ֻ26जֻ2௹ Кቂ࿐ჽ࿐Б(ሱಖ॓࿐ϱ) ୍6ᄅ JournalofHubeiUniversityforNationalities(NaturalScienceEdition) ҂ॖौളӁ༢༯֥ࣜ࠶ളӁਈଆ້սम1,କ ౪2(1.湖北民族学院理学院,湖北恩施445000;2.重庆邮电大学应用数学学院,重庆400065)ᅋေ:对一个设备寿命服从负指数分布,设备故障率与生产率有关的不可靠生产系统,建立了一个以计划生产时间a生产率和产品销售价格为决策变量的利润模型.并对给定生产率与产品销售价格,证明了目标函数的单峰性,求出了计划生产时间的上界与下界.ܱՍ:库存;经济生产批量;设备故障与维修;价格ᇏٳোݼ:໓ངѓ്:A໓ᅣщݼ:1008-8423(2008)02-0151-04AnEconomicProductionLot-sizeModelforanUnreliableProductionSystemWE2ID1ai-jun,MOUQiong(,HubeiUniversityforNationalities,Enshi445000,China;,ChongqingUniversityofPostsandTelecommunication,Chongqing400065,China)Abstract:Inthispaper,weconsideraproblemofeconomicmanufacturingquantityandsellpricingforanunreliableproductionsystemwherethemachinelifetimeissubjecttoexponentialdistribution,-tionuptime,,forgivenproductionrateandsellpricing,,theupboundandlowboundofproductionuptimeareobtained,:inventory;economicproductionquantity;machinebreakdownandrepair;pricing୍࣍ࠫট,ྸ؟࿐ᆀؓ҂ॖौളӁ༢༯ࣜ࠶ളӁਈ໙ีࣉྛਔնਈ࣮[1~5],ఃᇏ໓ང[3]ؓഡС൰ଁڛՖڵᆷඔٳ,҃ົྩൈࡗູਬ֥౦ঃ,ิԛਔਆᇕളӁҦ:NRҦაA/RҦ;C[4,5]hung۳ԛਔളӁਈ֥ഈa༯ࢸ.໓ང[6]ॉ੮ഡС൰ଁაົྩൈࡗڛՖෛࠏٳ,҃ѩࡼഡСܣᅰੱބֆ໊ളӁӮЧіൕӮളӁੱ֥ݦඔ,ࡹ৫၂۱ၛളӁਈބളӁੱູथҦэਈ֥ቋཬٮႨଆ;ႮႿҐ౼൙ުົྩٚൔ,ၹՎ໓ང[6]ޭਔഡС൰ଁ֥э߄.໓ང[7~10]ٳљՖᄍྸಌࠊ,ڪോ,ྟࠊлൈࡗࡎᆴࠣഡС҆ࡱูߐ֩࢘؇ࡆၛܼ.Ч໓ᄝഈඍ໓ང֥ࠎԤഈ,ࡼົྩٳູᆞӈ౦ঃ༯֥ყٝົྩაؿളܣᅰު(҂ٞӫູࣅࠤ౦ঃ)֥൙ުົྩ,ᄝࣅࠤ౦ঃ༯,ູਔх૧ԛགྷಌࠊ,ॖ๙ݖሔࡆӮЧ,෪؋ྩگൈࡗ,ᄝ९թࢆູਬൈ,ഡС၂קԩႿປݺ֥۽ቔሑ.ؓഡС൰ଁڛՖڵᆷඔٳ҃,ഡСܣᅰੱෛളӁੱᄹնطᄹն֥҂ॖौളӁ༢,൬۠ರ௹:2008-03-20.ࠎࣁཛଢ:Кസ࢝ტ๏॓ཛଢ(B20082907);Кസ࢝ტ๏ౝ୍ࠎࣁ(Q200729003);Кቂ࿐ჽౝ୍ཛଢ(myq2006041).ቔᆀࡥࢺ:້սम(1977-),ଳ(װቂ),ࢃഽ,ᇶေՖ൙ۀੱ࠹aඔ࿐ࡹଆ࣮.
