뗚24뻭뗚1웚ꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡ쒣ꆡ뫽ꆡ쾵ꆡ춳ꆡ폫ꆡ쫽ꆡ톧,쓪2퓂FuzzySystemsandMathematicsFeb.,2010컄헂뇠뫅:100127402(2010)0120098205쒣뫽탨쟳쿂뗄뿢듦럧쿕벰ퟮ폅뿢듦뻶닟Ξ췵뾭탋,맹쯃(쇉쓾릤돌벼쫵듳톧쫽톧폫쾵춳뿆톧퇐뺿쯹,쇉쓾뢷탂ꆡ123000)햪ꆡ튪:럖컶쇋퓚쒣뫽탨쟳쿂,내뺭뗤뿢듦쒣탍훐뗄뺭볃뚩믵엺솿뫍뚩믵훜웚쯹떼훂뗄뿢듦럧쿕쯰쪧ꆣ췆떼쇋쒣뫽탨쟳쿂뗄뺭볃럧쿕몯쫽ꆣ룸돶쇋럧쿕몯쫽퓚쒣뫽탨쟳럖늼쿂뗄훘탄뻶닟랽램,퓚듋믹뒡짏뗃떽쇋쒣뫽탨쟳쿂뺭볃엺솿뗄탞헽릫쪽,캪쒣뫽뿢듦럧쿕럖컶뗄퇐뺿쳡릩쇋튻훖랽램ꆣ맘볼듊:뿢듦;쒣뫽탨쟳;럧쿕몯쫽;뺭볃엺솿훐춼럖샠뫅:O159ꆡꆡꆡ컄쿗뇪쪶싫:A1ꆡ틽퇔ퟔ1934쓪Wilson쫗듎쳡돶뺭볃엺솿릫쪽(EOQ)틔뫳,탭뛠톧헟뛔뿢듦쒣탍훐뺭볃엺솿퇐뺿ퟶ쇋뫜뛠릤ퟷꆣ쒣뫽럖컶뗄랽램훷튪펦폃폚쓑틔뗃떽뻟폐춳볆맦싉쫽뻝뗄늻좷뚨탔컊쳢뎡뫏ꆣ퓚뿢듦컊쳢훐,폐킩늻좷뚨컊쳢쓑틔헒떽춳볆맦싉,춨뎣틀뾿맜샭헟뗄뺭퇩맀볆,헢캪쒣뫽뿢듦샭싛폫랽램뗄퇐뺿쳡릩쇋놳뺰ꆣ맺볊짏맘폚쒣뫽뿢듦쒣탍뗄퇐뺿쪼폚20쫀볍80쓪듺,K1]acpryzk폫Staniew[ski뫍P[2]arkퟮ쿈붫쒣뫽럖컶뗄랽램틽죫뿢듦맜샭ꆣ쯦뫳늻짙톧헟샻폃쒣뫽럖컶랽램퇐뺿쇋뿢듦컊쳢,죧퓚늻퓊탭좱믵뫳늹뗄쳵볾쿂,컄[3]뫍컄[4]럖뇰퇐뺿쇋뚩릺솿쫇죽뷇탎뫍쳝탎쒣뫽쫽뗄EOQ쒣탍ꆣ컄[5]쳖싛쇋퓊탭좱믵뫳늹쟩뿶쿂뗄EOQ쒣탍ꆣ컄[6]쳖싛쇋퓚늻퓊탭좱믵뫳늹쟩뿶쿂,뚩릺솿뫍탨쟳솿뻹쫇죽뷇탎쒣뫽쫽뗄EOQ쒣탍ꆣ놾컄훷튪퇐뺿퓚뺭뗤뗄ퟮ폅뿢듦뻶닟쿂,떱뿢듦뻶닟닎쫽(훷튪쫇탨쟳)랢짺뇤뮯뫳붫믡틽웰뗄뿢듦뻶닟럧쿕,틔벰퓚탨쟳캪쒣뫽쫽쿂죧뫎쪹럧쿕듯떽ퟮ킡뮯뗄컊쳢ꆣ2ꆡ뿢듦럧쿕폫쯰쪧몯쫽훚쯹훜횪,퓚뺭뗤뿢듦쒣탍훐뗄뺭볃뚩믵엺솿Q뫍뷸믵훜웚T럖뇰캪Q2C3r2C3=(C,T=1C1)1r웤훐,C1캪떥캻듦훼럑,C3캪뚩믵럑,r캪탨쟳쯙뛈ꆣ춨뎣퓚탭뛠쿖쪵컊쳢훐,쫐뎡ꆢ짺닺믲ퟔ좻뮷뺳뗄뇤뮯뚼뿉쓜틽웰뛔뿢듦컯탨쟳뗄뇤뮯,듋쪱,탨쟳쯙뛈뫜쓑놣횤쫇튻룶늻뇤뗄뎣쫽ꆣ튻떩샻폃ퟮ폅뿢듦릫쪽좷뚨쇋뿢듦솿,뫜뿉쓜붫튪