Page - 130 - in Algorithms for Scheduling Problems

Algorithms 2018,11, 54 thatmuchcaptivatingalternativesareselectedfrequently. Theresulting formulation ledtoaquadratic optimizationwith linearconstraints. Exactmethods like Benders’ decompositionmethod (Benders, 1962) are frequently found in applications of operationsmanagement. Bahl et al. [14]were amongst the first to usemulti-item productionscheduling. Benders’decompositionmethodshavealso foundapplications indiscretely constrained mathematical programs [15]. Even stochastic optimization problems have found applicationsofBenders’decompositionmethods. Archibaldet al. [16] compared theperformance ofDynamic programmingversus the nestedBenders’ decompositionmethod for optimization of hydro-electric generation problems. Velarde et al. [17] implemented a heuristic based Benders’ decompositionmethod for the robust international sourcingmodel. Themethodology involved generation of cuts via Tabu search, using the dual variables from the sub-problem to obtain the neighborhoods. Benders’ decompositionmethod has been employed to solve the strategic and operations management problems, especially in networks based problems, which as such can be solved by linear programming methods. Ali et al. utilized it for solving multi-commodity networkproblems [18]. Doganetal. [19]usedBendersdecompositionmethodfor solvingamixed integerprogrammingproblemfor the strategicproduction-distributionallocationproblemfor the supplychainnetwork. Benders’decompositionmethodisalsoutilized inproject timecompression problems inCriticalPathMethod(CPM)/ProgrammeEvaluationReviewTechnique (PERT)networks, byapproximating theconvexorconcaveactivitycost-durationfunctions topiecewise linear timecost curves [20]. TheFrank-Wolfealgorithmisusedtosolvequadraticprogrammingproblemswith linear constraints [21]. Lee et al. [22] investigatedaplant allocation and inventory level decisions for servingglobal supplychainsandrevealedthat the importingfirmescalates its inventory level if the transportation cost increasesor theexchangerateof the inventorycountry lessen. Theresultof this studyhasbeen empirically confirmedusingdata ofKoreanfirmsyielded from theExport-Import BankofKorea. Jean et al. [23] studied the relationship-based product innovation in global supply chainswhere this research offered a context-based explanation for the contradictory and conflicting empirical indication with respect to relational capital innovation links. In another study, a single period inventorymodel has been proposed to encapsulate the trade-off between inventory policies and disruptionrisksconsidering thescenarioofdual-sourcingsupplychain [24]. Tangetal. [25]examined multiple-attributedecisionmakingusingPythagorean2-tuple linguisticnumbers,andproposedtwo operators,namely,Pythagorean2-tuple linguisticweightedBonferronimean(WBM)andPythagorean 2-tuple linguisticweightedgeometricBonferronimean (WGBM). Further, the effectiveness of this approach isverifiedconsidering thegreensupplier selectionproblem. Zhangetal. [26]developed agreedy insertionheuristic algorithmusing amulti-stagefilteringmechanismcomprising coarse granularity andfinegranularity filtering for ameliorating the energy efficiency of singlemachine schedulingproblems. A two-product,multi-periodnewsvendorproblemhasbeen formulatedby ZhangandYang[27]consideringfixeddemand. Inaddition, this researchusedtheonline learning methodforperformingtheexperiment, andalsoproposedrealand integervaluedonlineordering policies. Egri andVancza [28]presentedanextendedversionof thenewsvendormodel to fulfilall demandsof thecustomerbythesupplier. Thismodelparticularlyminimizes the total cost comprising setup,obsolete inventoryandinventoryholdingcosts. Furthermore, themodelhasbeendeveloped consideringthedecentralizedsettingusingasymmetric informationofcustomerandsupplier. Renand Huang[29]summarizedseveralmethodsofmodelingcustomerboundedrationalityandalsosurveyed implementation of approacheswith respect to appropriate operationsmanagement settings. In a dyadicsupplychain,Duetal. [30]examinedfairnesspreferencesespecially individuals’psychological understanding.Moreover, to formulate the fairnessconcerns, theyusedNashbargainingsolutionas fairness reference. Dietal. [31]developedasystematicmethodology toobtainboundedly rational user equilibria (BRUE) solutions for networkswithfixeddemands that assist inpredictingBRUE linktrafficflowpatterns inagivennetworktoguideplanners formakingnetworkdesigndecisions 130