152 Кቂ࿐ჽ࿐Б(ሱಖ॓࿐ϱ) ֻ26ज࣮ࣜ࠶ളӁਈაӁקࡎ໙,ีࡹ৫ਔ၂۱ၛ࠹߃ളӁൈࡗ,ളӁੱބӁཧ൲ࡎູ۬थҦэਈ֥০ଆ;ಖ,ުؓ۳קളӁੱބӁཧ൲ࡎ,۬ᆣૼਔଢѓݦඔ֥ֆڂ,ྟ۳ԛ࠹߃ളӁൈࡗ֥ഈa༯ࢸ,Ⴈ༯ࢸቔູ࠹߃ളӁൈࡗ֥࣍රቋႪࢳ.1 ඔ࿐ଆ 符号说明与模型假设 ژݼඪૼA0ളӁሙСٮ;chֆ໊Ӂֆ໊ൈࡗ֥९թٮ;c1ֆ໊ൈࡗ֥൙ުົྩٮ;c2ֆ໊ൈࡗ֥ყٝົྩٮ(c1>x2);sֆ໊Ӂ֥ཧ൲ࡎ۬(थҦэਈ);pളӁੱ(थҦэਈ);T1࠹߃ളӁൈࡗ(थҦэਈ);T2၂۱ളӁᇛ௹ଽ֥٤ളӁൈࡗ;L1൙ުົྩൈࡗ;L2ყٝົྩൈࡗ(L1>L2);C(L1)ၹ෪؋൙ުົྩൈࡗطሔࡆ֥ӮЧ. ଆࡌഡ(1)ॉ੮ֆഡСളӁֆ၂Ӂ֥౦ঃ;(2)ഡС൰ଁڛՖڵᆷඔٳ-K(p)t,҃ఃٳ҃ݦඔFX(t,p)=1-e.ႮႿഡС۽ቔ఼؇ෛളӁੱ֥ᄹնطᄹն,෮ၛࡌקܣᅰੱK(p)൞ളӁੱp֥ᄹݦඔ[6];(3)ົྩ(ყٝົྩა൙ުົྩ)ൈࡗູӈඔ.ᄝളӁݖӱᇏ,ೂݔഡСؿളܣᅰ,৫ࠧࣉྛ൙ުົྩ,ڎᄵᄝളӁࢲඏൈ,ࣉྛყٝົ.ྩ֒൙ުົྩൈࡗնႿ٤ളӁൈࡗൈ,ູਔх૧ԛགྷಌࠊ,๙ݖሔࡆӮЧ෪؋൙ުົྩൈࡗ,֤ൌ࠽൙ުົྩൈࡗ֩Ⴟ٤ളӁൈࡗ,ၛЌᆣᄝ९թࢆູਬൈ,ഡСԩႿປݺ֥۽ቔሑ;(4)ഡСФྩگު֥۽ቔሑა௹Ԛ۽ቔሑ၂ဢ;(5)Ґ౼NRളӁҦ,ࠧഡСФྩگ,ުր९թࢆູਬൈ,ᄜषളӁ;(6)ླੱd(s)൞ཧ൲ࡎ۬s֥ࡨݦඔ,ഡ-Cd(s)=KS,ఃᇏK,CູնႿਬ֥ӈඔ;(7)ֆ໊Ӂ֥ളӁӮЧC(p)൞ളӁੱp֥ݦඔ,ഡC(p)=r0+r1/p+r2p,ఃᇏr0іൕֆ໊ჰਘٮ;r1/pіൕളӁֆ໊Ӂ෮ཨݻ֥স৯,ෛളӁੱ֥ᄹնطࢆ;֮r2pіൕളӁֆ໊Ӂ෮ླ֥ഡС,ෛളӁੱ֥ᄹնطᄹն[6]. 模型建立קၬ৵࿃ਆՑषളӁ֥ൈࡗࡗۯູ၂۱ളӁᇛ௹,ᄝ၂۱ളӁᇛ௹ଽ,ᇀ؟ؿള၂ՑഡСܣᅰ.ࡌഡᄝt=0ൈၛp֥ੱषളӁ,ᄝ[0,T1]ଽೂݔഡСໃؿളܣᅰ,ᄵᄝt=T1ൈख़๔ᆸളӁ,ࣉྛყٝົྩ,ր९թࢆູਬൈᇗྍषളӁ,ః९թሑೂ1෮ൕ;ڎᄵ,ᄝT1ᆭభ֥ଖ၂ൈख़x,ഡСؿളܣᅰ,ളӁФ௧๔ᆸ,৫ࠧࣉྛ൙ުົ.ྩႮࡌഡ(3)ॖᆩ,թᄝ၂ׄx=u,֤Վൈ֥٤ളӁൈࡗT2֩Ⴟ൙ުົྩൈࡗL1,෮ၛ֒x>uൈ,ᄝ९թඣࢆູਬᆭభ,ഡСၘࣜФྩگ,ః९թሑೂ2෮ൕ;ط֒x<uൈ,ࠧ൙ުົྩൈࡗնႿ٤ളӁൈࡗ,ሔࡆӮЧ,ࡼྩگൈࡗ෪؋ᇀ٤ളӁൈࡗ,ః९թሑೂ3෮ൕ.࠺ൌ࠽ളӁൈࡗູv,v=min{T1,x},۴ऌၛഈٳ༅ބ༢९թሑॖᆩ:T2(p-d(s))v/d(s),ࠧ٤ളӁൈࡗT2൞ൌ࠽ളӁൈࡗv֥ݦඔ,҂ٞ࠺ູT2(v).T2(u)=L1:֤u=d(s)L1/(p-d(s)).༯૫,ٳ༅༢֥௹ຬ൬ೆა۲ᇕٮႨቆӮ:T]௹ຬളӁਈ:Q=Q1-K(p)TptdFX(t,p)-ptdFTX(t,p)=p-e1)0Q1K(1(p)Ӂ௹ຬ९թٮ:ECI(T1,p,s)=chQ]0I(x|x=t)dFX(t,p)=