쏦뛔캴살뗄솽훖럧쿕:튻쫇좱믵쯰쪧럧쿕,쯼쫇평폚퓚튻룶뚩믵훜웚Ξ쫕믹룥뷰죕쿮웚쒿:2008211213:쇉쓾쪡뷌폽쳼룟뗈톧킣뿆톧퇐뺿쿮쒿(20060377)냗돇죋ퟷ헟볲뷩:췵뾭탋(19842),쓐,쇉쓾떤뚫죋,쇉쓾릤돌벼쫵듳톧쮶쪿,퇐뺿랽쿲:쒣뫽럖컶톧,쒣뫽퓋돯톧;맹쯃(19512),춨,쇉톶쓾ퟷ릤헟돌벼쫵듳톧뷌쫚쒣뫽풤닢폫뻶닟뗈ꆣ쓐,벪쇖,늩쪿짺떼쪦,퇐뺿랽쿲:쒣뫽럖컶톧,:맹쯃:guosizong@ꆣ
뗚1웚ꆡꆡꆡꆡꆡꆡꆡꆡꆡ췵뾭탋,맹쯃:쒣뫽탨쟳쿂뗄뿢듦럧쿕벰ퟮ폅뿢듦뻶닟99쓚춻좻탨쟳퓶볓,퓬돉퓚훜웚쓚뿢듦컯좱믵늢펰쿬떽뫳볌뗄짺닺뮷뷚뛸닺짺뗄쯰쪧;뛾쫇평폚탨쟳솿뗄춻좻쿂붵,퓬돉훜웚쓚뿢듦컯믽톹뛸듸살뗄쿠맘쯰쪧ꆣ컒쏇붫헢솽훖쯰쪧춳돆캪뿢듦럧쿕ꆣ볙뚨떥캻듦훼럑C1뫍뚩믵럑C3뚼늻뇤,틲듋,뿢듦럧쿕뷶평탨쟳솿뗄뇤뮯뛸틽웰,늢볙뚨컒쏇쎻폐맘폚탨쟳솿늻좷뚨뇤뮯뗄춳볆쇏,횻폐뛔탨쟳솿뇤뮯랶캧틔벰퓚룃랶캧쓚돶쿖뗄뿉쓜탔맀볆,벴붫탨쟳솿쫓캪튻룶죧춼1쯹쪾뗄쒣뫽쫽ꆫR,웤솥쫴몯쫽캪ΛꆫR(r)ꆣ웤훐,r0캪ퟮ폐뿉쓜뗄탨쟳솿(벴뿍맛뮷뺳늻랢짺틢췢뇤뮯쳵볾쿂뗄헽뎣탨쟳솿),r1뫍r2럖뇰쫇튻떩랢짺뇤뮯뫳뗄ퟮ킡뿉쓜탨쟳솿뫍ퟮ듳뿉쓜탨쟳솿,ΛꆫR(r)쫇탨쟳솿퓚뇤뮯랶캧[r1,r2]쓚뗄뿉쓜탔맀볆ꆣ쿂쏦,럖뇰쳖싛퓚풭폐뚩믵솿뫍뚩믵훜웚쳵볾쿂,쪵볊탨쟳솿r듳폚뫍킡폚헽뎣탨쟳쯙뛈r0쪱듸살뗄뿢듦럧쿕쯰쪧ꆣ춼1ꆡ쒣뫽탨쟳럖늼211ꆡr<r0쪱뗄뿢듦쯰쪧볙뚨헽뎣탨쟳쯙뛈캪r0쪱뗄ퟮ폅뿢듦솿캪Q0,떱쪵볊탨쟳쯙뛈r<r0쪱,훜웚T쓚뻍믡퓬돉뿢듦믽톹ꆣ듋쪱뗄쯰쪧훷튪쫇퓶볓뿢듦믽톹뗄럑폃ꆣ평폚틔r0캪탨쟳쯙뛈뫍틔r(r<r0)캪탨쟳쯙뛈쪱훜웚T쓚욽뻹듦훼솿럖뇰캪11tdt=r0TꇒTr0T1=Q0뫍1TꇒTrtdt=rT=Q10202퓲훜웚T쓚욽뻹믽톹솿캪Q0-Q1,C1캪떥캻컯듦훼럑,믽톹퓶볓뗄듦훼럑캪1f1(r)=C1(QTC0-Q1)=(r0-r)(2)2뿉틔뾴돶,f1(r)쫇맘폚r뗄떥뗷복몯쫽,떱r=r0쪱f1(r)=0ꆣ212ꆡr>r0쪱뗄뿢듦쯰쪧떱r>r0쪱,평폚훜웚T쓚탨쟳맽뿬붫믡퓬돉좱믵,뷸뛸닺짺평폚좱믵듸살뗄쯰쪧ꆣ떫쫇,평폚탨쟳맽뿬튲듸살뿢듦럑폃뗄뷚쪡ꆣ듋쪱뗄쯰쪧캪좱믵쯰쪧복좥뿢듦뷚쪡(죧춼2쯹쪾)ꆣ춼2ꆡ좱