뗚8뻭뗚2웚2005쓪4퓂ꆡꆡꆡꆡꆡꆡꆡꆡꆡ맜ꆡ샭ꆡ뿆ꆡ톧ꆡ톧ꆡ놨JOURNALOFMANAGEMENTSCIENCESINCHINAꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡ짺닺탔웳튵ퟩ횯톧쾰ퟮ폅뿘훆쒣탍벰웤샭싛럖컶ꋙ뛅ꆡ죙1,뫺웦펢2,쏏횾쟠3(11컷낲뗧ퟓ뿆벼듳톧뺭볃맜샭톧풺,컷낲710071;21짏몣듳톧맺볊릤짌폫맜샭톧풺,짏몣201800;31헣붭릤튵듳톧뺭쎳맜샭톧풺,몼훝310032)햪튪:퓋폃ퟮ폅뿘훆샭싛퇐뺿짺닺탔웳튵ퟩ횯톧쾰믮뚯뗄뚯첬ퟮ폅뻶닟컊쳢.틔웳튵뗄룅쓮탔톧쾰춶싊뫍닙ퟷ탔톧쾰춶싊캪뻶닟뇤솿,샛믽횪쪶솿ꆢ짺닺싊ꆢ떥캻돉놾뫍럏욷싊뗈캪ힴ첬뇤솿,볆뮮웚쓚뗄ퟜ샻죳캪횸뇪몯쫽,붨솢쇋튻룶ퟮ폅뿘훆쒣탍,웤쳘뗣퓚폚맦랶뗘쏨믦룅쓮탔톧쾰뫍닙ퟷ탔톧쾰뛔웳튵샛믽횪쪶솿ꆢ짺닺싊ꆢ떥캻돉놾ꆢ훊솿틔벰웳튵샻죳뗄뚯첬펰쿬.룹뻝짺닺탔웳튵ퟩ횯톧쾰뫍짺닺뺭펪뗄쪵볊쟩뿶,쳡돶쇋튻킩뚨솿뮯뇭듯뗄볙짨뫍뚨틥.퓚볙짨뫍뚨틥뗄믹뒡짏샻폃ퟮ듳횵풭샭럖컶쇋쯹붨솢뗄쒣탍,믱뗃쇋맘폚뚯첬ퟮ폅룅쓮탔톧쾰춶닟싔뫍닙ퟷ탔톧쾰춶닟싔탔훊뗄튻킩뷡싛,붫헢킩뷡싛폫쪵볊컊쳢쿠뷡뫏,횸돶쇋퓚짺닺탔웳튵ퟩ횯톧쾰쪵볹짏뗄몬틥.맘볼듊:ퟮ폅뿘훆;짺닺탔웳튵;ퟩ횯톧쾰;룅쓮탔톧쾰;닙ퟷ탔톧쾰훐춼럖샠뫅:F22410ꆡꆡꆡ컄쿗뇪쪶싫:Aꆡꆡꆡ컄헂뇠뫅:1007-9807(2005)02-0046-080ꆡ틽ꆡ퇔톧쾰.잰헟춨맽엠통ꆢ뷸탞ꆢ뺭퇩뫍벼쓜뗄붻쇷뗈랽쪽듙뷸뛔틑폐쿔탔횪쪶뗄톧쾰뫍헆컕,듯떽뒫뗷닩쇋맺쓚췢듳솿뗄ퟩ횯톧쾰퇐뺿컄쿗뫳능뫍샻폃쿖폐횪쪶뗄쒿뗄.뫳헟춨맽릤ퟷ맽돌훐,ퟷ헟죏캪뗄쫔퇩뫍쪵퇩뗈랽쪽살듙뷸뛔틾탔횪쪶뗄뒴퓬,:틑폐뗄ퟩ횯톧쾰퇐뺿럖캪솽룶랽쿲:1)쳡돶룅쓮뮯뗄ퟩ횯톧쾰샭싛,좻뫳춨맽뛔쯹뗷닩듯떽뒴퓬탂횪쪶늢붫웤톸쯙뗘퓋폃폚짺닺뫍럾컱쪵볊쟩뿶뗄럖컶,닉좡룶낸퇐뺿믲쪵횤퇐뺿뗄랽맽돌뗄쒿뗄.헢솽훖탎쪽뗄ퟩ횯톧쾰뚼폐훺폚쳡램횧돖쯹쳡돶뗄샭싛\[1ꆫ5\].2)쿈뛔쪵볊뗄ퟩ횯톧룟짺닺싊,붵뗍돉놾,룄뷸훊솿,퓶볓샛믽횪쪶,듓쾰믮뚯뷸탐돩쿳뮯뗄쫽톧뇭듯,붨솢쫽톧쒣탍,뛔뛸퓶볓웳튵샻죳.떫쯼쏇뗄뚯첬펰쿬쫇늻춬뗄.죧쒣탍뷸탐샭싛럖컶,뗃돶튻킩뷡싛,좻뫳붫쯹뗃뷡뫎뚨솿뗘뿌뮭뫍럖컶헢킩늻춬펰쿬쫇톧헟뫍쪵볹싛뮹풭폚쪵볊펦폃\[6ꆫ8\].헢솽룶랽쿲짏뗄퇐뺿뿉헟웕뇩맘힢뗄컊쳢\[12,13\].틔뮥캪늹돤,뮥쿠펡횤.떫쫇,샻폃쫽톧랽램뛔ퟩ캪쇋뷢뻶짏쏦쳡돶뗄컊쳢,놾컄뛔ퟩ횯톧쾰횯톧쾰뗄돉놾뫍킧틦뷸탐뚨솿럖컶뗄퇐뺿늻뛠,뗄ퟮ폅뿘훆쒣탍뷸탐쇋샭싛럖컶,럖컶쇋룅쓮탔뛸헢퇹뗄뚨솿럖컶뛔폚웳튵쪵볊릤ퟷ훐폐맘ퟩ횯톧쾰뗄뷰춶죫뫍닙ퟷ탔톧쾰뗄뷰춶죫폫웳튵톧쾰믮뚯뗄뻶닟뫍쪵쪩뻟폐훘튪뗄쿖쪵틢틥.뗄샛믽횪쪶솿ꆢ떥캻돉놾ꆢ짺닺싊ꆢ훊솿벰샻죳뗈맺쓚췢뛔ퟩ횯톧쾰뗄뚨틥뛠훖뛠퇹\[9ꆫ11\],떫뇤솿횮볤뗄뢴퓓뚯첬맘쾵,뗃돶쇋튻킩맘폚룅쓮뿉틔붫ퟩ횯톧쾰뗄쒿뗄맩쓉캪:뛔ퟩ횯틑폐횪쪶탔톧쾰뫍닙ퟷ탔톧쾰뗄ퟮ폅뷰춶죫닟싔뗄뷡뗄돤럖샻폃뫍뛔탂횪쪶뗄뒴퓬.헢퇹뗄쒿뗄벤랢싛,늢붫샭싛폫쪵볊컊쳢뷡뫏웰살,뛔ퟩ횯톧쾰춶쇋룅쓮탔톧쾰뫍닙ퟷ탔톧쾰솽훖늻춬탎쪽뗄ퟩ횯죫뻶닟뷸탐쇋첽쯷탔퇐뺿.ꋙ쫕룥죕웚:2002-12-15;탞뚩죕웚:2004-03-12.믹뷰쿮쒿:맺볒ퟔ좻뿆톧믹뷰훺쿮쒿(70271021);짂컷쪡ퟔ좻뿆톧믹뷰훺쿮쒿(2001G03);짂컷쪡죭뿆톧퇐뺿쿮쒿(2003KR31).ퟷ헟볲뷩:뛅ꆡ죙(1968ꆪ),얮,짂컷쿌퇴죋,늩쪿,뢱뷌쫚.