ֻ2௹ ້սम֩:҂ॖौളӁ༢༯֥ࣜ࠶ളӁਈଆ 153p-d(s))2(s))chQT11p(0tdFX(t,p)+Q]1p(p-dTT1dFX(t,p)=2d1(s)2d(s)p(p-d(s))1-K(p)T-e1-K(p)Tc1h)-K(p)T1e]d(s)K2[(1(p)௹ຬົྩٮ:uT1]ECR(T1,p,s)=,p)+c2L2dFX(t,p)+ 0Q[c1T2+C(L1)]dFX(tQc1L1dFX(t,p)+uT1Qu-K(p)u)+c1L1e-(c1L1-c2L2)+0Q[c1T2+C(L1)]dFX(t,p-K(p)T(c11L1-c2L2)(1-e)u-K(p)uB=Q[c1T2+C(L1)]dFX(t,p)+c1L1e-(c1L1-c2L2),ᄵ:0ECR-K(p)Te1(T1,p,s)=B+(c1L1-c2L2)(1-).၂۱ളӁᇛ௹֥௹ຬሹ০:ETR(T1,p,s)=ཧ൲൬ೆ-ളӁӮЧ-ളӁሙСٮ-ົྩ-ٮ९թٮ=1-K(p)T(S-C-K(p)T1(p))K(1-e1)-A0-B-(c1L1-c2L2)(1-e)-(p)p(p-d(s))1-K(p)T-K(p)Tc1hd(s)K2[(1-e)-K(p)T1e1](p)T]௹ຬᇛ௹:E1-K(p)T(T1,p,s)=0Q1ptdFdX(t,p)+(s)TQpTdF1dX(t,p)=pT(1-e1)(s)d(s)K(p)ၹՎ,ֆ໊ൈࡗ֥௹ຬ০:ETP(TE1,p,s)d(s)K(p)(A0+B)AP(T1,p,s)==(S-C(p))d(s)-ET(T-K(p)T-1,p,s)p1(1-e)-K(p)Td(s)K(p)p-d(s)K(p)T11e(c1L1-c2L2)-chpK1--K)(p)T(1(p)1-e1Ⴟ൞,ॖࡹ৫ೂ༯٤ཌྟܿ߃ଆ:max EAP(T1,p,s)-s..td(s)<p[p(2)p-d(s)T1\L2d(s)ଢѓ൞ቋႪ࠹߃ളӁൈࡗT1,ളӁੱpބӁཧ൲ࡎ۬s,֤ֆ໊ൈࡗ֥௹ຬ০EAP(T1,p,s)ቋն.ֻؽ۱ჿඏ่ࡱіൕᄝളӁݖӱᇏ,ೂݔഡСໃؿളܣᅰ,ᄵՎൈ֥٤ളӁൈࡗႋ҂ཬႿყٝົྩൈࡗ. 模型性质ྟᇉ1 ؓ۳ק֥ളӁੱpބӁཧ൲ࡎ۬s,ֆ໊ൈࡗ֥௹ຬ০EAP(t1,p,s)൞T1֥ֆڂݦඔ.ᆣૼ ؓEAP(t1,p,s)T1֥ொ֝,:֤5EAP-K(p)Te1-K(p)T=1+K(p)T1-1]}=5T-K(p)T{d(s)K2(p)(A0+B)-chp(p-d(s))[e1p1(1-e)-K(p)Tc1hp(p-d(s))e--K(A(p)T0+B)K2(p)d(s)-K(p)Te12e1+K(p)T1-1-p(1-)chp(p-d(s))2(AF-K(p)d(s)(p)T0+B)K1(T1)=e+K(p)T1-1-,ᄵ:chp(p-d(s))(A0+B)K2(p)d(s)F-K(p)T(0)=-<0,F(])>0,Fc(T1)=K(p)[1-e1]>0chp(p-d(s))Ⴟ൞*,թᄝື၂֥*T1,֤F*(T1)=0,ࠧթᄝື၂֥T1,֤5EAP=0EAP,֒*T1<T1ൈ5,>0;֒5T1T*5T1=T11
154 Кቂ࿐ჽ࿐Б(ሱಖ॓࿐ϱ) ֻ26ज*T1>T1ൈ5EAP,<0,෮ၛEAP(T1,p,s)൞T1֥ֆڂݦඔ.5T1ഡ:M=d(s)K2M/3+4M2/9+8Mp/K(p))))M+M2+8Mp/K(p)(p)(A0+B)/ch(p-d(s)),T1=,T1=.2p2pྟᇉ2 ؓ۳ק֥ളӁੱpބӁཧ൲ࡎ۬s,ቋႪ࠹߃ളӁൈࡗ**T1ડቀ:T1[T1[ᆣૼ-xx