Seite - 178 - in Algorithms for Scheduling Problems

Algorithms 2018,11, 35 riskprotocolsgeneratedatdifferentSCunits.Assessmentof the levelofentropyfor therisksallows thedecisionmaker, stepbystep, toassess theentropyin theSCmodeland,consequently, to increase theamountofusefulknowledge.Asaresult,wearriveatareducedgraphmodelof thesupplychain suchthat it containsessentially thesameamountof informationaboutcontrollableparametersas the completeSCgraphbutmuchsmaller insize. Anattractivedirectionfor furtherresearch is to incorporate thehumanfactorand, inparticular, theeffectofhumanfatigue (see [22])onperformanceof industrial supplychainsunderuncertainty in dynamicenvironments. Acknowledgments:Therearenograntsorothersourcesof fundingof this study. AuthorContributions:BorisKriheli contributedto theoverall idea,modelandalgorithm,aswellas thedetailed writingof themanuscript; EugeneLevner contributed to theoverall ideas anddiscussionson the algorithm, aswellas thepreparationof thepaper. Conflictsof Interest:Theauthorsdeclarenoconflictof interest. References 1. Fera,M.;Fruggiero,F.;Lambiase,A.;Macchiaroli,R.;Miranda,S.Theroleofuncertainty insupplychains underdynamicmodeling. Int. J. Ind. Eng.Comput. 2017,8, 119–140. [CrossRef] 2. Calinescu,A.; Efstathiou, J.; Schirn, J.; Bermejo, J.Applying andassessing twomethods formeasuring complexity inmanufacturing. J.Oper. Res. Soc. 1998,49, 723–733. [CrossRef] 3. Sivadasan,S.;Efstathiou, J.;Calinescu,A.;Huatuco,L.H.Advancesonmeasuringtheoperationalcomplexity ofsupplier–customersystems.Eur. J.Oper. Res. 2006,171, 208–226. [CrossRef] 4. Sivadasan,S.;Efstathiou, J.; Frizelle,G.;Shirazi,R.;Calinescu,A.Aninformation-theoreticmethodology formeasuringtheoperationalcomplexityofsupplier-customersystems. Int. J.Oper. Prod.Manag. 2002,22, 80–102. [CrossRef] 5. Sivadasan, S.; Smart, J.; Huatuco, L.H.; Calinescu,A.Reducing schedule instability by identifying and omittingcomplexity-adding informationflowsat thesupplier–customer interface. Int. J.Prod. Econ. 2013, 145, 253–262. [CrossRef] 6. Battini,D.;Persona,A.TowardsaUseofNetworkAnalysis:QuantifyingtheComplexityofSupplyChain Networks. Int. J.Electron.Cust. Relatsh.Manag. 2007,1, 75–90. [CrossRef] 7. Isik,F.AnEntropy-basedApproachforMeasuringComplexity inSupplyChains. Int. J.Prod. Res. 2010,48, 3681–3696. [CrossRef] 8. Allesina,S.;Azzi,A.;Battini,D.;Regattieri,A.PerformanceMeasurement inSupplyChains:NewNetwork AnalysisandEntropic Indexes. Int. J.Prod. Res. 2010,48, 2297–2321. [CrossRef] 9. Modraka,V.;Martona,D.StructuralComplexityofAssemblySupplyChains:ATheoreticalFramework. Proced. CIRP2013,7, 43–48. [CrossRef] 10. Ivanov,D.Entropy-BasedSupplyChainStructuralComplexityAnalysis. InStructuralDynamicsandResilience in Supply Chain Risk Management; International Series inOperations Research&Management Science; Springer: Berlin,Germany,2018;Volume265,pp.275–292. 11. Kogan,K.;Tapiero,C.S.SupplyChainGames:OperationsManagementandRiskValuation; Springer:NewYork, NY,USA,2007. 12. Levner,E.;Ptuskin,A.Anentropy-basedapproachto identifyingvulnerablecomponents inasupplychain. Int. J.Prod. Res. 2015,53, 6888–6902. [CrossRef] 13. Aven,T.RiskAnalysis;Wiley:NewYork,NY,USA,2015. 14. Harremoës,P.;Topsøe,F.Maximumentropyfundamentals.Entropy2001,3, 191–226. [CrossRef] 15. Herbon,A.;Levner,E.;Hovav,S.; Shaopei,L.SelectionofMost InformativeComponents inRiskMitigation AnalysisofSupplyNetworks:AnInformation-gainApproach. Int. J. Innov.Manag. Technol. 2012,3, 267–271. 16. Knight,F.H.Risk,Uncertainty, andProfit;Hart,Schaffner&Marx: Boston,MA,USA,1921. 17. Zsidisin,G.A.;Ellram,L.M.;Carter, J.R.;Cavinato, J.L.AnAnalysisofSupplyRiskAssessmentTechniques. Int. J.Phys.Distrib. Logist.Manag. 2004,34, 397–413. [CrossRef] 18. Tapiero, C.S.; Kogan, K. Risk andQuality Control in a SupplyChain: Competitive andCollaborative Approaches. J.Oper. Res. Soc. 2007,58, 1440–1448. [CrossRef] 178