믵쪱뿢듦쇮Q∆0=T-T1=T-캪좱믵쪱볤(r>r0),∆쪱볤쓚좱믵솿캪r∆,훜웚쓚욽뻹좱믵솿캪r∆ꆣ볙뚨좱믵rT쯰쪧럑폃폫좱믵솿벰좱믵쪱볤돉헽뇈,쟒떥캻좱믵쯰쪧럑캪C2,퓲훜웚T쓚욽뻹좱믵쯰쪧캪1Cf2(r)=C2Q22r∆2=C02Tr+-2C2Q0(3)TTrf2(r)캪r뗄떥뗷퓶몯쫽,떱r=r0쪱f2=0ꆣ훜웚T쓚욽뻹뿢듦뷚쪡럑캪C1C1C1Q2r2C10f3(r)=TꇒTrtdt=rT-(T-∆)=rT-(4)T-∆2TꇒT-∆C1C1rtdt=rT-022T2Tr
100쒣ꆡ뫽ꆡ쾵ꆡ춳ꆡ폫ꆡ쫽ꆡ톧ꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡ2010쓪f3(r)캪r뗄떥뗷퓶몯쫽,떱r=r0쪱f3=0ꆣ틲듋,떱r>r0쪱뗄ퟛ뫏쯰쪧럑폃캪2C2T-C1T(2C2+C1)Q201f2(r)-f3(r)=r+-2C2Q022Tr폚쫇,쇮Θ(r)캪뿢듦럧쿕몯쫽,폐TC1(r0-r)=A-Br,rꇜr02Θ(r)=(5)2C2T-C1T(2C2+C1)Q201r+-2C2Q0=Cr+D1-E,r0<r22Trr웤훐TC1r0TC12C2T-C1T(,D2C2+C1)Q20A=,B=,C==,E=2C2Q0(6)2222T늢볇ΘΘ1(r),ꆡrꇜr0(r)=(Θ7)2(r),ꆡr>r0ꆡꆡ쿂쏦럖뇰룸돶C1,C2좡늻춬횵쪱뛔펦뗄뿢듦럧쿕몯쫽Θ(r)쟺쿟ꆣ헢샯늻럁좡ퟮ킡탨쟳쯙뛈r1=90,ퟮ듳탨쟳쯙뛈r2=110,헽뎣탨쟳쯙뛈r0=100,C1뫍C2럖뇰캪듦뒢럑뫍좱믵럑ꆣ춼3ꆡC1,C2좡늻춬횵쪱뛔펦뗄뿢듦럧쿕몯쫽Θ(r)쟺쿟평춼3뿉틔뾴돶,떱C2폫C1뗄뇈횵풽듳쪱,럧쿕쯰쪧훐좱믵쯰쪧뗄뇈훘튲뻍풽듳,틲듋떱C2폫C1뗄뇈횵쟷뷼컞쟮듳쪱,럻뫏뺭뗤쒣탍늻퓊탭좱믵뗄볙짨ꆣ
뗚1웚ꆡꆡꆡꆡꆡꆡꆡꆡꆡ췵뾭탋,맹쯃:쒣뫽탨쟳쿂뗄뿢듦럧쿕벰ퟮ폅뿢듦뻶닟1013ꆡ럧쿕몯쫽쿂뿢듦솿뗄뻶닟뿢듦럧쿕몯쫽Θ(r)뿌뮭쇋퓚샻폃뺭뗤뿢듦쒣탍좷뚨뗄뺭볃엺솿Q쳵볾쿂,떱쪵볊탨쟳솿r좡늻춬횵쪱믡닺짺뗄럑폃퓶볓횵ꆣ볙짨틑횪탨쟳솿뇤뮯랶캧틔벰퓚룃랶캧쓚돶쿖뗄뿉쓜탔럖늼죧춼1쯹쪾뗄쒣뫽쫽ꆫR,웤솥쫴몯쫽캪ΛꆫR(r),r0캪뿍맛뮷뺳늻랢짺틢췢뇤뮯쳵볾쿂뗄헽뎣탨쟳솿ꆣ캪쪹뗃뿢듦