变质物品库存决策模型研究

华中科技大学硕士学位论文变质物品库存决策模型研究姓名：黄松申请学位级别：硕士专业：管理科学与工程指导教师：黄卫来20061025IWeibullIIAbstractWiththedevelopmentofmodernadvancedmanufacturingtechnologyandproductivity,theconsumptionlevelofcustomershasincreasedconstantly,whichleadstothelifecycleofproductsshortened.Iftheproductsproducedcannotcometothecustomers,theirvalueswillcontinuouslydecreasebecauseofdeterioration,breakageorothermorecompetitiveproducts’disappearing,whichwillbringgreatereconomiclosstotheenterprise.Therefore,itisveryimportanttostudytheinventoryproblemfordeterioratingitems.Firstly,therelatedliteraturesbothathomeandabroadaboutinventorymodelsfordeterioratingitemsarereviewed.Theextensionsofthemodelsareresearchedfromthreeaspects.Firstly,thedeterioratingrateisassumedtobethefunctionofcurrentinventorylevelatanytimeandstoragetime,undertheassumptionsthatshortagesareallowedwithzeroleadtime,andthebackloggingrateistime-varying,anEOQmodelfordeterioratingitemsisestablished,andtheoptimalsolutionsarealsoanalyzed.Secondly,thesingleordercycleisextendedtomultiordercycles,undertheassumptionsthatthedeterioratingratefollowstwoparametersWeibulldistribution,thedemandrateisthelinearfunctionofinventory,shortagesareallowedwithcompletebacklogging,anEOQmodelisestablishedandtheoptimalsolutionsofthemodelisalsoanalyzed.Atlast,takingaccounttheeffectofdelayinpaymentofpurchasecost,anEOQmodelisestablishedundertheassumptionsthatthesellingrateisthelinearfunctionofinventorylevel;shortagesareallowedwithcompletebacklogginginplannedhorizon,thetimevalueofmoneyisalsotakenintoconsideration.Theoptimalsolutionsarealsoanalyzed.Accordingtotheresearchcontentabove,theaimofthispaperliesinexploringtheinventorycharacteristicsofdeterioratingitems,improvingenterprise’competence,andprovidingsometheoreticevidenceformanagingtheinventoryofdeterioratingitemseffectively.Keywords:InventoryDeterioratingitemsDeterioratingrateTime-valueofmoneyDelayinpayment111.1“”“”EOQ21.21.2.1[1]-[4](stockdependentsellingrate)3[5]-[12][5]ChangEOQ[13]Sana-[14]Giri[15]GuptaVrat[1]PadmanabhanVrat[2]PadmanabhanVrat[3],BerrotoniWeibull4[16]ChanduriCharabarty[17]CovertPhilp[18]Weibull(Nobacklogging)(Partialbacklogging)[19]-[22](Completebacklogging)PadmanabhanVrat[3]WilliamsPatuwo[23]ChungNewton-Raphson[24]Moon)](1/[1tT-+ll)(tT-[25]DyeOuyanPadmanabhanVratEOQ[26]NPVChen[27],WeeLaw[28]Sarker[29]ChungTsai[30]WeeLaw[31]Hou[32]5TengChang[33]TengChang[34]YangWee[35]Chu[36]TsaiSu[37]YangWeeLiao[38]Yang[39]1.2.2EOQ[43]EOQ[44]6Ramp[45][46]WeibullWeibull[47]EOQ[48],[49]EOQEOQ[50]PadmanabhanVrat[40][s,S][0,T]7[51],[52][53],[54]1.312Weibull922.1112345ttRtQRtQ=3CKKRtC+31CtKRtC+3tRtRTdttt2110=∫t121RtCt)(tCRtCKRtCtC1321)(++=RCCt1302=(2.1)13002CRCRtQ==(2.2)RCCtC3102)(=(2.3)RCCt1302=3012CRQC=RCCtC3102)(=10212345QTTQP=RPR],0[TRP-],[tTRTtRtPT=tTRP)(21-tTtRPC)(211-)(tC⎥⎦⎤⎢⎣⎡+-=⎥⎦⎤⎢⎣⎡+-=32131)(211)(211)(CPRtRPCtCTtRPCttC(2.4))(2130RPRCPCt-=(2.5))(2130RPCRPCQ-=(2.6)PRPRCCtC)(2)(310-=(2.7))(2130RPPCRCT-=(2.8)311123451C3C2CRS1t1tS21)(1tt-)(211ttR-S1t1RtS=tRSCStC21112121=tRSRtCttRC22212)(21)(21-=-⎥⎦⎤⎢⎣⎡+-+=322212)(1),(CRSRtCRSCtStC212130)(2RCCCCCt+=(2.9)31200122()CRCCQRtCC+==⋅(2.10))(2211320CCCRCCS+=(2.11)0t31002122()RCCQSCCC-=+(2.12)21321002),(CCRCCCStC+=(2.13)0t0Q0Q0S41212345],0[t1t],0[2tB],[21tt],0[1t],[32ttRP-S3t],[3ttR],0[t))()((212231ttttRPC---21221tRtC3C⎥⎦⎤⎢⎣⎡+-+--=32222212)(21)()(211),(CtPRRPCttPRRPCtttCRPPCCCRCCt-⋅+⋅=2211302(2.15)RPPCCCCRCQ-⋅+⋅=2211302(2.16)PRPCCCCRCS-⋅+⋅=2121302(2.17)13PRPCCCRCCB-⋅+=221310)(2(2.18)PRPCCCRCCC-⋅+⋅=2123102(2.19)2.21khr)(rP1)(0=∑∞=rrPQ∑=-QrrPrQh0)()(∑∞+=-1)()(QrrPQrkQ∑∑∞+==-+-=10)()()()()(QrQrrPQrkrPrQhQC(2.20)Q∑∑=-=+QrQrrPhkkrP010)()((2.21)2Kp1Cr)(rf∫=adrraF0)()(fQ],min[Qr:14⎩⎨⎧≤-=QrQrrQCQC0)()(11(2.22)KQQ)(QW)]([QWEQCKQQrPQW1],min[)(--⋅=(2.23))]([QWE∫∫∫---+=∞∞QQQdrrrQCKQdrrPQdrrQWE01)()()()(Pr)]([fff(2.24)KQdrrrQCdrrQrPQCEQQ+-+-=∫∫∞01)()()()()]([ff(2.25)0≤-KP.0)()()]([01=+-=∂∂∫∫∞KdrrPdrrCQQCEQQff∫=QdrrQF0)()(fQPCKPQF+-=1)((2.26)PC2KQdrrrQCdrrQrCQCEQQ+-+-=∫∫∞012)()()()()]([ff(2.27)Q212)(CCKCQF+-=(2.28)*Q*QI≥*QIIQQ-=**Q153(s,S)K1C2C3Cr)(rf1)(0=∫∞drrf∫=adrraF0)()(fIQQIS+=KQC+3∫=+-SQIdrrrSC01)()(f∫∞=+-SQIdrrSrC)()(2f∫∫∞-+-++==+SSdrrSrCdrrrSCKQCSCQIC)()()()()()(2013ff(2.29)0)()()(201=-+=∫∫∞SSdrrCdrrCKdSSdCff2120)()(CCKCdrrSFS+-==∫f(2.30)2120)(CCKCdrrS+-=∫fSISQ-=.s),(Sss0)()()()()()()()()(20013≥⎥⎦⎤⎢⎣⎡---+⎥⎦⎤⎢⎣⎡---+-+∫∫∫∫∞∞sSsSdrrsrdrrSrCdrrrsdrrrSCsSKCffff(2.31)sIQISQ-=sI≥rmrrr,,,10Λ1+iirr16)(,),(),(10mrPrPrPΛ1)(0=∑=miirPIQQI+KQC+3∑+≤-+QIrrPrQIC)()(1∑+--QIrrPQIrC)()(2∑∑≤-+-+-+=SrSrrPCSrrPCrSISKCSC)()()()()()(213(2.32)S)(SCSmrrr,,,10ΛSiriS)(iSCSiS10)()(1≥-+iiSCSC20)()(1≤--iiSCSC∑∑≤≤≤+--iiSrSrrPCCKCrP)()(2121(2.33)iSiSS=ISQ-=s∑∑∑∑≤≤-+-++≤-+-+SrSrsrsrrPCSrrPCrSKSCrPCsrrPCrsKs)()()()()()()()(21321(2.34)Smrrr,,,10Λir(Sri≤)ssI≤S17QISQ-=sI2.31t)(tD)(tIba+ab)(tIt232C4q5CiCi6SRASRA7T1tBQ1t{})()()(tItIdttdIbaq+-=+Tt≤≤0(2.35)0)(=TI{}1)())((-+=-+tTetIqbqba(2.36){}[]⎭⎬⎫⎩⎨⎧+--++=++∫)(1)()()(20qbqbababaqbTeTSdttISTT(2.37)18{}CeT1)(-++qbqba(2.38){})(1)()()(20qbqbaqb+--+=+∫TeCidtCitITT(2.39)[]⎭⎬⎫⎩⎨⎧+--++=+)(1)()()(2qbqbabaqbTeTTSTPT[