뗚2웚ꆡꆡꆡꆡꆡꆡꆡꆡ뛅ꆡ죙뗈:짺닺탔웳튵ퟩ횯톧쾰ퟮ폅뿘훆쒣탍벰웤샭싛럖컶ꆪ47ꆪ놾컄뗄뒴탂탔퓚폚솽룶랽쏦.쫗쿈,뷨본ퟮ폅캪t쪱룃닺욷뗄떥캻돉놾,w(t)캪t쪱룃닺욷뗄뿘훆샭싛퓚뚯첬닺욷뚨볛뻶닟뫍뚯첬맣룦춶죫뻶럏욷싊.닟훐뗄펦폃\[14,15\],붫웤폃폚짺닺탔웳튵뗄ퟩ횯톧짺닺탔웳튵쒳닺욷퓚쒳쪱뿌뗄샻죳룺떱쪱룃쾰쒣탍럖컶,뛔ퟩ횯톧쾰뗄돉놾뫍킧틦ퟶ쇋뚨솿닺욷뗄샛믽횪쪶솿ꆢ짺닺쓜솦ꆢ떥캻돉놾뫍럏욷싊뮯퇐뺿.웤듎,뚨솿뿌뮭쇋룅쓮탔톧쾰뫍닙ퟷ탔톧횱뷓쿠맘.틲듋,캪쇋뿌뮭샻죳뗄뚯첬뇤뮯,폃몯쾰뛔웳튵뗄늻춬뚯첬펰쿬.쫂쪵짏,웳튵퓚뾪햹ퟩ쫽ꛐ(S,q,c,w,t)뇭쪾t쪱닺욷뗄짺닺샻죳.횯톧쾰믮뚯쪱,탨튪뺫좷뗘쇋뷢ퟩ횯톧쾰뗄돉놾짺닺탔웳튵뷸탐룅쓮탔톧쾰뫍닙ퟷ탔톧쾰뇘뫍킧틦,튲탨튪뷢뻶ퟩ횯톧쾰샠탍톡퓱ꆢퟩ횯톧쾰좻믡닺짺돉놾,냼삨춶죫폚쿠펦ퟩ횯톧쾰뗄뷰쪵쪩쪱볤톡퓱ꆢ뷰춶죫솿뻶닟뗈쪵볊컊쳢\[16\],춶죫뫍평ퟩ횯톧쾰틽웰뗄쯰쪧뫍믺믡돉놾.틲듋,놾컄뗄퇐뺿뿉틔캪헢킩쪵볊컊쳢뗄뷢뻶쳡릩튻뚨폃몯쫽c1(s(t),t)ꇝ0뇭쪾t쪱룅쓮탔톧쾰뗄돉샭싛틀뻝.놾,c2(p(t),t)ꇝ0뇭쪾t쪱닙ퟷ탔톧쾰뗄돉놾.떽볆뮮웚쒩,평폚웳튵쿂튻룶볆뮮웚뗄닺욷짺1ꆡ짺닺탔웳튵ퟩ횯톧쾰ퟮ폅뿘훆쒣탍닺췹췹폫틔잰폐튻뚨맘솪,틲듋,잰튻룶볆뮮웚쒩뗄샛믽횪쪶솿ꆢ짺닺쓜솦ꆢ돉놾쮮욽뫍훊솿쮮욽뗈뛔틔놾컄훐뫳뛸퇔믡뻟폐튻뚨볛횵,뿉틔폃닐횵뗄탎쪽뇭듯.틲,짺닺탔웳튵쫇횸듓쫂짺닺믮뚯뫍폫짺닺쿠맘뗄럾컱믮뚯,캪싺ퟣ짧믡탨튪ퟔ훷뺭펪ꆢ듋,짨v1(S(T))ꆢv2(q(T))ꆢv3(c(T))ꆢv4(w(T))럖ퟔ뢺펯뿷ꆢힷ쟳샻죳뗄뺭볃쪵쳥,폫쏅듓쫂쇷춨뇰캪웚쒩쪱샛믽횪쪶솿ꆢ짺닺쓜솦ꆢ떥캻돉놾쮮욽뫍믲탅쾢럾컱뗄웤쯼럇짺닺탔웳튵쟸럖.짺닺탔웳훊솿쮮욽뛔웳튵폐탎믲컞탎닺쯹릱쿗뗄닐횵.튵탨튪뷸탐닺욷뗄볓릤뫍짺닺,짦벰떽짺닺쓜솦ꆢ틔룅쓮탔톧쾰춶싊s뫍닙ퟷ탔톧쾰춶싊짺닺싊ꆢ럏욷싊ꆢ닺욷돉놾뗈랽쏦뗄컊쳢.틲듋,짺p캪뿘훆뇤솿,틔샛믽횪쪶솿Sꆢ짺닺쓜솦qꆢ떥캻닺탔웳튵뗄ퟩ횯톧쾰믮뚯뗄쒿뇪뻍퓚폚,춨맽ퟩ돉놾c뫍럏욷싊w캪ힴ첬뇤솿,볙뚨쯼쏇뻹럇뢺,횯톧쾰살룄짆짏쫶랽쏦뗄벨킧,쳡룟웳튵샻죳.쯤늢볙뚨몯쫽ꛐꆢc1ꆢc2ꆢv1ꆢv2ꆢv3ꆢv4뻹캪틑횪몯쫽.좻ퟩ횯톧쾰뛔웳튵뗄뎤웚벨킧폐샻,떫쫇,짺닺탔평폚짺닺탔웳튵뗄놾훊쒿뇪쫇ힷ쟳샻죳ퟮ듳뮯,웳튵뗄닙ퟷ탔톧쾰췹췹탨튪햼폃짵훁웆뮵믺웷짨퓲퓚늻뾼싇뷰쪱볤볛횵뗄잰쳡쿂,뿉틔폃웳튵놸,펰쿬헽뎣뗄짺닺.벴쪹쫇룅쓮탔톧쾰,튲탨튪퓚짺닺볆뮮웚쓚뗄ퟜ샻죳ꚰퟷ캪횸뇪몯쫽,붨솢햼폃튻뚨뗄죋솦뫍뷰풴,늢쿻뫄튻뚨뗄쪱볤.죧쿂ퟮ폅뿘훆쒣탍:헢쫇짺닺탔웳튵ퟩ횯톧쾰쏦쇙뗄쪵볊컊쳢.mꢻxꚰ=캪쇋폃쫽톧쒣탍뿌뮭짺닺탔웳튵ퟩ횯톧쾰뗄ꇒT{ꛐ(S,q,c,w,t)-0쪵볊컊쳢,쳡돶룅쓮탔톧쾰춶싊뫍닙ퟷ탔톧쾰c1(s(t),t)-c2(p(t),t)}dt+춶싊솽룶룅쓮.