Ⴎ໓ང[5]֥ྟᇉ1Ⴕx:>e-1+x>,෮ၛ:2+2x/32+x2s)(K(p)TF-K(p)T(A10+B)K2(p)d(1)(A0+B)K2(p)d(s)(T1)=e+K(p)T1-1-<-chp(p-d(s))2+2K(p)T1/3chp(p-d(s))ഈൔႷ؊֩Ⴟਬ,ࠧ(K2(p)T1)(A0+B)K2(p)d(s)-=0,֤:2+2K(p)T1/3chp(p-d(s))2M/3+4M2/9+8Mp/K(p)T1=2p෮ၛF*(T1)<0=F*(T1),ႻF(T1)൞[0,])ഈ֥၂۱۬־ᄹݦඔ,ၹՎT1[T1;22Ⴛၹູ(K(p)T1)(A0+B)K(p)d(s)F-K(p)T(A0+B)K2(p)d(s)(T1)=e1+K(p)T1-1->-chp(p-d(s))2+2K(p)T1chp(p-d(s))22ഈൔႷ؊֩Ⴟਬ)(A0+B)K2(p)d,ࠧ(K(p)T1(s)=0+8Mp/K(p),:֤T1=M+M2+2K-(p)T1chp(p-d(s))2p෮ၛF*(T1)>0=F(T1),Ⴟ൞*T1[ 模型求解ႮႿଆ(2)൞၂۱Ⴕჿඏ֥٤ཌྟܿ߃໙,ี֤֞ቋႪࢳ֥ऎุіղൔбࢠ.ၹՎ,০Ⴈ໓ང[12]ิԛ֥ـݦඔمটଆ֥ቋႪࢳ.൮,༵ࡼଆ(2)іൕӮೂ༯ྙൔ:min f(T1,p,s)=-EAP(T1,p,s)(3)s..t c1(T1,p,s)=p-K-Ks>0)c2(T1,p,s)=p-p\0-Kc3(T1,p,s)=(p-K-Ks)T1-L2Ks>0ၹՎ,ॖࡹ৫ـݦඔ:L(T1,p,s,L)=f(T1,p,s)+LB(T1,p,s)(4)3ఃᇏB=(T1,p,s=6logci(T1,p,s),LູӲـၹሰ,L>0.০Ⴈ໓ང[11]ิԛ֥ଽׄـݦඔ֥ࢳෘم,ࠧॖi=1֤ଆ֥ቋႪࢳ,ఃऎุෘم҄ᇧ:ູstep0ҕඔൻ,ೆ۳קL0>0,NI(0,1)ބᄍྸ༂ҵE>0,k=1;step1ـݦඔL(T1,p,s,L)֥ቋႪࢳ(T1,k,pk,sk,Lk);step2ೂݔ|LkB(T1,k,pk,sk)|[E,ෘمᇔᆸ,(T1,k,pk,sk)ູଆ(2)֥ቋႪࢳ;ڎᄵ,Lk+1=NLk,k=k+1,ሇೆstep1.ႮႿֆ໊ൈࡗ֥௹ຬ০EAP(T1,p,s)࠻҂൞ݦඔ,္҂൞χݦඔ,෮ၛ҂ିЌᆣ෮֤֥ቋႪࢳ൞ಆअቋႪࢳ,ॖିᆺ൞၂۱अ҆ቋႪࢳ.2 ଆࡎଆॉ੮ਔഡС൰ଁڛՖڵᆷඔٳ҃,ഡСܣᅰੱෛളӁੱᄹնطᄹն֥҂ॖौളӁ༢,ࡹ৫ਔ၂۱ၛ࠹߃ളӁൈࡗ,ളӁੱބӁཧ൲ࡎູ۬थҦэਈ֥০ଆ,ѩᄝ၂קളӁੱބӁཧ൲ࡎ۬༯,ᆣૼਔଢѓݦඔ֥ֆڂྟ,֤֞࠹߃ളӁൈࡗ֥ഈa༯ࢸ,ऎႵࢠ఼֥ંބൌႋႨࡎᆴ,ު࿃࣮ᇏࡼ࿙ൌ࠽২ሰ֥ቑᆣބဒ.ҕॉ໓ང:[1] BieleckiT,-inventorypoliciesforunreliablemanufacturingsystems[J].OperationsResearch,1988,36(4):532-541.(下转第182页)
182 Кቂ࿐ჽ࿐Б(ሱಖ॓࿐ϱ) ֻ26जਈ:ೂݔ֡࢘؇ݖཬ,ପહࣼсྶᄹࡆHe_O2,ೂݔݖն,ᄵေൡ֒ࡨཬHe_O2ੀਈ[10].4 ࢲંЧ໓ࢺകਔRIE༢,ѩՖჰ֥࢘؇ࢃඍਔ࿊ᄴ؟ࣖ݁ോख़గุູHBr,NF3,He_O2,ࢳਔ৯ބЌྟగุHe_O2ؓ֡ྙ֥႕ཙ,ѩᄝൌဒ่ࡱ༯ോख़ԛ෮ླေ֥݁֡,॥ᇅᆜ۱֥֡ྙ,ѩЌݺᅃࠞ,Ч໓֥۽ቔؓັሰᇅᄯ۽ӱႵҕॉ֥ၩၬ.