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algorithms Article HybridFlowShopwithUnrelatedMachines, SetupTime,andWorkinProgressBuffers for Bi-ObjectiveOptimizationofTortillaManufacturing VictorHugoYaurima-Basaldua1,AndreiTchernykh2,3,*,FranciscoVillalobos-Rodríguez1 and RicardoSalomon-Torres1 ID 1 SoftwareEngineering,SonoraStateUniversity,SanLuisRioColorado,Sonora83455,Mexico; victor.yaurima@ues.mx(V.H.Y.-B.); fco.vr1@gmail.com(F.V.-R.); ricardo.salomon@uabc.edu.mx(R.S.-T.) 2 ComputerScienceDepartment,CICESEResearchCenter,Ensenada22860,Mexico 3 SchoolofElectricalEngineeringandComputerScience,SouthUralStateUniversity,Chelyabinsk454080, Russia * Correspondence: chernykh@cicese.mx;Tel.:+521-646-178-6994 Received: 27February2018;Accepted: 1May2018;Published: 9May2018 Abstract:Weaddressaschedulingprobleminanactualenvironmentof the tortilla industry. Since theproblemisNPhard,wefocusonsuboptimalschedulingsolutions.Weconcentrateonacomplex multistage,multiproduct,multimachine,andbatchproductionenvironmentconsideringcompletion timeandenergyconsumptionoptimizationcriteria. Theproductionofwheat-basedandcorn-based tortillasofdifferentstyles is considered. Theproposedbi-objectivealgorithmisbasedontheknown NondominatedSortingGeneticAlgorithmII (NSGA-II).Totune itup,weapplystatisticalanalysis ofmultifactorialvariance.Abranchandboundalgorithmisusedtoassertobtainedperformance. We show that theproposedalgorithms canbe efficientlyused in a real production environment. Themono-objectiveandbi-objectiveanalysesprovideagoodcompromisebetweensavingenergy andefficiency. Todemonstrate thepractical relevanceof theresults,weexamineoursolutiononreal data.Wefindthat it cansave48%ofproductiontimeand47%ofelectricityconsumptionover the actualproduction. Keywords: multiobjectivegenetic algorithm; hybridflowshop; setup time; energyoptimization; productionenvironment 1. Introduction Tortillas are averypopular foodas a favorite snack andmeal option invarious cultures and countries. Thereare twotypesof tortillas:wheat-basedandcorn-based. Theiroverall consumption is growingallover theworld.Originally, tortillasweremadebyhand: grindingcorn intoflour,mixing thedough,andpressingtoflatten it. In fact,manysmallfirmstodaystilluseprocesses thataremore labor-intensive, requiringpeople toperformamajorityof the taskssuchaspackaging, loading,baking, anddistributing. This trendisexpectedtochangeover thenextyears.Dueto itsconsiderablepractical significance, optimization of tortilla production is important. To improve the production timing parameters (setup,changeover,waiting),operationalcost (energyconsumption, repairing, service), throughput,etc., carefulanalysisof theprocessandofadvanceschedulingapproaches isneeded. This industry is a typical case of a hybrid flow shop, which is a complex combinatorial optimizationproblemthatarises inmanymanufacturingsystems. In theclassicalflowshop,asetof jobshas topass throughvariousstagesofproduction. Eachstagecanhaveseveralmachines. There is also theflexibilityof incorporatingdifferent-capacitymachines, turningthisdesign intohybridflow shopscheduling(HFS). Algorithms 2018,11, 68;doi:10.3390/a11050068 www.mdpi.com/journal/algorithms74