쒳쪱뿌뗄룅쓮탔톧쾰춶싊폃v1(S(T))+v2(q(T))+룃쪱뿌떥캻쪱볤쓚춶죫폚룚잰엠통ꆢ췑룚엠통ꆢ횪v3(c(T))+v4(w(T))(1)쪶붻쇷ꆢ뺭퇩붻쇷뗈룷훖톧쾰믮뚯뗄뷰뗄퓶솿ꇊ[0,T]뇭쪾SÛ(t)=ꛂ1(t)s(t)+ꛂ;쒳쪱뿌뗄닙ퟷ탔톧쾰춶싊폃룃쪱뿌떥캻2(t)p(t),쪱볤쓚춶죫폚퇐랢쪵퇩ꆢ룚캻쫔퇩ꆢ맽돌뒴탂ꆢ훊S(0)=S0솿돉놾뿘훆뗈룷훖릤돌믮뚯뗄뷰뗄퓶솿뇭쪾.Ûq(t)=-ꛗp(t)+ꇒt-ꇞf1[S(ꛓ),p(ꛓ)]듋췢,쳡돶샛믽횪쪶솿뗄룅쓮.쒳쪱뿌뗄샛믽횪쪶솿폃떱쪱샛믽횪쪶뗄볛횵뇭쪾(돵쪼뗄샛믽횪쪶ꆡꆡꛘ1(t-ꛓ)dꛓ,ꆡq(0)=q0(3)솿뿉틔춨맽컞탎닺움맀뗄랽램믱뗃).Ûc(t)=ꛆp(t)-ꇒt-ꇞf2(S(ꛓ),p(ꛓ))ꆤ볙짨웳튵짺닺떥튻닺욷,볆뮮짺닺웚캪T.짨ꛘ2(t-ꛓ)dꛓ,ꆡc(0)=c0(4)쪱볤tꇊ[0,T\],s(t)캪t쪱룅쓮탔톧쾰춶싊,p(t)캪t쪱닙ퟷ탔톧쾰싊,S(t)캪t쪱웳튵뗄샛ꆡꆡwÛ(t)=ꛇp(t)-ꇒt-ꇞf3(S(ꛓ),p(ꛓ))ꆤ믽횪쪶솿,q(t)캪t쪱쒳닺욷짺닺쓜솦쮮욽,c(t)ꛘ3(t-ꛓ)dꛓ,ꆡw(0)=w0(5)
ꆪ48ꆪ맜ꆡ샭ꆡ뿆ꆡ톧ꆡ톧ꆡ놨ꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡ2005쓪4퓂평폚룅쓮탔톧쾰뫍닙ퟷ탔톧쾰폐훺폚퓶볓샛믽횪쪶솿,틲듋,폃쪽(2)뿌뮭t쪱뗄샛믽횪쪶솿ꇒTꛘ3(ꛓ-t)ꛋ3(ꛓ)dꛓ(6)tS(쪹웳튵볆뮮짺닺웚쓚뺻샻죳ퟮ듳뗄컊쳢뻍뇤t)폫듋쪱룅쓮탔톧쾰춶싊s(t)뫍닙ퟷ탔톧쾰춶싊p(t)뗄맘쾵캪쪹몺쏜뛻뛙몯쫽H좡뗃ퟮ듳횵뗄컊쳢.뛔i=.웤훐,ꛂ1(t)ꇝ0뇭쪾쎿떥캻뗄룅쓮탔톧쾰춶뛮뛔웳튵샛믽횪쪶솿뗄릱쿗1,2,3,쇮x(it)=ꇒTꛘ(ꛓi-t)ꛋ(ꛓ)idꛓ럖뇰뇭쪾t돌뛈t,ꛂ2(t)ꇝ0뇭쪾쎿떥캻뗄닙ퟷ탔톧쾰춶뛮뛔웳튵샛믽횪쪶솿뗄릱쿗돌뛈쪱튻룶떥캻닙ퟷ탔톧쾰춶뛮뗄훍뫳뫃뒦듓t떽.짺닺탔웳튵뗄ퟩ횯톧쾰쪵볊컊쳢훐,쒳쪱뿌T웚볤뛔짺닺쓜솦ꆢ떥캻돉놾뫍럏욷싊듸살뗄샛뗄짺닺쓜솦ꆢ돉놾ꆢ훊솿쮮욽믡쫜떽닙ퟷ탔톧쾰퓬믽펰쿬.룹뻝폃ퟮ듳횵풭샭쟳뷢훕뛋쪱볤만뚨ꆢ훕돉뗄퓝쪱탔웆뮵,떫쫇믡듓샛믽횪쪶솿뫍맽좥뗄뛋ힴ첬ퟔ평뗄뿘훆컊쳢뗄뇘튪쳵볾[18]뫍쪽(1)ꆫ333닙ퟷ탔톧쾰뺭퇩훐믱뗃뫃뒦.틲듋,폃쪽(3)ꆢ(4)ꆢ(6),죧맻3(S,q,c,w33,s,p)쪹H듯떽ퟮ듳,쓇쎴웤뇘탫싺ퟣ잰쏦뗄ힴ첬랽돌(2)ꆫ(5)럖뇰뿌뮭t쪱뗄짺닺쓜솦쮮욽q(t)ꆢ떥캻돉놾(5),쿂쏦뗄킭첬랽돌쪽(7)ꆫ(10),돵쪼쳵볾ꆢ훕c(t)뫍럏욷싊w(t)폫ퟩ횯톧쾰횮볤뗄맘쾵.웤훐,럇뢺뎣쫽ꛗꆢꛆ뫍ꛇ럖뇰쫇뿌뮭t쪱떥캻닙ퟷ탔뛋쳵볾(11)ꆢ(12)틔벰쪽(13).톧쾰춶뛮틽웰뗄짺닺쓜솦솢벴쯰쪧돌뛈,떥캻ꛒÛ3=9H-=-ꛐ39S|S-돉놾솢벴퓶볓돌뛈뫍럏욷싊솢벴퓶볓돌뛈;뛔3933f1(S,p)x9S1(t)i=1,2,3,f+i[S(t),p(t)]ꇝ0럖뇰폃살뿌뮭t쪱p떥캻뗄닙ퟷ탔톧쾰뫍S떥캻뗄샛믽횪쪶솿룸쳡933f2(S,p)룟짺닺쓜솦x,붵뗍떥캻돉놾뫍붵뗍럏욷싊듸살뗄9S2(t)+뎤웚뫃뒦,ꛘ(it-ꛓ)럖뇰뇭쪾평폚ꛓ쪱쪵쪩톧쾰933f3(S,p)뛸퓚xt쪱쪵쿖뗄짺닺쓜솦퓶뎤뗄늿럖ꆢ떥캻돉놾9S3(t)(7)붵뗍뗄늿럖뫍럏욷싊붵뗍뗄늿럖,ꛓꇜt.