Page - 140 - in Algorithms for Scheduling Problems

Algorithms 2018,11, 54 Table5.Cont. Market1 Market2 Market3 Market4 Market1 Market2 Market3 Market4 Market9 Market10 Plant8 0 0 0 0 0 1836 0 0 0 0 Plant9 0 0 0 1566 0 0 0 0 0 0 Plant10 1724 0 0 0 0 0 0 0 0 0 Objective functionvalue=723,977 2. ScenarioofBoundedRationalDecisionMaker TheProfitsunderboundedrationality for test case3arepresented inTable6. Boundedrationality factorβ=100. Table6.Profitsunderboundedrationality for test case3. CasesforBoundedRationalityConditionswithVaryingβParameter β Totalprofits %DeviationfromAchievableProfits 0 723,908 0.53 10 615,322 2.19 100 553,790 2.85 1000 498,411 2.68 10,000 448,570 2.61 100,000 723,908 3.45 4.4. ComparativeAnalysis Foraproblemsizeof2 (dualmarket scenario), therearevariouspossiblecasesandscenarios that mightarisedue to the tradeoffsbetweenthepricesandthecosts. Inorder toevaluate thefinancial desirabilityof theoptionsprocessingactions for everyproduct, the investmentdecisionsdeclined. For theanalysisofvariouspossiblecases in thedualmarketscenario,wetake thevalueaddition into consideration,whichrepresents theper-unitprofitof thecompany,dueto theparticularpathtaken in theproductionallocation. Letv1denote thevalueadditiondue topath fromplant 1 tomarket 1, similarly, v2 be for plant 1 tomarket 2, v3 for plant 2 tomarket 1 andv4 for plant 2 tomarket 2. Theprobableorderingsof the fournetvaluesare24 (=4!) without consideringanyassumption, buttheirdefinitionssuggestaninterdependence,v4≥v1⇒v2≥v3,whichremoves6orderings(where, asmentionedearliervi represents theperunitprofitvalueaddition inanypath). Theoutstanding18 aredistributedintotwoclusters,oneofwhichisareplicaof theother. Thefollowingstudyemphasizes the 9 orderings because of symmetry in results. These result in 4possible allocation strategies of market focused,centralizedwith twopossiblecentralizationandhybridtypeofmodelas indicated inFigure6. Table 7 depicts 1 of the 9 possible scenarioswhich is analyzed under cases of deterministic demand,uniformdemandanduniformdemandunderboundedrationality,andthe totalprofits (T.P) ineachcase is found. For thecaseofuniformdistribution, theFrankWolfe’sBenderdecomposition methodiscomparedwith theRosen’sgradientsearchmethodwhich isdepicted in theFigure7. 140