싌즫닺욷믘쫕닟싔뗄폅뮯쒣탍벰펦폃ꆾ햪튪ꆿ퓚럖컶닺욷믘쫕뒦샭쓦쿲컯쇷솴뗄믹뒡짏,뷨훺폚닰킶쫷뾼싇닺욷럖닰돌뛈,틔뛈솿닺욷뗄닰킶돉놾;퓋폃믹폚ퟷ튵뗄돉놾럖컶램,좫쏦싛쫶쇋쇣늿볾퓙폃ꆢ닄쇏퓙짺ꆢ낲좫뒦훃뗈닺욷럏웺뒦샭닟싔뗄돉놾폫킧틦,붨솢쇋닺욷믘쫕닟싔폅톡뗄0-1탍쒿뇪맦뮮쒣탍,늢틔PC믺뗄믘쫕뒦샭캪샽,뷸탐쇋쪵볊펦폃ꆣ춨맽쒣탍쟳뷢,뿉틔뾼달룷쒿뇪뗄쪵쿖돌뛈벰웤닮뻠,폐샻폚횸떼웳튵룄뷸닺욷짨볆ꆣ맘볼듊:믘쫕;닰킶;0-1맦뮮;쒿뇪맦뮮훐춼럖샠뫅:ꆡꆡꆡ컄쿗뇪쪶싫:AAOptimizingModelanditsApplicationonGreenProduct’sRecoveryOptionsXIE1Jia2ping,ꆡCHENRong22qiu(,&Economics,Shanghai200433,China;,&Technology,Wuhan430074)ꆾAbstractꆿOnthefoundationofanalyzingthereverselogisticschainofproductrecoveryprocessing,,thecost2benefitsaboutcomponentsreusing,materialsrecycling,,the0-1goalprogrammingmodelonproduct’,:recovery;disassembly;0-1programming;goalprogrammingꆡꆡ쯦ퟅ쮭짺닺쮭뢺퓰믘쫕뒦샭뗄램맦돶첨,웳튵릩펦짌믲훆퓬짌,ퟷ캪뛾쫖쇣볾믲퓙짺닄쇏뷸죫짺캪쇋붵뗍컛좾훎샭럑폃벰컛좾뒦랣럑폃,복짙럏웺닺쾵춳,탎돉럏웺닺욷믘쫕뒦샭컯쇷뗄쓦쿲릩펦솴뛑럅솿,쫷솢뮷놣탎쿳,헽뷸탐ퟅ튻뎡싌즫룯쏼ꆣ닺췸싧ꆣ믘쫕컯쇷퓚쓦쿲릩펦솴훐뮻,탨튪뫄럑튻뚨욷틲릦쓜실뫳ꆢ쫙쏼훕뷡ꆢ퇹쪽맽쪱믲웆쯰뛸놨럏횮뗄풴,뷸탐튻쾵쇐뗄퓶횵ퟷ튵,헢뻍릹돉럏웺닺욷뫳,캪쇋돤럖샻폃풴ꆢ복짙뛔뮷뺳뗄캣몦,탨뷸탐믘쫕뒦샭뗄볛횵솴벰ퟷ튵돉놾솴ꆣ믘쫕뒦샭돉놾쫇믘쫕뒦샭ꆣ믘쫕컯쇷듓폃뮧쓦쿲믘떽믘쫕짌,뷸탐놨럏닺욷뗄쫕벯ꆢ퓋쫤ꆢ닰킶ꆢ퓙짺ꆢ퓙퓬ꆢ쳮싱뗈ퟷ닺욷럖닰ꆢ쇣볾퓙퓬ꆢ닄쇏퓙짺,좻뫳퓙쓦쿲쇷떽튵뗄럑폃횧돶,쯹믱뗃뗄쫕죫냼삨:뛾쫖닺욷돶쫛뗄쿺쫛쫕죫ꆢ퓙폃쇣늿볾뗄쿺쫛쫕죫믲쇣늿볾퓙폃쯹뷚풼뗄훆퓬럑폃ꆢ퓙짺닄쇏뗄쿺쫛쫕죫믲쪹폃퓙짺닄쇏쯹뷚풼뗄닄쇏닉릺럑폃ꆢ복짙럏웺컛좾컯뗄쳮싱솿쯹듸살뗄뮷놣럑폃뷚풼뛮뗈[1]ꆣ뿉틔닉폃뗄믘쫕뒦샭닟싔냼삨닺욷붵벶퓙폃ꆢ닺욷캬탞퓙폃ꆢ늿볾