ꛋÛ31=9H-=-ꛐ9q|q(8)3ꛋÛ32=9H2ꆡ쒣탍뗄샭싛럖컶-=-ꛐ9q|c(9)3ꛋÛ33=9H내헕ퟮ폅뿘훆샭싛[17],뿉틔폃ퟮ듳횵풭샭쟳-=-ꛐ9q|w(10)3뷢짏쫶ퟮ폅뿘훆컊쳢.짨ힴ첬쿲솿x=\[S,q,c,돵쪼쳵볾wT3],뿘훆쿲솿u=\[s,pT],킭첬쿲솿r=\[ꛒ,ꛋ1,S(03)=S0,q(0)=q0ꛋT32,ꛋ3],웤훐킭뇤솿ꛒ(t)ꇝ0뇭쪾t쪱튻룶떥캻샛c(0)=c0,w3(0)=w0믽횪쪶솿뗄럇뢺뇟볊볛횵,ꛋ1(t)ꇝ0,ꛋ2(t)ꇜ0뫍훕뛋쳵볾ꛋ3ꇜ0럖뇰뇭쪾퓶볓튻룶떥캻짺닺쓜솦뗄럇뢺뇟볊볛횵,떥캻돉놾퓶볓튻룶떥캻뗄럇헽뇟볊볛횵뫍ꛒ39v139v2(T)=9S|3,ꛋ1(T)=S(T)9q|3q(T)럏욷싊퓶볓튻룶떥캻뗄럇헽뇟볊볛횵.룹뻝컄쿗(11)[18\],잰쫶ퟮ폅뿘훆컊쳢뗄몺쏜뛻뛙몯쫽캪ꛋ39v339v42(T)=3(T)=H=ꛐ9c|3,ꛋc(T)9w|3w(T)(S,q,c,w,t)-c1(s,t)-c2(p,t)+ꛒꛂ1s+ꛒꛂ2p-ꛋ(12)1ꛗp+s뫍p쪹H좡뗃ퟮ듳횵뗄뇘튪쳵볾f1(S(t),p(t))ꇒTꛘ1(ꛓ-t)ꛋ1(ꛓ)dꛓ+t9H9Hꛋ0,2ꛆp-f2(S(t),p(t))ꆤ93=s9p3=0(13)ꇒTꛘ캪쇋뛔쒣탍뷸탐샭싛럖컶,탨튪튻킩볙짨쳵2(ꛓ-t)ꛋ2(ꛓ)dꛓ+t볾.컄쿗[13]뛔짺닺탔웳튵룅쓮탔톧쾰뫍닙ퟷ탔ꛋ3ꛇp-f3(S(t),p(t))톧쾰뗄쪵볊쟩뿶틔벰짺닺뺭펪쪵볊쟩뿶뷸탐쇋럖
뗚2웚ꆡꆡꆡꆡꆡꆡꆡꆡ뛅ꆡ죙뗈:짺닺탔웳튵ퟩ횯톧쾰ퟮ폅뿘훆쒣탍벰웤샭싛럖컶ꆪ49ꆪ컶,늢쳡돶쇋튻킩럻뫏쪵볊뗄뚨탔뮯볙짨.헢샯,웳튵쒿뇪뗄펰쿬.놾컄붫훘뗣횤쏷튻킩훐볤탔뷡룸돶헢킩볙짨뗄쫽톧뇭듯.싛뫍ퟮ훕럖컶탔뷡싛.볙짨A틽샭1ꆡx1(t)ꇝ0,x2(t)ꇜ0,x3(t)ꇜ0,쟒1)9fi/9pꇝ0,92fi/92pꇜ0,i=1,2,3.뇭쪾x1(T)=0,x2(T)=0,x3(T)=0.닙ퟷ탔톧쾰춶싊풽듳,룸짺닺쓜솦뗄쳡룟(떥캻횤쏷ꆡ평볙짨A뗄3)뿉횪0ꇜꛘ(it-ꛓ)ꇜ돉놾ꆢ럏욷싊뗄붵뗍)듸살뗄뎤웚뫃뒦풽듳,떫쯦ퟅ닙ퟷ탔톧쾰춶싊뗄쮲쪱퓶볓,뛔짺닺쓜솦(떥1,ꇒꇞꛓꛘ(it-ꛓ)dt=1,폖폐ꛋ1(t)ꇝ0,ꛋ2(t)ꇜ0,캻돉놾ꆢ럏욷싊)뗄뎤웚뫃뒦뗄퓶볓싊믡쿂붵ꛋ.3(t)ꇜ0,틲듋,x1(t)ꇝ0,x2(t)ꇜ0,x3(t)ꇜ2)9fi/9Sꇝ0,i=1,2,3.뇭쪾샛믽횪쪶솿풽0.평x1(t)ꆢx2(t)ꆢx3(t)뗄뚨틥뿉췆돶x1(T)=뛠,뛔짺닺쓜솦(떥캻돉놾ꆢ럏욷싊)뗄뎤웚뫃뒦0,x2(T)=0,x3(T)=0.횤뇏.풽뛠.틽샭2ꆡ죧맻(S,q,c,w,s,p)싺ퟣ쪽(7),퓲ꛒ(t)쫇쪱볤뗄럇퓶몯쫽,벴ꛒÛ(t)ꇜ)0ꇜꛘ(it-ꛓ)ꇜ1,ꇒꇞꛓꛘ(it-ꛓ)dt=1,i=횤쏷ꆡ룹뻝킭첬랽돌(7),폐1,2,3.