简介：Amathematicalmodeltodeterminetheoptimalproductionlotsizeforadeterioratingproductionsystemunderanextendedproductinspectionpolicyisdeveloped.Thelast-Kproductinspectionpolicyisconsideredsothatthenonconformingitemscanbereduced,underwhichthelastKproductsinaproductionlotareinspectedandthenonconformingitemsfromthoseinspectedarereworked.Considerthattheproductsproducedtowardstheendofaproductionlotaremorelikelytobenonconforming,isproposedanextendedproductinspectionpolicyforadeterioratingproductionsystem.Thatis,inaproductionlot,productinspectionsareperformedamongthemiddleK_1itemsandafterinspections,allofthelastK_2productsaredirectlyreworkedwithoutinspections.Ourobjectivehereisthejointoptimizationoftheproductionlotsizeandthecorrespondingextendedinspectionpolicysuchthattheexpectedtotalcostperunittimeisminimized.Sincethereisnoclosedformexpressionforouroptimalpolicy,theexistencefortheoptimalproductioninspectionpolicyandanupperboundfortheoptimallotsizeareobtained.Furthermore,anefficientsolutionprocedureisprovidedtosearchfortheoptimalpolicy.Finally,numericalexamplesaregiventoillustratetheproposedmodelandindicatethattheexpectedtotalcostperunittimeofourproductinspectionmodelislessthanthatofthelast-Kinspectionpolicy.