Seite - 75 - in Algorithms for Scheduling Problems

Algorithms 2018,11, 68 Theproductiondecisionsscheduleworktomachines ineachstage todeterminetheprocessing order according to one ormore criteria. Hybrid flow shop scheduling problems are commonly encountered in manufacturing environments. A large number of heuristics for different HFS configurationsconsideringrealisticproblemshavebeenproposed[1–6]. Inspiteof significant researchefforts, someaspectsof theproblemhavenotyetbeensufficiently explored. For example, previousworksdealmostlywith improving the efficiency of production, whereobjective functionsareusuallyusedtominimize the totalproduction time(makespan), the total tardiness, etc. [7].Althoughtheproductionefficiency isessential, it isnot theonly factor toconsider in manufacturingoperations.Oneof themainmotivationsof thiswork is toreduceenergyconsumption. Inrecentyears, ithasbeenrecognizedthathighenergyconsumptioncan increaseoperational costand causenegativeenvironmental impacts [8]. In thispaper,weproposeageneticalgorithmthatcontributes to thesolutionofabi-objectiveHFS problemofareal tortillaproductionenvironment,withunrelatedmachines, setuptime,andwork in progressbufferstakingintoaccountthetotalcompletiontimeandenergyconsumptionofthemachines. Therestof thepaper isorganizedas follows.Afterpresentingthedescriptionandcharacteristics of theproduction lineand jobs inSection2,wediscuss relatedwork inSection3. Wedescribe the modelof theprobleminSection4.Wepresent thedetailsof theproposedsolution inSection5and thealgorithmcalibration inSection6.Wediscusscomputationalexperimentsandresults inSection7. Finally,weconcludewithasummaryandanoutlook inSection8. 2. ProductionProcess Figure 1 shows the eightmain stages of the productionprocess: (1) Preparation, (2)Mixing, (3)DivisionandRounding, (4)Repose, (5)Press, (6)Bake, (7)Cooling, (8)StackingandPacking. Figure1.Tortillaproduction line. In thispaper,weconsiderahybridflowshopwithsixstages (from2to7),withdifferentnumbers ofmachines in thestages2, 4, and6. In theproductionofwheatflour tortillas, the rawingredients prepared in Stage 1 are transferred to a largemixer (Stage 2), where they are combined to create thedough. Corntortillaproductionstartswithaprocesscallednixtamalization, inwhichthecorn is soaked inanalkali solutionof lime(calciumhydroxide)andhotwater. Thedoughisdividedinto fragments withroundshapes (Stage3). These fragmentsrepose inacontrolledenvironment toobtainacertain consistencyas to the temperatureandhumidity (Stage4).Next, theyarepressedto take theshapeofa tortilla (Stage5). Rowsof tortillasareheated instoves (Stage6). Thenextstepsare tocool (Stage7), stack,andpackthem(Stage8). 75