뇭쪾ꛓ쪱뗄톧쾰뛔쳡룟짺닺쓜솦(붵뗍떥ꛒÛ(t)=-9H/9S=캻돉놾ꆢ럏욷싊)쫇췪좫폐킧뗄.-ꛐS-(9f1(S,p)/9S)x1(t)+4)뛔폚ꛓꇊ[-ꇞ,0\],s(ꛓ)뫍p(ꛓ)틑횪,뇭(쪾잰쏦룷룶볆뮮짺닺웚뗄톧쾰쟩뿶쫇룸뚨뗄9f2(S,p)/9S)x2(t)+.(9f3(S,p)/9S)x3(t)5)9ꛐ/9Sꇝ0,뇭쪾짺닺샻죳쫇샛믽횪쪶솿뗄럇복몯쫽평볙짨A뗄2)뫍5)틔벰틽샭1뿉췆돶.ꛒÛ(t)ꇜ0.횤뇏.6)9c1/9sꇝ0,922c1/9sꇝ0,9c2/9pꇝ0,틽샭3ꆡ죧맻(S,q,c,w,s,p)싺ퟣ쪽(8)ꆫ92c2/9p2ꇝ0,뇭쪾쯦ퟅ톧쾰뗄퓶볓,톧쾰뗄돉놾튲믡퓶볓,뛸쟒퓶볓쯙싊퓚퓶듳(10),퓲ꛋ1(t)쫇쪱볤뗄럇퓶몯쫽,ꛋ2(t)뫍ꛋ3(t)쫇.쪱볤뗄럇복몯쫽,벴ꛋ1ꇜ0,ꛋ2ꇝ0,ꛋ3ꇝ)92c1(s,t)/9s9tꇝ0,뇭쪾룅쓮탔톧쾰뗄뇟볊돉놾쫇쪱볤뗄럇복몯쫽횤쏷ꆡ룹뻝ꛋi싺ퟣ뗄킭첬랽돌(8)ꆫ(10).뫍볙짨B뗄1)ꆫ(3)뿉솢벴뗃횤.횤뇏.8)dꛂ1(t)/dtꇜ0,뇭쪾룅쓮탔톧쾰뛔샛믽횪쪶솿뗄뇟볊릱쿗쫇쪱볤뗄럇퓶몯쫽웳튵퓚룅쓮탔톧쾰뗄쪵볊릤ퟷ훐,쾣췻톰쟳.볙짨뺡솿싺틢뗄랽낸.룹뻝헢룶쪵볊쟩뿶,뚨솿럖컶늻Bힷ쟳쫽톧틢틥짏퇏룱뗄ퟮ폅닟싔.캪쇋뇣폚뫳쏦1)9ꛐ/9qꇝ0,92ꛐ/92qꇜ0,뇭쪾뺭펪샻죳쫇짺닺쓜솦쮮욽뗄럇복몯쫽,떫평폚뇟볊쫕틦뗝뗄럖컶,룹뻝웳튵뗄쪵볊탨튪,룸돶죧쿂뚨틥.복맦싉뚨틥1ꆡ볇,쯦ퟅ짺닺쓜솦쮮욽뗄퓶볓,샻죳퓶볓싊믡붵뗍ꚵ1(s,t)=9H/9s=.ꆡꆡꆡ-9c1(s,t)/9s+ꛂ1(t)ꛒ(t)(14)2)9ꛐ/9cꇜ0,91ꛐ/92cꇜ0,뇭쪾뺭펪샻죳쫇떥캻돉놾뗄럇퓶몯쫽,떫쯦ퟅ떥캻돉놾뗄붵뗍1)죧맻뛔폚죎뫎tꇊ[03,T\],s(t)쪹,샻죳퓶볓싊믡붵뗍ꚵ331(s(t),t)=0,퓲돆s(t)캪ퟮ폅룅쓮탔톧쾰.3)9ꛐ/9wꇜ0,92ꛐ/9w2ꇜ0,뇭쪾뺭펪샻죳춶닟싔.쫇럏욷싊뗄럇퓶몯쫽,떫쯦ퟅ럏욷싊뗄붵뗍,샻죳2)죧맻뛔폚쒳룶tꇊ[0,T\],s(t)쪹뗃퓶볓싊믡붵뗍.ꚵ1(s(t),t)ꇝ0,퓲돆퓚t쪱뿌뷸탐룅쓮탔톧쾰4)9v2/9q(T)ꇝ0,뇭쪾짺닺쓜솦쮮욽뗄닐횵춶뛔웳튵폐샻.럱퓲,돆퓚t쪱뿌뷸탐룅쓮탔톧쫇웚쒩짺닺쓜솦쮮욽뗄럇복몯쫽.쾰춶뛔웳튵늻샻.쿂쏦헫뛔룸뚨뗄(S,q,c,w,s,p)싺ퟣ쪽(7)쪽(14)폒뇟뗚1쿮뇭쪾t쪱룅쓮탔톧쾰뗄뇟ꆫ(10)뫍볙짨Aꆢ볙짨B뗄쟩뿶,쳖싛룅쓮탔톧쾰볊돉놾,뗚2쿮뇭쪾t쪱룅쓮탔톧쾰뛔쫕죫뗄뇟볊춶싊s뫍닙ퟷ탔톧쾰춶싊p맘폚H뗄뇤뮯뛔릱쿗.
ꆪ50ꆪ맜ꆡ샭ꆡ뿆ꆡ톧ꆡ톧ꆡ놨ꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡꆡ2005쓪4퓂뚨샭1ꆡ죧맻(S,q,c,w,s,p)쪹쪽(7)ꆫ(10)뻝뚨샭1,횪뷡싛돉솢.돉솢,늢쟒Ûs(t)ꇝ0(Πtꇊ[0,T]).죧맻듦퓚t쪹뗃3)룹뻝뚨틥1,평뚨샭1쿔좻췆뗃.횤뇏.ꚵ1(s(t),t)=0,퓲퓚tꇊ[0,t]웚볤뷸탐룅쓮탔톧웳튵퓚닙ퟷ탔톧쾰뗄쪵볊릤ퟷ훐,튲쾣췻톰쾰춶뛔웳튵폐샻,퓚tꇊ[t,T]웚볤뷸탐룅쓮탔톧쟳뺡솿싺틢뗄랽낸.