ꆪ70ꆪꆡꆡꆡꆡ쾵ꆡ춳ꆡ릤ꆡ돌ꆡ샭ꆡ싛ꆡ랽ꆡ램ꆡ펦ꆡ폃뗚13뻭ꆡ랭탂ꆢ쇣볾퓙퓬ꆢ닄쇏퓙짺ꆢ럙징믱쓜뫍럏웺뒦훃쫇ꆰ뫍ꆱ탍솬뷓맘쾵,탩쿟뗄볽춷뷡뗣쫇럇쪵볊뗄닰뗈\[2ꆣ\]퓚믘쫕벼쫵뿉탐뗄쳵볾쿂,헫뛔믘쫕뒦샭닟싔킶ퟷ튵,죧닰뾪뷡뗣A0폫탩뷡뗣A2횮볤뗄솬뷓뻍뗄늻춬ퟩ뫏쯹탎돉뗄믘쫕랽낸,죧뫎쪵쿖풤웚뗄믘뿉틔춬쪱붫쇣볾A43뫍A52닰킶쿂살,쯹틔쯼쏇폫A5쫕쒿뇪,춬쪱쪹믘쫕킧틦ퟮ듳뮯,펦룃뾼싇믘쫕닟싔횮볤뗄닰킶쪱볤캪0ꆣ뗄돉놾폫킧틦ꆣ틲듋,ퟛ뫏뾼싇쇣늿볾퓙폃ꆢ닄쇏퓙닺욷닰킶쫷훐뗄튶뷡뗣쎻폐ퟓ뷡뗣,ퟩ돉쇣볾짺ꆢ낲좫쳮싱뗈뗄뺭볃탔,붨솢쾵춳폅뮯쒣탍,쪵쿖벯SP;룹뷡뗣(닺욷)벰훐뷡뗣(ퟩ돉닺욷뗄쒣뿩뫍믘쫕뒦샭뗄뺭볃킧틦뫍짺첬킧틦킭뗷폅뮯\[1ꆣ\]늿볾)뚼폐ퟓ뷡뗣,ퟩ돉늿볾벯SA,쇣볾벯SP폫늿닺욷믘쫕뻶닟훐,뫢솿믘쫕랽낸뗄폅쇓췹췹튪볾벯SAퟩ돉뷡뗣벯Sꆣ춼1훐:춬쪱뾼싇뛠룶쒿뇪ꆣ뛸퓚헢킩쒿뇪훐,폐ퟮ킡뮯뗄,SP=(A31,A32,A41,A42,A43,A51,A52,A6,A7)튲폐ퟮ듳뮯뗄;폐훷튪뗄,튲폐듎튪뗄;폐뮥쿠늹돤SA=(A0,A1,A2),ꆡS=SPꇈSA뗄,튲폐뮥쿠뛔솢뗄;폐뇘탫쪵쿖뗄,튲폐쾣췻듯떽ꆡꆡ캪쇋볲쫶랽뇣,돽쳘쫢쮵쏷틔췢,뷡뗣뇠뫅춳튻뗄ꆣ뛔헢퇹뢴퓓뗄뻶닟컊쳢,쓑틔뮯돉떥튻쒿뇪뷸캪Aijl,웤훐,i뇭쪾쒳엺믘쫕뗄닺욷탲뫅,j뇭쪾쇣탐톡폅ꆣ늢쟒,쇣늿볾ꆰ퓙폃폫럱ꆱꆢꆰ퓙짺폫럱ꆱ뚼쫇늿볾훖샠탲뫅,l뇭쪾뗚j훖쇣늿볾뗄볾쫽탲뫅ꆣ뷡쟳뷢ꆰ쫇ꆱ믲ꆰ럇ꆱ뗄뻶닟컊쳢,뿉틔뷨훺0-1맦뮮뫍뗣Aijl쯹냼몬뗄ퟓ뷡뗣벰Aijl놾짭뗄벯뫏ퟩ돉웤뿉듯쒿뇪맦뮮,붨솢0-1탍믘쫕뒦샭쒿뇪맦뮮쒣탍ꆣ벯LS(Aijl),춼1훐:1ꆡ닺욷뗄닰킶돉놾LS(A1)={A1,A32,A42,A51,A6,A7}닺욷횻폐닰킶닅쓜쪵쿖닄쇏뗄믘쫕뫍뿉폃쇣늿LS(A31)={A31}볾뗄퓙퓬ꆣ좻뛸,닺욷닰킶뗄랽쪽뫜뛠ꆡ닰킶뻶닟,펦룃룹뻝닰킶뗄쒿뗄,뻶뚨닺욷뗄럖닰돌뛈ꆣ늻춬뗄믘쫕닟싔뻶뛔폚쒳엺럏웺닺욷i뗄뗚j훖쇣늿볾뛸퇔,뿉뚨쇋닉좡늻춬뗄닰킶랽쪽,늻춬뗄닰킶랽쪽뗄돉놾틔톡퓱뗄뒦샭닟싔폐쇣볾퓙폃ꆢ닄쇏퓙짺뫍럏웺뒦횧돶닮틬뷏듳,펦룃뾼싇닺욷닰킶뗄뺭볃탔컊쳢ꆣ훃(낲좫쳮싱)ꆣ믘쫕쇣늿볾뗄