allocationof tasksbetweenproduction centersand distributioncenters andretailers(demand) for minimizingcosts, that thecosts includethe costof establishingplants and distribution centers, and maintenancecost of productsin distribution centersandtraortation costsofgoods,In additiontoorderingcostperunit timeis considered.Rememberalsotoconsiderthe safety stock for all distribution center, the model include themaintenance cost of safety stock. Stochasticdemand forgoods tobe sentto distribution centersbythe demandcentersandfrom thereordered to theplants (or plant). Eachretailer,the amountof productneededonlyonedistribution centerreceives and it is impossible to send theproducts directlyfrom the plantstoretailers.As well asdistribution centers, productrequirementsbased ondemandcontentreceived fromretailer (or retailers),maketoorderplant and receivedgoodsstoredintheir warehousesand thensendingthemtodemandcenters.sincecustomer demandisrandomandis assumedtofollowanormal distribution with meanand variancegiven, thevaluesafety stockinthedistribution center, to prevent unforeseenshortagesof goodsis maintained.Alsofor consider thestochastic demand,five demand scenariohas been developed.Demandof retailers ineach scenariois representedasa vectorthat the demandvectorsfollowa normal distribution with equal meanand differentvariance.Finally,the bestscenarioisto havethe lowest valueof the objective function, isselectedas theanswer toevery problem.Animportant feature ofthis model, consider the selectablelevels ofcapacityfor thedistributioncentersthatleadtoflexibility indeterminingthesize ofthedistribution centers.This isaintegerprogramming modelis formulatedto beintegrated and exact solutionforsmallsized problemsusingLingosoftwareis provided.Also,given that theproblemi-Hard, ameta-heuristic algorithmssuch as geneticsto solve thisproblemhave been proposed. The resultsobtained fromgenetic algorithmandcompare it with theresultsobtained fromLingosoftwaresolutionforsmall sized problems, indicate theeffectiveness ofthe proposedgenetic algorithm.