ҕॉ໓ང:[1] TudaM,ShintaniK,-pressurehigh-densityCl2/HBr/O2plasmachemistries[J].JVacSciTechnol(A),2001,19:711-717.[2] DesvoivresL,VallierL,:Towardssomelimitationsoftheplasmatechnology[J].JVacSciTechnol(B),2000,18:156-165.[3] LowCH,ChinWS,TanKL,(100)surfaceafterhighdensityHBr/Cl/Oplasmaetching[J].JpnJApplPhys,222000,39:14-19.[4] NishikawaK,OomoriT,OnoT, RuegerNR,BeulensJJ,SchaepkensM,[J].JVacSciTechnol(A),1997,15:1881-1889.[6] KimB,[J].IEEETransCompPackManufactTechnolC,1996,19:3-8.[7] HoriikeY,KubotaK,[J].JVacSciTechnol(A),1995,13:801-809.[8] ByungwhanKim,SukYongLee, ByungwhanKim, SiddharthaPanda,RichardWise,AelanMosden,[J].MicroelectronicEngineering,2004,75:275-284.(上接第154页)[2] KimCH,[J].InternationalJournalofProductionE-conomics,1997,49:215-223.[3] GroeneveltH,PintelonL,[J].ManagementSciences,1992,38:104-123.[4] [J].ComputersandIndustrialEngineering,1997,32:139-144.[5] [J].Computers&OperationsResearch,2003,30:1499-1507.[6] GiriBC,YunWY,-inventorysystemswithvariableproductionrate[J].EuropeanJournalofOp-erationResearch,2005,162:372-386.[7] GiriBC,[J].InternationalJournalofProductionEconomics,2005,95:229-243.[8] LinGC,-inventorysystemofdeterioratingitemssubjecttorandommachinebreakdownswithafixedrepairtime[J].MathematicalandComputerModelling,2006,43:920-932.[9] GiriBC,[J].InternationalJournalofProductionEconomics,2004,92:157-167.[10] HsiehCC,[J].EuropeanJour-nalofOperationResearch,2005,162:359-371.[11] ჯན,໓ᠺ.ቋႪ߄ંაٚم[M].Кࣘ:॓࿐ԛϱഠ,2001.