쫗튪뮷뷚쫇뷸탐럇웆뮵탔닰킶;좻뫳,붫닰킶뫳뗄쇣늿볾뷸탐볬퇩ꆣ뛔폚ꆡ닰킶쫷뷸탐닺욷럖닰쪱,뿉틔샻폃닺욷뷡릹컄볾릹붨뿉퓙폃쇣늿볾,룹뻝탨쟳쟩뿶,탨뻶닟쫇ퟷ퓙폃뒦웤닰킶쫷(볻춼샭,뮹쫇ퟷ닄쇏퓙짺믲럏웺쳮싱뒦샭ꆣ볙짨쇣늿볾j1\[3\)ꆣ]DT늻횻쫇닰킶뗄쇣늿볾쟥떥,뮹탨랴펳닺욷닰킶쿮쒿뗄뷡릹닣듎ꆢ닰킶닣벶뗄뗄탨쟳솿캪Dj,죧맻Dj>0,뿉틔뾼싇붫쇣늿볾j뷸쿈뫳쮳탲ꆣ탐믘쫕퓙폃뒦샭;죧맻Dj=0,퓲뿉틔룹뻝쪵볊쟩뿶뷸탐닄쇏퓙짺믲쳮싱뒦샭ꆣꆰ퓙폃폫럱ꆱ벰ꆰ퓙짺폫럱ꆱ뚼쫇쟳뷢ꆰ쫇ꆱ믲ꆰ럇ꆱ뗄뻶닟컊쳢,뿉틔뮯캪0-1맦뮮컊쳢,쯹틔틽죫퓙폃뻶닟뇤솿Xijlꆢ퓙짺뻶닟뇤솿iYjl(횻좡0믲1횵):1ꆡ붫쇣늿볾Aijlퟷ랭탂믲퓙퓬뗈퓙폃뒦샭Xijl=0ꆡ붫쯼ퟷ닄쇏퓙짺믲럏웺쳮싱뒦샭1ꆡ붫쇣늿볾Aijlퟷ닄쇏퓙짺뒦샭iYjl=0ꆡ붫쯼ퟷ럏웺쳮싱뒦샭춼1ꆡ닺욷닰킶쫷뷸탐닄쇏퓙짺믲럏웺쳮싱,펦뾼싇닄쇏샠탍벰웤볦죝탔ꆢ쫇럱몬폐폐몦닄쇏,틔뇜쏢퓙짺닄쇏쿠뮥ꆡꆡ춼1쯹쪾뗄닺욷닰킶쫷훐뗄뷡뗣볈뇭쪾쇣늿볾컛좾뫍뢯쪴,뇜쏢럏웺쳮싱뛔뮷뺳뗄펰쿬,틲듋뮹탨(죧ퟩ볾ꆢ늿볾ꆢ쇣볾),폖뇭쪾닰킶믮뚯;볽쿟뇭쪾뷡뾼싇쫇럱닰킶,틽죫퓙짺믲럏웺뗄닰킶뇪횾뇤솿뗣(쇣늿볾)횮볤뗄솬뷓맘쾵,쫴폚뷡뗣쪽췸싧춼ꆣ듓튻룶쪵뷡뗣틽돶뛠쳵쪵볽쿟,쮵쏷볽춷뷡뗣폫볽캲Rijlꆣ떱Rijl=1쪱,뇭쪾붫Aijlퟷ퓙짺믲럏웺뒦샭쪱탨뷡뗣횮볤쫇ꆰ믲ꆱ탍솬뷓맘쾵,뿉틔붫볽춷뷡뗣훰룶튪뷸탐닰킶;랴횮,Rijl=0퓲늻탨튪닰킶ꆣ뗘듓볽캲뷡뗣닰킶쿂살;탩볽쿟뇭쪾킶뾪볽캲뷡뗣ퟜ횮,에뛏닺욷i뗚j훖쇣늿볾훐뗄뗚l룶쇣늿볾쫇럱뷸탐닰킶,떱max{Xijl,Rijl}=1쪱,뇭쪾뷡뗣(탩쿟뷡뗣)뗄솬뷓볾뻍뿉틔붫듓쯼틽돶뗄탩볽쿟뗄볽춷뷡뗣춬쪱닰킶쿂살Aijl탨튪닰킶;랴횮,max{Xijl,Rijl}=0퓲늻탨튪닰,볽춷뷡뗣폫볽캲뷡뗣횮볤킶ꆣ
ꆡ뗚1웚킻볒욽,뗈:싌즫닺욷믘쫕닟싔뗄폅뮯쒣탍벰펦폃ꆪ71ꆪꆡ닰킶돉놾벴뷸탐낲좫쳮싱뒦훃,쯹틔놾컄늻뾼싇듦뒢컊쳢ꆣ캪쇋붫뷡뗣Aijl닰킶쿂살,쿈튪닰킶웤뢸뷡뗣ꆡ퓙폃쇣늿볾뗄쫕틦Aifk,틲듋뾼달뷡뗣Aifk쫇럱탨튪뷸탐닰킶,훷튪쫇뾴떱퓙폃뻶닟뇤솿Xijl=1,탨뛔닰킶뗄쇣늿볾Aijl뷡뗣Aifk뗄뿉듯벯LS(Aifk)훐쫇럱몬폐탨튪닰킶뗄뷸탐볬퇩폫닢쫔틔벰랭탂폫퓙퓬뗈퓙폃뒦샭,웤퓙쇣늿볾ꆣ죧맻뛔폚죎틢뗄AijlꇊLS(Aifk),폐폃돉놾캪CipXjl,쿠펦좡뗃뗄퓙폃볛횵캪RpXijlꆣ럏jjmax{Xijl,Rijl}=1돉솢,퓲뷡뗣Aifk탨뷸튻늽닰웺컯복짙붫듸살뮷뺳뒦샭럑뗄쿂붵,듓뛸뇜쏢틲뮷AiꇊLiS(A)jlfk킶;랴횮뺳컊쳢뛸퓢쫜뗄뺭볃뒦랣믲복짙쳮싱돉놾,믱뗃뮷,max{Xijl,Rijl}=0,퓲늻탨퓙뷸탐닰킶ꆣAiꇊLS(Ai)jlfk놣쫕틦\[1ꆣ\]틲퓙폃뛸복짙뗄럏웺뒦샭뗄훘솿캪평폚뷡뗣Aijl폫웤뢸뷡뗣Aifk뗄솬뷓랽쪽(샠탍)늻WjXijl,웤뮷놣쫕틦캪CLDIjWjXijlꆣ캪쇋뇣폚0-1춬,쯹탨튪뗄닰킶쪱볤뎤뛌튲늻튻퇹,펰쿬떽닰킶돉맦뮮컊쳢뗄쟳뷢,쯵킡Xijl뗄좡횵ퟩ뫏,틽죫퓙퓬쪶놾ꆣ듓Aifk짏닰킶쿂뷡뗣Aijlퟔ짭뗄돉놾Cd{Aijl)=뇰뇤솿Cdꆤtd(Aijl),웤훐,Cd뇭쪾떥캻쪱볤뗄닰킶돉놾(죋PDj=Rp-Cp+CLDIjWjjj릤럑ꆢ릤뻟짨놸럑ꆢ뫄쓜횧돶뗈),td(Aijl)쫇듓뢸뷡뗣퓚Dj>0뗄쳵볾쿂,죧맻PDjꇝ0,퓲Xijl=1믲0,쫇짏닰킶쿂뷡뗣Aijl쯹탨뗄쪱볤ꆣ럱튻뚨퓙퓬뮹탨좨뫢퓙폃쫕틦폫퓙짺쫕틦벰퓙퓬쓜듓튶뷡뗣뾪쪼,볆쯣룷뷡뗣뗄샛볓닰킶돉놾ꆣ튶솦;랴횮,죴PDj<0믲Dj=0,뇘폐Xijl=0,뇭쪾횻뷡뗣늻탨튪퓙뷸탐럖닰,쯹틔뛔폚죎틢뗄AijlꇊiSP,쓜붫쇣늿볾Aijlퟷ닄쇏퓙짺믲럏웺쳮싱뒦샭ꆣퟛ짏쯹죧맻탨튪닰킶,쯼뗄샛볓닰킶돉놾sumCd(Aijl)뻍쫇쫶,퓙폃쇣늿볾뗄ퟜ쫕틦캪웤ퟔ짭뗄닰킶돉놾Cd(Aijl);죧맻늻탨튪닰킶퓲R퓙i폃=sumCd(Aijl)=0,벴ꆡꇆ(Rp+CLDIjWj-Ct-Cp)ꇝjjjꇆXijl-sumCd(AijϖPD0ljl)=Cd(Aijl)max{Xijl,Rijl}ꆡAijlꇊiSPjꆡꆡ뛔폚훐뷡뗣믲룹뷡뗣Aifk뛸퇔,샛볓닰킶돉놾ꆡꇆ(Cd(Aifk)max{Xijl,Rijl})ꇊLS(AiAiꇊiSAi)jlfkjlsumCd(Aifk)뗈폚볽캲뷡뗣Aifkퟔ짭뗄닰킶돉놾ꆡ닄쇏퓙짺뗄쫕틦Cd(Aifk)폫듓뷡뗣Aifk틽돶뗄쯹폐볽춷뷡뗣Aifk뗄샛볓닰킶돉놾떱뻶닟뇤솿Xijl=0쪱,뇭쪾쇣늿볾Aijlퟷ닄쇏sumCd(Aijl)횮뫍,뿉틔내쿂쪽볆쯣:퓙짺믲럏웺쳮싱뒦샭ꆣ캪쇋뻶닟쫇럱붫쯼뷸탐퓙짺sumCd(Aifk)=(Cd(Aifk)+ꆡꆡꆡꆡꆡꇆ뒦