틲듋,룸돶죧쿂뚨틥.쾰춶뛔웳튵늻샻.뚨틥2ꆡ쇮ꚵ2(p,t)뇭쪾H맘폚p뗄욫떼쫽,횤쏷ꆡ평쪽(14)쟳ꚵ1(s(t),t)맘폚t뗄떼퓲쫽,뗃ꚵ2(p,t)=-9c2(p,t)/9p-ꛗꛋ1(t)+dꚵ21(s,t)92c=1(s,t)ds9c1(s,t)-+ꆡꆡꛆꛋ2(t)+ꛇꛋ3(t)+ꛂ2(t)ꛒ(t)+dt92-sdt9s9tꛂ1(t)ꛒÛꆡꆡ(9f1/9p)x1(t)-(9f2/9p)x2(t)-(t)+ꛒ(t)ꛂÛ1(t)평볙짨A뗄6)뫍Ûs(t)ꇝ0횪짏쪽폒뇟뗚1쿮늻듳폚ꆡꆡ(9f3/9p)x3(t)(15)1)죧맻뛔폚죎뫎tꇊ[0,T30\],p(t)쪹,평볙짨A뗄7)뿉횪,92c1(s,t)/9s9tꇝ0;평틽샭2)횪ꛒÛ(t)ꇜ0,폖폐ꛂ1(t)ꇝ0,ꛒ(t)ꇝ0,평볙짨Aꚵ32(p(t),t)=0,퓲돆3p(t)캪ퟮ폅닙ퟷ탔톧뗄8)횪ꛂÛ1(t)ꇜ0.퓲dꚵ1(s,t)/dtꇜ0.틲듋,ꚵ1(s,쾰춶닟싔.t)쫇쪱볤t뗄떥뗷럇퓶몯쫽.틑횪ꚵ1(s(t),t)=0,2)죧맻뛔폚쒳룶tꇊ[0,T\],p(t)쪹뗃퓲tꇜt쪱,ꚵ1(s(t),t)ꇝ0;뛸tꇝt쪱,ꚵ1(s(t),ꚵ2(p(t),t)ꇝ0,퓲돆퓚t쪱뿌뷸탐닙ퟷ탔톧쾰t)ꇜ0.룹뻝뚨틥1,퓚tꇊ[0,t)웚볤튻횱뷸탐룅쓮춶뛔웳튵폐샻.럱퓲,돆퓚t쪱뿌뷸탐닙ퟷ탔톧탔톧쾰춶뛔웳튵폐샻,뛸퓚tꇊ(t,T]웚볤뷸탐룅쾰춶뛔웳튵늻샻.쓮탔톧쾰춶뛔웳튵늻샻.쪽(15)폒뇟뗚1쿮뇭쪾t쪱닙ퟷ탔톧쾰뗄뇟뚨샭2ꆡ죧맻(S,q,c,w,s,p)쪹쪽(7)ꆫ(10)돉솢,늢쟒Û볊돉놾,뗚2훁뗚4쿮럖뇰뇭쪾t쪱쪵쪩닙ퟷ탔톧s(t)ꇝ0(Πtꇊ[0,T]).쾰룸짺닺쓜솦ꆢ떥캻돉놾뫍훊솿듸살뢺쏦펰쿬퓬1)죴9c1(s,T)/9sꇜꛂ1(T)ꛒ(T),퓲퓚헻룶닺욷볆뮮웚,틔ퟮ듳룅쓮탔톧쾰춶싊s뷸탐룅돉뗄뇟볊쯰쪧,뗚5쿮뇭쪾t쪱닙ퟷ탔톧쾰틔탎돉쓮탔톧쾰춶뛔웳튵폐샻샛믽횪쪶솿뗄탎쪽뛔쫕죫뗄뇟볊볛횵,뗚6훁뗚8.쿮럖뇰뇭쪾t쪱닙ퟷ탔톧쾰뗄훍뫳뫃뒦폫샛믽횪2)죴9c1(s,T)/9s>ꛂ1(T)ꛒ(T),9c1(s,쪶솿릲춬ퟷ폃춨맽퓶볓짺닺쓜솦ꆢ붵뗍떥캻돉놾0)/9s<ꛂ1(0)ꛒ(0),퓲듦퓚t0ꇊ(0,T),퓚0<뫍쳡룟훊솿룸쫕죫듸살뗄뫃뒦.t<t0쪱,틔퓶볓뗄쯙싊뷸탐룅쓮탔톧쾰춶뛔웳튵폐샻;퓚t0<t<T쪱,늻뷸탐룅쓮탔톧춨맽뛔쪽(15)뗄럖컶뿉뗃돶죧쿂뷡맻:샛믽쾰춶뛔웳튵폐샻횪쪶솿S(t)뷏뛠뗄웳튵퓚t쪱닉좡뷏듳뗄닙ퟷ.3)죴9c1(s탔톧쾰춶싊p(t)뛔웳튵폐샻;뻟폐뷏룟샛믽횪,0)/9sꇝꛂ1(0)ꛒ(0),퓲퓚헻룶볆뮮웚쓚늻뷸탐룅쓮탔톧쾰춶뛔웳튵폐샻.쪶솿쮮욽뗄웳튵퓚볆뮮웚쓚뛔닙ퟷ탔톧쾰뗄춶횤쏷ꆡ1)평9c1(s,T)/9sꇜꛂ1(T)ꛒ(T),뗃솿뷏듳.뇭쏷쇋웳튵뗄횪쪶쮮욽폫웤닙ퟷ탔톧쾰ꚵ1(s(T),T)ꇝ0,평뚨샭1뿉횪,퓚tꇊ[0,T]쪱,춶닟싔횮볤뗄솪쾵.평듋뿉뾴떽샛믽횪쪶솿뛔9H/9s(t)ꇝ0,맊퓚헻룶닺욷볆뮮웚쓚틔ퟮ듳춶폚ퟮ폅닙ퟷ탔톧쾰춶닟싔뗄맘볼ퟷ폃.싊뷸탐룅쓮탔톧쾰춶뛔웳튵폐샻.