Page - 131 - in Algorithms for Scheduling Problems

Algorithms 2018,11, 54 accordinglywhentravellersbehaveboundedlyrational.DiandLiu[32]presentedacomprehensive reviewofmodelsaswellasmethodologiesofboundedrationalityroutechoicebehavior. Themodels aremainlydivided into twoparts: substantiveandproceduralboundedrationalitymodels.While methodologies appliedon these twomodels aregame theoryand interactive congestiongame for substantiveboundedrationality,andrandomutilityandnon-orsemi-compensatoryforprocedural boundedrationality. 3.MathematicalModelFormulation Thepresentresearchinvestigatestheoperationspolicyofamulti-nationalfirmwhichmakesgoods forservinggeographicallydisjointedmarketswith localizedfinalassembliesand jointparts. The joint partcanbeshippedfromthemarketswithdiversefinancialanddemandfeatures. Thecostrequiredfor transferringthe jointcomponents (intermediategoodsbetweenmarkets),andfor foreigntradebarriers like tariffs andduties provides the total transportation cost. The generalized operations strategy structure is illustrated inFigure1 formultiple-productandmultiple-marketmodelwithcommonality. Figure1.Generalizedmulti-productmulti-marketnetworkdesign. Thisstudydealtwith thestrategic facility locationdecisionofengineproductionbytaking into account thefinancialanddemandfeatures. Thenewsvendornetworkapproach isusedtoevaluate themodel. Firstly, we analyze the scenario under deterministic demand. The sensitivity of the trade-off between themanufacturing costs and the transportation costs are examined. Secondly, thesituationunderdemanduncertainty isevaluated.Here,weassumeuniformlydistributeddemand. Theprofit function is accordingly formulated and similar analysis is carried out. The function is solvedusingFrankWolfe’s sequential linearizationtechniquewithBender’sDecompositionmethod. Thirdly, theresultsofoptimaldecisionscenario iscomparedwith thescenarioofboundedrationality consideringuniformlydistributeddemand.Whenweconsider theboundedrationality, thebestoption isnotalwayspickedbyindividuals,however, theyopt forbetteroptionsoften. Finally,we intendto giveastatisticalproofof the superiorityof thealgorithmusedover the traditionalgradient search 131