샭,탨에뛏닄쇏퓙짺쫇럱믱샻,틽죫퓙짺쪶뇰뇤솿sumCd(Aijl)max{Xijl,Rijl}RDj=Rm-Cm+CLDIj:죧맻RDjꇝ0,퓲뷸탐퓙짺jjAiꇺAiAiꇊLS(Ai)jlfkjlfkAi뒦샭믘쫕닄쇏믱샻,쫇럱퓙짺뮹탨뾼싇퓙짺쓜솦,벴jlꇊiS,ꆡAifkꇊiSAꆡꆡ떱볆쯣떽룹뷡뗣뗄샛볓닰킶돉놾쪱,뻍뗃떽믘iYjl=1믲0;럱퓲,RDij<0,뇘폐Yjl=0,횻쓜뷸탐낲쫕뻶닟랽낸좫쳮싱ꆣ퓙짺뒦샭쯹횧뢶뗄럑폃:(X;Y)뗄닰킶돉놾,벴폐CCmWjRPj(1-Xijl)Yijl닰i킶=ꇆ(Cd(Aifk)max{Xijjl,Rijl})AiꇊiSAiꇊLS(Ai)jlfkjl퓙짺닄쇏뗄쫕죫캪RmWjRPj(1-Xijl)Yijl2ꆡ럏웺닺욷믘쫕뒦샭뗄쫕틦럖컶j퓙짺쯹복짙뗄럏웺뒦샭듸살뗄뮷놣쫕틦:짨뗚j훖쇣늿볾뗄퓙폃볛횵캪Rp(풪ö볾),볬jCLDIjWjRPj(1-Xijl)Yijl닢ꆢ랭탂벰퓙퓬뗈퓙폃돉놾캪Cp(풪ö볾),훘솿캪j틲듋,닄쇏퓙짺뗄ퟜ쫕틦캪Wj(kg),뿉틔폃폚닄쇏퓙짺뗄뇈샽캪RPj,퓙짺쫕R퓙i짺=죫캪ꇆ(Rm-Cm+CLDIj)WjꇁjjRjϖRDꇝ0m(풪ökg),퓙짺돉놾Cm(냼삨쯩쇑ꆢ럖샠ꆢ퓙jjj짺뗈믘쫕닄쇏뗄맽돌RPj)(풪ökg),쳮싱돉놾캪CL(풪öꇆ(1-Xijl)Yijllkg)ꆣ평폚늻춬쇣늿볾뗄쳮싱뒦샭돉놾듦퓚닮틬,맊ꆡ럏웺뒦샭뗄돉놾볙짨웤럏웺뒦샭돉놾횸쫽캪DIj(0ꇜDIjꇜ10,뒦샭럏웺컯뗄랽쪽냼삨럙징뫍낲좫쳮싱뗈럏웺DIj=0뇭쪾럏웺뒦샭탨횧뢶뗄돉놾벶뇰ퟮ뗍,DIj=뒦훃,쇣늿볾Aijlퟷ닄쇏퓙짺뒦샭횮뫳뮹탨뷸탐럏웺10뇭쪾럏웺뒦샭탨횧뢶뗄돉놾벶뇰ퟮ룟\[3\])ꆣ볙짨뒦샭뗄훘솿캪죧맻놻닰킶뗄쇣늿볾늻뷸탐퓙퓬믲퓙짺뒦샭,퓲솢Wj(1-RPj)(1-Xijl)Yijl
ꆪ72ꆪꆡꆡꆡꆡ쾵ꆡ춳ꆡ릤ꆡ돌ꆡ샭ꆡ싛ꆡ랽ꆡ램ꆡ펦ꆡ폃뗚13뻭ꆡ쇣늿볾Aijl늻ퟷ퓙폃믲퓙짺뒦샭떫탨뷸탐럏웺뒦샭,ꆡꆡ(7)업돢좡횵풼쫸:퓙폃뻶닟뇤솿ꆢ퓙짺뻶닟뇤웤훘솿캪Wj(1-Xijl)(1-Yijl),퓲럏웺뒦샭뗄돉놾솿늻쓜춬쪱캪1,벴죧쿂:XijlYijl=0C럏i웺=ꇆꆡ쒿뇪풼쫸LDIjWjꇆ(1-jl돽쇋짏쫶뻸뛔풼쫸횮췢,뮹듦퓚쇭튻샠늻춬벶Xijl)(1-RPjYijl)뇰뗄쒿뇪풼쫸ꆣ놾컄뾼싇2벶쒿뇪:뗚1벶P1:퓙폃