Approximationsoflead-timedistributionsinanassemble-to-ordersystem under abase-stockpolicy

In thispaper,weconsideranassemble-to-orderproductionsysteminwhichaproductwithmultiple componentsisproducedunderabase-stockpolicy.ThedemandfollowsaPoissonarrivalprocess,and the productiontimeateachfacilityisexponentiallydistributed. Our mainresultsareclosed-formformulaeforapproximatingthelead-timedistributionsin equilibrium.Theapproximationformulaeforthelead-timedistributionscanbeobtainedwithalinear combinationofbounds,inwhichcertainconstantsareobtainedfromauxiliarypropertiesand simulationexperiments.Todeterminethequalityoftheapproximations,weobtainedsamplelead-time distributionsfrommanysimulations.Kolmogorov–Smirnovtestsshowthatourformulaeareverygood fits ofthesampledistributions.Theapproximationsaregoodovertheentirerangeoftrafficintensities and areevenmoreaccurateinlightorheavytraffic.