럧쿕듯떽ퟮ킡,컒쏇뿉틔좡럧쿕몯쫽ퟮ듳뒦뗄r횵ퟷ캪볆쯣뺭볃엺솿Q뗄닎쫽,떫쫇,춬쪱뮹튪볦맋뾼싇r좡횵뗄뿉쓜탔돌뛈ΛꆫR(r)(죧춼4쯹쪾)ꆣ폚쫇,컒쏇좡럧쿕몯쫽Θ(r)퓚쒣뫽쯙뛈럖늼ΛꆫR(r)쿂폫r훡캧돉쏦믽뗄훘탄r,ퟷ캪퓚쒣뫽틢틥쿂뗄ퟮ병탨쟳쯙뛈뗄맀볆횵,ퟮ훕샻폃r살볆쯣뺭볃엺솿춼4ꆡ뿢듦럧쿕몯쫽폫탨쟳솿뗄뿉쓜탔럖늼Q2C3r=C1웤훐ꇒr2rõΛꆫR(r)õΘ(r)drr1Vr=ꇒr=(8)2ΛSꆫR(r)õΘ(r)drr1ꆡꆡ캪쇋볆쯣짏뗄랽뇣,춨뎣뿉틔볙짨쒣뫽탨쟳쯙뛈캪죽뷇쒣뫽쫽ꆫR=<r1,r0,r2>,웤솥쫴몯쫽캪r-r1,r1ꇜrꇜr0r0-r1ΛꆫR(r)=r2-r,r0ꇜrꇜr2r2-r00,웤쯼폚쫇,뿉틔볆쯣돶r-r1V=ꇒr0rΛꆫRΘ1dr+ꇒr1rΛꆫRΘ2dr=r1rꇒr0rΘ2-r1dr+Θ2drꆡꆡꆡꆡꆡꆡꆡꆡ-r0rr101ꇒr1rrrr02-r0(B2r1+A)(r0+r0r1+2r1)2Ar1(r0+r1)+B2(r0+2r1)(r0+r1)=-342ꆡ(Cr2+E)(r2+r2r0+2r0)(r2+r0)[2r2E+C2(r2+2r0)(r0+r0)+2D]+-+r2D34r-r1S=ꇒr0ΛrꆫRõΘ1dr+ꇒr1ΛꆫRõΘ2dr=rꇒr0Θ1dr+Θ2drꆡꆡꆡꆡꆡꆡꆡꆡr1r0rrr10-1ꇒr1r2-r02-r0(A+B2r1)(r0+r1)B(r0+r0r1+2r1)(Cr2+E)(r2+r0)=--Ar1+2322ꆡC(r2+r2r0+2r0)Dr2(lnr2-lnr0)++-(Er2+D)3r2-r0퓲훘탄λVr=,웤훐A,B,C,D,E평쪽(6)뚨틥ꆣS4ꆡ쪾샽튻엺믵컯웤듦뒢럑캪C1=50풪ö볾,좱믵럑캪C2=2500풪ö볾,튻듎뚩믵럑캪C3=1000풪,헽뎣탨
102쒣ꆡ뫽ꆡ쾵ꆡ춳ꆡ폫ꆡ쫽ꆡ톧ꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡ2010쓪쟳쯙뛈r0=100볾ö쳬,ퟮ킡탨쟳쯙뛈캪r1=90볾ö쳬,ퟮ듳탨쟳쯙뛈캪r2=110볾ö쳬,캪쇋맦뇜탨쟳쯙뛈뇤뮯듸살뗄럧쿕,듋쪱펦죧뫎좷뚨뚩믵엺솿?