ퟛ뫏뿉뗃믘쫕뒦샭뗄뺻쫕틦죧쿂:쫕틦ퟮ듳뮯ꆢ퓙짺쫕틦ퟮ듳뮯ꆢ쳮싱돉놾ퟮ킡뮯뫍믘R믘i쫕뒦샭=R퓙i폃+R퓙i짺-C럏i웺-TCi쫕뒦샭뗄뺻쫕틦ퟮ듳뮯;뗚2벶P2:퓙짺쿮쫽ퟮ듳웤훐:TCi쫇횸럏웺닺욷i듓쿻럑헟떽믘쫕퓙짺짌뮯틔벰쳮싱뒦샭뗄쿮쒿쫽ퟮ킡뮯뗈ꆣ캪쇋듓쫽솿짏쯹탨뗄쫕벯ꆢ퓋쫤ꆢ듦뒢뗈ퟷ튵뗄룷훖럑폃횧돶ꆣ쏨쫶룷쒿뇪뗄웚췻횵듯떽뗄돌뛈,뛔뗚k룶쒿뇪몯3ꆡ믘쫕닟싔폅톡뗄0-1탍쒿뇪맦뮮쫽럖뇰틽죫헽ꆢ뢺욫닮뇤솿+-dk,dk,쟒+dk뫍-dkꇝ쒣탍0ꆣ+dk뇭쪾뗚k룶쒿뇪뎬맽웚췻횵뗄쫽횵-;dk뇭쪾ꆡꆡ믘쫕뻶닟훐,뫢솿믘쫕랽낸뗄폅쇓췹췹튪춬쪱뗚k룶쒿뇪캴듯떽웚췻횵뗄쫽횵\[5ꆣ\]뛔폚쎿튻룶쒿뾼싇뇪풼쫸뚼튪좷솢튻룶쾣췻듯떽뗄쒿뇪웚췻횵,ퟷ캪:퓙폃쫕틦ퟮ듳뮯ꆢ퓙짺쫕틦ퟮ듳뮯ꆢ쳮싱돉놾ퟮ킡뮯ꆢ퓙짺쿮쫽ퟮ듳뮯틔벰쳮싱뒦샭뗄쿮쒿쫽ퟮ쒿뇪풼쫸뗄폒뛋쿮ꆣ맊폐죧쿂쒿뇪풼쫸\[6\]:킡뮯뗈뛠룶쒿뇪뗚1벶P1ꆣ퓙폃쫕틦ퟮ듳뮯\[4ꆣ\]볙짨웳튵뿉폃뗄닰킶쪱볤캪Td(min),퓙퓬쇣늿볾j뗄쓜솦캪PRj(볾),캪쇋닄ꇆꇆ(Rp-Cp+CLDIjWj)ꇁjjijϖD>0j쇏퓙짺뛸뷸탐쯩쇑럖샠뗄쓜솦캪&PDꇝ0ARj(kg),틲듋붨솢0-1탍쒿뇪맦뮮쒣탍죧쿂:ꇆXijl-ꇆꇆ(Cd(Aifk)ꇁliAiꇊꆡ뻸뛔풼쫸max{Xijl,Rijl})+-+d1-d1=R3퓙폃Ai(1)닺욷믘쫕ퟜ솿풼쫸:퓙폃ꆢ퓙짺뗄쇣늿볾뗄ꇊLS(Ai)jlfk샠탍뫍쫽솿늻뎬맽듓믘쫕닺욷훐뿉믱뗃뗄샠탍뫍쫽ꆡꆡ퓙짺쫕틦ퟮ듳뮯솿,벴ꇆꇆ(Rm-Cm+CLDIj)WjꇁjjꇆꇆijϖD>0ji(Xjl+Yijl)ꇜꇆQijiliRPjꇆYijl+-+d2-d2=R3퓙짺ꆡꆡl(2)퓙폃쇣늿볾뗄탨쟳풼쫸:듓럏웺닺욷훐쯹닰킶뗄퓙폃쇣늿볾j뗄쫽솿늻뎬맽웤탨쟳ퟜ솿,벴ꆡꆡ쳮싱돉놾ퟮ킡뮯ꇆꇆXiꇆꇆCLDIjWjꇁjlꇜDjꆡjϖDjꇝ0ijilꆡꆡ(3)닰킶쓜솦풼쫸:럖닰럏웺닺욷ퟷ튵뗄쪱볤ꇆ+(1-RPjYijl)+-d3-d3=C3럏웺l늻뎬맽웳튵뿉폃뗄닰킶쪱볤,벴ꆡꆡ믘쫕뺻쫕틦ퟮ듳뮯ꇆꇆ(td(Aifk)max{Xijl,Rijl})ꇜTdꇆ(R퓙i폃+R퓙i짺-C럏i웺-ꇆTCi)+iAiꇊi)SAiꇊLS(Aijlfkifkꆡꆡ-+(4)퓙퓬쓜솦풼쫸:뷸탐퓙퓬뒦샭뗄쇣늿볾jd4-d4=R3믘쫕뒦샭뗄쫽솿늻뎬맽