The productionschedulingprobleminamulti-pageinvoiceprintingsystem

This paperaddressestheproductionschedulingprobleminamulti-pageinvoiceprintingsystem.The system comprisesthreestages:thestencilpreparationstage,thepageprintingstageandtheinvoice assemblystage.Sinceeachpagecanbeconsideredasacomponentandtheinvoiceasthefinished product,theproductionsystemformulti-pageinvoicescanbetreatedasanassembly-typeflowshop with parallelmachinesatthelasttwostages.Moreover,twotypesofsequence-dependentsetup operationsareconsideredatthesecondstage.Theobjectiveistominimizethemakespanforallthe invoice orders.Wefirstformulatethisproblemintoamixed-integerlinearprogramming(MILP).Thena hybrid geneticalgorithm(HGA)isproposedforsolvingitduetoitsNP-hardness.Toevaluatethe performanceoftheHGAheuristic,alowerboundforthemakespanisdeveloped.Numericalexperiment indicatesthatouralgorithmcansolvetheproblemefficientlyandeffectively.