뚨샭3ꆡ죧맻(S,q,c,w,s,p)쪹쪽(7)ꆫ(10)2)평틑횪,뗃ꚵ1(s(T),T)<0뫍ꚵ1(s(0),돉솢,쟒p캪ퟮ폅닙ퟷ탔톧쾰춶닟싔,죴쪽(16)폒0)>0,룹뻝뚨샭1,ꚵ1(s,t)쫇쪱볤t뗄떥뗷럇퓶몯뛋캪헽(뢺),퓲t쪱ퟮ폅닙ퟷ탔톧쾰춶싊쫇쪱볤뗄쫽,틲듋,듦퓚t0ꇊ(0,T)쪹뗃ꚵ1(s(t0),t0)=0,룹퓶(복)몯쫽.ꆡꆡꆡÛp[92c2/92p-(92f1/92p)x1(t)+(92f2/92p)x2(t)+(92f3/92p)x3(t)]=ꆡꆡ-92c2/9p9t-ꛗꛋÛ1(t)+ꛆꛋÛ2(t)+ꛇꛋÛ3(t)+9[ꛂ2(t)ꛒ(t)\]/9t+\[9f1/9p]Ûx1(t)+ꆡꆡ[92f1/9p9S]SÛ(t)x1(t)-\[9f2/9p]Ûx2(t)-\[92f2/9p9S]SÛ(t)x2(t)-ꆡꆡ[9f3/9p]Ûx3(t)-\[92f3/9p9S]SÛ(t)x3(t)(16)
뗚2웚ꆡꆡꆡꆡꆡꆡꆡꆡ뛅ꆡ죙뗈:짺닺탔웳튵ퟩ횯톧쾰ퟮ폅뿘훆쒣탍벰웤샭싛럖컶ꆪ51ꆪ늢쟒,퓚헻룶닺욷볆뮮웚쓚뷸탐닙ퟷ탔톧쾰춶탔톧쾰,춶죫폚룅쓮탔톧쾰뗄뷰뗄퓶솿뗝퓶,벴뛔웳튵폐샻.춶죫뗄죋솦ꆢ닆솦ꆢ컯솦뚼돊퓶볓쟷쫆,퓲듦퓚튻횤쏷ꆡp캪ퟮ폅닙ퟷ탔톧쾰춶닟싔,평뚨틥2룶쪱볤뷧쿞,듋쪱룅쓮탔톧쾰뗄뇟볊샻틦캪0.퓚뿉횪ꚵ2(p,t)=0.룹뻝쪽(15)ꚵ2(p(t),t)=0벰듋쪱볤뷧쿞횮잰뷸탐룅쓮탔톧쾰춶뛔웳튵쫇폐9[ꚵ2(p,t)\]/9t=0뿉췆돶쪽(16).샻뗄,뛸퓚듋횮뫳퓙춶죫폚룅쓮탔톧쾰뻍믡뛔웳평볙짨A뗄1)뫍6)뿉횪92c2/92pꇝ0튵늻샻.,92뚨샭2뇭쏷:1)죧맻볆뮮웚쒩룅쓮탔톧쾰뗄f1/9p2ꇜ0,92f2/9p2ꇜ0,92f3/9p2ꇜ0,평틽샭1뿉횪,x1(t)ꇝ0,x2(t)ꇜ0,x3(t).틲듋,뿉횪쪽뇟볊돉놾틀좻킡폚뇟볊샻틦,쓇쎴,웳튵퓚헻룶볆(16)ퟳ뛋랽삨뫅쓚뗄횵럇뢺.죴폒뛋캪헽(뢺),퓲Û뮮웚쓚틔ퟮ듳뗄퓶뎤싊춶죫폚룅쓮탔톧쾰뛔웳튵p(t)>폐샻;2)죧맻볆뮮웚쒩룅쓮탔톧쾰뗄뇟볊돉놾듳0(Ûp(t)<0),벴p(t)쯦쪱볤뗝퓶(뗝복).평뚨틥2뿉횪,퓚헻룶닺욷볆뮮웚쓚뷸탐닙폚뇟볊샻틦,뛸볆뮮웚돵룅쓮탔톧쾰뗄뇟볊돉놾ퟷ탔톧쾰춶뛔웳튵폐샻.횤뇏킡폚뇟볊샻틦,쓇쎴,듦퓚튻룶쪱볤뷧쿞,퓚듋횮.잰웳튵늻뛏퓶볓룅쓮탔톧쾰춶죫뛔웳튵폐샻,퓚듋횮뫳춣횹룅쓮탔톧쾰춶죫뛔웳튵폐샻;3)죧맻3ꆡ샭싛럖컶뛔폚뷢뻶쪵볊컊쳢뗄틢틥볆뮮웚돵룅쓮탔톧쾰뗄뇟볊돉놾뻍듳폚뇟볊샻틦,쓇쎴,웳튵퓚헻룶볆뮮웚쓚늻춶죫폚룅쓮탔톧샭싛럖컶뗄훐볤탔뷡싛뫍ퟮ훕뷡싛뛔폚뷢뻶쾰뛔웳튵ퟮ폐샻.짺닺탔웳튵ퟩ횯톧쾰훐뗄쪵볊컊쳢뚼뻟폐쿖쪵뚨샭1뫍뚨샭2뿉틔냯훺웳튵룹뻝ퟔ짭쪵볊틢틥.ힴ뿶뷢뻶룅쓮탔톧쾰뷰뫍쪱볤뗄뫏샭낲업틽샭1뇭쏷,짺닺탔웳튵죎뫎쪱뿌뗄닙ퟷ탔컊쳢.톧쾰뚼믡틲캪틾탔횪쪶뗄톧쾰뫍뒴퓬뛸캪틔뫳믽뚨샭3뇭쏷,웳튵퓚헻룶볆뮮웚쓚튻횱춶죫샛뺭퇩뷌통,뛔룃쪱뿌틔뫳뗄웳튵믮뚯닺짺훍뫳폚닙ퟷ탔톧쾰뛔웳튵폐샻,떫쫇춶죫뗄퓶복좡뻶뫃뒦,헢룶훍뫳뗄뫃뒦폐훺폚쳡룟짺닺쓜솦,붵뗍폚닙ퟷ탔톧쾰뛔웳튵샻틦뗄뇟볊믘놨뗄뇤뮯.헢돉놾,룄뷸훊솿.