뷢:틔헽뎣탨쟳쯙뛈r0=100볾ö쳬C3r0,볆쯣뗄뺭볃뚩믵솿캪Q2=C=6312465볾ꆣ1뾼싇떽쪵볊뗄탨쟳쯙뛈폐뿉쓜랢짺뇤뮯,늢볙짨탨쟳쯙뛈캪죽뷇쒣뫽쫽ꆫR=<90,100,110>,폚쫇,평짏쫶릫쪽(8)뿉쯣뗃λr=10315621(듋쪱C2쫇C1뗄50놶),뷸뛸뗃돶탞뚩뗄뚩믵엺솿캪λQ32C3r=C=6413621볾1죧맻좱믵럑C2=500000풪ö볾,퓲평짏쫶릫쪽(8)뿉쯣뗃λr=10519525,듋쪱뗃돶탞뚩뗄뚩믵솿캪Q32Cλ3r=C=6511007볾ꆣ평듋뿉볻,떱C2폫C1뗄뇈횵풽듳쪱,럧쿕쯰쪧훐좱믵쯰쪧뗄뇈훘튲뻍풽듳,틲1뛸뗃돶탞뚩뗄뚩믵솿튲풽룟ꆣ5ꆡ뷡쫸폯놾컄뛔뺭뗤뿢듦퓚탨쟳랢짺뇤뮯쪱닺짺뗄쯰쪧뷸탐쇋쳖싛ꆣ헫뛔탨쟳뗄뇤뮯쯹듸살뗄뺭볃쯰쪧뚨틥쇋럧쿕몯쫽ꆣ퓚룸돶탨쟳뇤뮯뗄쒣뫽럖늼쳵볾쿂,뛔뒫춳뗄뺭볃엺솿쒣탍뷸탐쇋탞헽,늢뗃떽쇋쒣뫽틢틥쿂뗄뿢듦럧쿕맦뇜랽낸,벴춨맽쟳럧쿕몯쫽퓚쒣뫽틢틥쿂뗄훘탄뻶닟랽램뗃돶쒣뫽탨쟳쿂뗄ퟮ폅듦뒢솿ꆣ닎뾼컄쿗:[1]ꆡKacpryzkJ,[J].FuzzySetsandSystems,1982,8:117ꆫ132.[2]ꆡ[J].IEEETransactionsonSysterms,Man,andCybernetics,1987,(SMC217):1082ꆫ1084.[3]ꆡChangSC,YaoJS,[J].EuropeanJournalofOp2erationalResearch,1998,109(1):183ꆫ202.[4]ꆡWuKM,[J].Euro2peanJournalofOperationalResearch,2003,150(2):320ꆫ352.[5]ꆡYaoJS,[J].FuzzySetsandSystems,1999,105(3):311ꆫ337.[6]ꆡYaoJS,ChangSC,[J].ComputersandOperationsResearch,2000,27(10):935ꆫ,GUOSi2zong(InstituteofMathematicsandSystemsScience,LiaoningTechnicalUniversity,Fuxin123000,China)Abstract::Inventory;FuzzyDemand;RiskFunction;EconomicOrderQuantities