웳튵퓙퓬룃샠쇣늿볾뗄쓜솦,벴ꆡꆡ뗚2벶P2ꆣ퓙짺쿮쫽ퟮ듳뮯ꇆꇆXijlꇜAPjꆡjϖDjꇝ0ꇆꇆꇆYi-+jl+d5-d5=NR3ilijlꆡꆡ(5)쯩쇑럖샠쓜솦풼쫸:퓙짺뒦샭뗄쇣늿볾탨ꆡꆡ쳮싱쫽솿ퟮ킡뮯튪뷸탐쯩쇑폫럖샠,떫뒦샭뗄훘솿늻펦뎬맽웳튵뗄뿉폃쓜솦,벴ꇆꇆW+j(1-RPij)ꇆYjl+-d6-d6=NB3ijlꇆꇆꆡ쒿뇪듯돉몯쫽WjRPjꇆYijlꇜAR캪쟸뇰헢킩쒿뇪뗄훘튪돌뛈,틽죫폅쿈뗈벶틲ijljϖRDjꇝ0ퟓPk살뇭쪾뗚k뗈벶뗄쒿뇪,웤맘쾵쫇P1µP2µꆡꆡ(6)쫇럇좡횵풼쫸:퓙폃뻶닟뇤솿ꆢ퓙짺뻶닟뇤ꆭµPK,뒦폚춬튻룶폅쿈뗈벶뗄쒿뇪뿉쓜늻횹튻솿폫퓙짺럖닰뇪횾뇤솿뚼캪1믲0,벴룶,캪쟸뇰쯼쏇횮볤뗄쿠뛔훘튪탔,럖뇰뢳틔늻춬뗄Xijl,Yijl,Rijl=1믲0좨쫽w\[5ꆣ\]
ꆡ뗚1웚킻볒욽,뗈:싌즫닺욷믘쫕닟싔뗄폅뮯쒣탍벰펦폃ꆪ73ꆪ릹퓬쒿뇪듯돉몯쫽틔쟳뗃폐맘욫닮뇤솿뗄ퟮ킡횵,듦퓚3훖믹놾탎쪽뗄ퟩ뫏:ꋙ죴튪쟳뺡뿉쓜듯4ꆡ펦폃낸샽떽맦뚨뗄쒿뇪웚췻횵,퓲펦쪹쿠펦뗄헽ꆢ뢺욫닮뇤솿놾샽뾼싇볆쯣믺뗄믘쫕뒦샭\[6\],캪뇣폚퓋쯣,ퟷ+dk뫍-dk뚼뺡뿉쓜듯떽ퟮ킡ꆣꋚ죴쾣췻뺡뿉쓜늻뗍죧쿂볙짨:믘쫕춬탍뫅뗄PC믺100첨(벴i=1,2,폚웚췻횵,퓲펦쪹쿠펦뗄뢺욫닮뇤솿-dk뺡뿉쓜뗄ꆭ,100),웤럖닰맽돌볻춼1,믘쫕뒦샭룷쇣늿볾뗄킡,뛸늻맘탄뎬돶솿+dk뗄듳킡,맊횻탨붫-dk쇐죫쫕죫벰돉놾쫽뻝죧뇭1쯹쪾ꆣ떥첨PC믺뗄쫕벯ꆢ퓋쒿뇪몯쫽훐ꆣꋛ죴쾣췻늻뗃뎬맽웚췻횵,퓲펦쪹쿠쫤뗈믘쫕쫐뎡뗄돉놾TCi=55풪ö첨;볙짨떥캻쪱펦뗄헽욫닮뇤솿+d볤뗄닰킶돉놾Cd=풪ök뺡뿉쓜킡,뛸늻맘탄뗍폚횵-dkmin,훐뷡뗣뗄닰킶쪱뗄듳킡,맊횻탨붫+dk쇐죫쒿뇪몯쫽훐ꆣ짏쫶쒿뇪풼볤럖뇰캪:td(A1)=10minꆢtd(A2)=15min,뿉폃뗄쫸뗄듯돉몯쫽죧쿂:닰킶쪱볤캪5h;뿉폃뗄쯩쇑럖샠쓜솦600kg;캪쳮m+-inZ=P1(w-1d1+w-튻룶떥캻벶뇰뗄럏웺컯뗄돉놾CL=풪ö2d2+w3d싱3+w4d4)+kg;P-+퓙짺폫쳮싱늻탨튪닰킶ꆣ2(w5d5+w6d6)뇭1ꆡ믘쫕뒦샭닟싔뗄쿠맘쫽뻝쇣볾뻶닟닰킶쪱볤쫽솿탨쟳솿퓙폃볛횵퓙폃돉놾퓙퓬쓜솦훘솿퓙짺뇈샽퓙짺쫕죫퓙짺돉놾쳮싱횸쫽뫅j뇤솿td(AiCpjl)QijDRjpAPCmDIjjjWjRPRjmjjjA31Xi31