헢룶틽샭뿉틔냯훺웳튵쿠맘죋풱룶뷡싛뿉틔냯훺짺닺탔웳튵죏쪶떽:횼퓚뒴퓬탂헽좷죏쪶쿖쪵훐닙ퟷ탔톧쾰뗄ퟷ폃믺샭.횪쪶뗄닙ퟷ탔톧쾰뛔폚쎿룶웳튵뚼쫇쪮럖훘튪틽샭2뇭쏷,쯤좻ퟩ횯톧쾰뿉틔퓶볓웳튵뗄뗄,떫쫇늻춬뗄웳튵펦룃쫓ퟔ벺뗄뻟쳥쟩뿶낲업샛믽횪쪶솿,떫쫇샛믽횪쪶솿뗄뇟볊볛횵쯦ퟅ쪱쫊떱뗄닙ퟷ탔톧쾰.볤뗄퇓탸믡랢짺뇡횵,돤럖랴펳쇋뻉횪쪶뗄뿬쯙쳔청.헢튻뗣뿉틔죃웳튵폐맘죋풱쇋뷢떽늻뛏ퟩ4ꆡ뷡ꆡ싛횯톧쾰ꆢ퓶볓탂횪쪶뗄훘튪탔.틽샭3뇭쏷,쯤좻ퟩ횯톧쾰뗄훍뫳뫃뒦폐훺놾컄붨솢쇋짺닺탔웳튵ퟩ횯톧쾰뗄ퟮ폅뿘훆폚쳡룟짺닺쓜솦,붵뗍돉놾,룄뷸훊솿,떫쫇쯦ퟅ쒣탍,믹폚튻쾵쇐볙짨뫍뚨틥뛔쒣탍뷸탐쇋샭싛쪱볤뗄퇓탸,쳡룟짺닺쓜솦,붵뗍돉놾,룄뷸훊솿럖컶,뗃돶쇋튻킩맘폚ퟮ폅룅쓮탔톧쾰춶닟싔뗄뇟볊볛횵믡붵뗍,돤럖랴펳쇋웳튵뫍헻룶쫐뎡뫍ퟮ폅닙ퟷ탔톧쾰춶닟싔뗄뷡싛,붫헢킩샭싛뗄뚯첬랢햹.웳튵듓헢룶뷡싛뿉틔뾴떽,ퟔ벺퓚짨폫짺닺탔웳튵뗄쪵볊컊쳢솪쾵웰살,닻쫶쇋쯼쏇램쳡룟짺닺쓜솦,붵뗍돉놾,룄뷸훊솿,웤쯻웳튵퓚웳튵맜샭랽쏦뗄몬틥.뷸튻늽뗄퇐뺿뿎쳢쫇:쫕튲퓚짨램헢퇹ퟶ,죧맻탐뚯동뮺,뻍믡돔뿷실뫳.벯웳튵ퟩ횯톧쾰랽쏦뗄쫽뻝,춨맽룶낸퇐뺿믲쪵뚨샭1뇭쏷,죧맻짺닺탔웳튵럇뎣힢훘룅쓮횤럖컶볬퇩놾컄쯹뗃돶뗄뷡싛.
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뗚2웚ꆡꆡꆡꆡꆡꆡꆡꆡ뛅ꆡ죙뗈:짺닺탔웳튵ퟩ횯톧쾰ퟮ폅뿘훆쒣탍벰웤샭싛럖컶ꆪ53ꆪWanLunlai,\[J\].JournalofManagementSciencesinChina,2003,6(2):89ꆪ94.(inChinese)\[17\쇵]탋솼.ퟮ폅뿘훆벰펦폃\[M\].놱뺩:뿆톧돶냦짧,ꆪ\[M\].Beijing:SciencePress,ꆪ859.(inChinese)\[18\H]artlRF,:Dynamicprogrammingapproachandeconomicin2terpretations\[J\]..,1984,4(31):73ꆪ,HUQ2i-ying,,XidianUniversity,Xiꆯan710071,China;,ShanghaiUniversity,Shanghai201800,China;,ZhejiangUniversityofTechnology,Hangzhou310032,ChinaAbstract:,takinginvestingratesforconceptuallearningandoperativelearningasdecisionvariables,cumulativeknowledgelevel,productivity,pro2ductioncostperunit,anddefectiveproductratioasstatevariables,,productivity,productioncostperunit,andproductquality,,,:optimalcontrol;manufacturingfirms;organizationallearning;conceptuallearning;operationallearning
