Page - 129 - in Algorithms for Scheduling Problems

Algorithms 2018,11, 54 maximize the totalprofitof thefirm,byoptimallydecidingwhere to locate thecommoncomponent manufacturing setup, andalso the individual transportationquantities. This situation is analyzed usingtheNewsvendorModel. The notion of bounded rationality in operationmanagementwas taken from the economics literature. Initially, the “bounded rationality” termwas introduced by Simon [2] to denote the decision-makingbehaviorswherethedecisionmakerfindsthealternatives. Later, scholarsconstructed diversemodel frameworks to cover agents’ bounded rationality by the quantal responsemodel. Toaccount for the limitations in thenormativeapproachadoptedbyatraditionalNewsvendorModel, which assumes that decisionmakers areperfect optimizers, thedescriptive approachof bounded rationality is incorporated. Thedecisionmodelofboundedrationality isbasicallybasedonclassical quantal choice theory [3]. Consideringallpossibleutilitygeneratingalternatives tobe thecandidates forselection,decisionmakers try tochoosemuchcaptivatingalternatives (obtaininggreaterutility) because theirprobabilityof selection ishigh. For thispurpose, theanalyticallyconvenient logit choice modelcanbeusedwhereselectionprobabilityofalternate j isproportional toexp(uj) [4]. Thequantal choicemodels take intoaccount thatdecisionmakersmaycommiterrors. It isnotnecessary thatone alwaysmakes thebestdecisions;betterdecisionsaremadefrequently. Thus,weformulate theproblemwith the frameworkofboundedrationality for themulti-market network design. The resulting formulation leads to a quadratic objective function with linear constraints. Since theconstraintsarenotall equalityconstraints, it isnot simple toreduce theproblem into linear systemof equations. Theproblem is solved throughanovel approachof Frank-Wolfe linearization method along with Generalized Benders’ Decomposition method. The results are comparedwithstandardgradientsearchmethodandthesuperiorconvergence isempiricallyproved. The remainingpartof the text is organizedas follows. InSection2, the literature is reviewed. Themodel andmethodology are described in Section 3. Section 4 discusses the test results and comparativeanalysis. Someconcludingremarksalongwith futureworkaregiven inSection5. 2. LiteratureReview AbroadreviewhasbeenpresentedbySnyder[5]onstochasticandrobust facility locationmodels, illustrating theoptimizationtechniques thathaveevolved in thisarea.HayesandWheelwright [6] describe several approaches such as geographical network analysis, physical facilities analysis, functional analysis and organizational mission analysis, and product-process analysis for the formulationofmulti-plant facility strategy. Skinner [7] proposes the concept of operational focus usingtheproduct-processapproach,andVanMieghem[8]models theapproachofproduct-process focus for amulti-market scenario. CohenandLee [9] are thepioneers towards formulatingglobal manufacturing strategyasamathematicalprogrammingproblemaccounting factors suchas local demand, sourcingconstraintsandtaxations. Organizationsmayselect fordeveloping their facility withrespect toproduct,volumes,orprocess. Luetal. [1]analyzesuchscenariosunderknowndemand andincorporatingscaleeconomies. Theirmodel includes twoproductswithdistinctdemandfeatures, twogeographicallydisjointedmarketswithdiverseeconomicfeatures,andtwoprocesseswithdistinct goalscomprisesofcommoncomponentmanufacturinganddedicatedassembly.Multi-productfirms frequentlyusage thecommonalityof fosterflexibility for theirprocessnetworks. Inanother study, the trade-offs between risk pooling and logistics costwith respect to two extreme configurations suchasprocess andproducthasbeen investigated for commonality inamulti-plantnetwork [10]. Melkoteetal. [11]developsanoptimizationmodel for facility locationandtransportationnetwork designproblem. Rationalityrefers toperfectoptimizationfor thegivenscenario.Onthecontrary, theconceptof boundedrationality identifies the intrinsic imperfections inhumandecisionmaking.Chenetal. [12] describedutilityfunctionsforthedecisionmakerandinferredstochasticprobabilities. Su[13]modeled theboundedrationality includingstochasticelements in thedecisionprocess.Despiteselectingthe utility-maximizingalternativeconstantly,decisionmakersembraceaprobabilisticoptingrulesuch 129