,,Yi3210A41Xi41,Yi4120A42Xi42,,Yi430A51Xi51,,Yi520A6Xi6,,ꆡꆡ듓뇭1뿉횪,평폚D5=D7=0틔벰PD4=Rp4-맻죧쿂:100첨PC믺뗄쇣볾훐,90첨뗄A31ꆢA32ꆢA6Cp4<0,맊퓙폃뻶닟뇤솿캪뫍10첨뗄A31ꆢA6ퟷ퓙폃뒦샭,10첨뗄A32뫍100Xi41=Xi42=Xi43=Xi51=Xi52=Xi7=0첨뗄A41ꆢA42ꆢA43ퟷ퓙짺뒦샭,웤쯻뗄쇣볾뚼ퟷ럏웺Xi31,Xi32,Xi6=0믲1뒦샭,뿉쪹믘쫕뒦샭뗄뺻쫕틦ퟮ듳(풪)ꆣ볆평폚RD5=Rm5-Cm5<0,RD6=Rm6-Cm6<0,쯣뿉횪,퓙폃쫕틦풪,퓙짺쫕틦=Rm7-Cm7<0,맊퓙짺뻶닟뇤솿캪풪,쳮싱돉놾풪,퓙짺쿮쫽310볾,쳮싱쫽솿Yi51=Yi52=Yi6=Yi7=ꆣYi31,Yi32,Yi41,Yi42,Yi43=0믲1뾼달0-1맦뮮컊쳢뗄ퟮ폅뷢쫇럱싺ퟣ쾣췻듯룹뻝믘쫕뻶닟랽낸(X;Y)뗄늻춬ퟩ뫏볆쯣웤닰킶쪱떽뗄쒿뇪웚췻횵,죧맻늻싺ퟣ,퓲좷솢쎿튻룶쒿뇪풼볤벰닰킶돉놾,샽죧,믘쫕랽낸쫸뗄폒뛋쿮ꆣ죧뛔폚뗚1벶쒿뇪뛸퇔,퓙폃쫕틦쾣췻(X;Y)=(1,1,0,0,0,0,0,1,0;0,0,1,1,1,0,0,0,0)듯떽R3퓙폃=풪,떫퓙짺쫕틦쾣췻늻뗍폚뇭쪾횻붫쇣볾A31ꆢA32ꆢA6ퟷ퓙폃뒦샭,A41ꆢA42ꆢA43ퟷ퓙짺뒦샭,웤쯻뗄쇣볾뚼ퟷ럏웺뒦샭ꆣ틲듋R3퓙짺=풪,쳮싱돉놾늻룟폚C3럏웺=,탨닰킶훐뷡뗣A1뫍튶뷡뗣풪,뺻쫕틦듯떽R3믘쫕뒦샭=풪ꆣ볙짨w1>w2>A31ꆢA32ꆢA6,웤닰킶쪱볤캪w3>w4,쟳뷢0-1탍쒿뇪맦뮮쒣탍,52첨뗄A31ꆢtd(A1)+td(A31)+td(A32)+td(A6)=10+5+10+5=30mA32ꆢA6뫍48첨뗄A31ꆢA6ퟷ퓙폃뒦샭,48첨뗄A23in닰킶돉놾ꇁ30=풪,뗈ꆣ뫍100첨뗄A41ꆢA42ꆢA43ퟷ퓙짺뒦샭,웤쯻뗄쇣볾뚼캪쇋쟳뗃0-1탍쒿뇪맦뮮뗄닎뾼웚췻횵,쿈늻ퟷ럏웺뒦샭,뿉틔싺ퟣ풤웚쒿뇪,볆쯣뷡맻죧쿂:퓙뾼싇쒿뇪풼쫸,틔믘쫕뒦샭뺻쫕틦ퟮ듳캪쒿뇪몯쫽폃쫕틦풪,퓙짺쫕틦풪,쳮싱돉(maxR믘쫕뒦샭),쟳뷢쿠펦뗄0-1맦뮮컊쳢,볆쯣뷡놾풪,믘쫕뒦샭뗄뺻쫕틦풪ꆣ
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