Page - 94 - in Algorithms for Scheduling Problems

Algorithms 2018,11, 68 (2) Weproposedabi-objectivesolutiontosolveahybridflowshopwithunrelatedmachines, setup time,andwork inprogressbuffers. It isbasedontheknownNSGA-IIgeneticalgorithm; (3) Wecalibratedouralgorithmusingastatisticalanalysisofmultifactorialvariance. TheANOVA technique isusedtounderstandthe impactofdifferent factorsonthesolutionquality.Abranch andboundalgorithmwasusedtoassert theobtainedperformance. (4) Weprovidedacomprehensive experimental analysis of theproposedsolutionbasedondata fromatortillaproductioncompanyinMexico. (5) Wedemonstratedthatoursolutionsarenotmorethan3.5percentoff theglobaloptimumforboth criteria. Theysavemorethan48percentofproductiontimeand47percentofenergyconsumption comparedwith theactualproductionplanfollowedbythecompany. AuthorContributions:Allauthorscontributedto theanalysisof theproblem,designingalgorithms,performing theexperiments,analysisofdata,andwriting thepaper. Funding: This work is partially supported by Russian Foundation for Basic Research (RFBR), project No.18-07-01224-a. Conflictsof Interest:Theauthorsdeclarenoconflictof interest. References 1. Linn,R.;Zhang,W.Hybridflowshopscheduling:Asurvey.Comput. Ind. Eng. 1999,37, 57–61. [CrossRef] 2. Quadt,D.;Kuhn,H.Ataxonomyofflexibleflowlineschedulingprocedures.Eur. J.Oper. Res. 2007,178, 686–698. [CrossRef] 3. Yaurima,V.;Burtseva,L.;Tchernykh,A.Hybridflowshopwithunrelatedmachines, sequence-dependent setuptime,availabilityconstraintsandlimitedbuffers.Comput. Ind. Eng. 2009,56, 1452–1463. [CrossRef] 4. Ruiz,R.;Vázquez-Rodríguez, J.A.Thehybridflowshopschedulingproblem.Eur. J.Oper. Res. 2010,205, 1–18. [CrossRef] 5. Pei-Wei,T.; Jeng-Shyang,P.;Shyi-Ming,C.;Bin-Yih,L.Enhancedparallel cat swarmoptimizationbasedon theTaguchimethod.ExpertSyst.Appl. 2012,39, 6309–6319. 6. Javanmardi, S.; Shojafar,M.;Amendola,D.;Cordeschi,N.; Liu,H.;Abraham,A.Hybrid JobScheduling AlgorithmforCloudComputingEnvironment. InProceedingsof theFifthInternationalConferenceonInnovations inBio-InspiredComputingandApplications IBICA2014;Komer,P.,Abraham,A.,Snasel,V.,Eds.;Advances in IntelligentSystemsandComputingBookSeries;Springer: Berlin/Heidelberg,Germany,2014;Volume303, pp.43–52. 7. Ribas, I.; Leisten,R.; Framiñan, J.M.Reviewandclassificationofhybridflowshopschedulingproblems fromaproductionsystemandasolutionsprocedureperspective.Comput.Oper. Res. 2010,37, 1439–1454. [CrossRef] 8. Luo,H.;Du,B.;Huang,G.;Chen,H.;Li,X.Hybridflowshopschedulingconsideringmachineelectricity consumptioncost. Int. J.Prod. Econ. 2013,146, 423–439. [CrossRef] 9. Mori,M.;Fujishima,M.; Inamasu,Y.;Oda,Y.Astudyonenergyefficiency improvement formachine tools. CIRPAnn.Manuf. Technol. 2011,60, 145–148. [CrossRef] 10. Blum,C.;Chiong,R.;Clerc,M.;DeJong,K.;Michalewicz,Z.;Neri,F.;Weise,T.Evolutionaryoptimization. InVariants ofEvolutionaryAlgorithms forReal-WorldApplications;Chiong,R.,Weise,T.,Michalewicz,Z.,Eds.; Springer: Berlin/Heidelberg,Germany,2012;pp.1–29. 11. Liu,Y.;Dong,H.; Lohse,N.; Petrovic, S.Reducingenvironmental impactofproductionduringa rolling blackout policy—Amulti-objective schedule optimisation approach. J. Clean. Prod. 2015, 102, 418–427. [CrossRef] 12. Nilakantan, J.;Huang,G.;Ponnambalam,S.Aninvestigationonminimizingcycle timeandtotal energy consumption inroboticassembly linesystems. J.Clean. Prod. 2015,90, 311–325. [CrossRef] 13. Wang,S.;Lu,X.;Li,X.;Li,W.Asystematicapproachofprocessplanningandschedulingoptimizationfor sustainablemachining. J.Clean. Prod. 2015,87, 914–929. [CrossRef] 14. Liu,C.;Huang,D.Reductionofpower consumptionandcarbon footprintsbyapplyingmulti-objective optimisationviageneticalgorithms. Int. J.Prod. Res. 2014,52, 337–352. [CrossRef] 94