合肥工业大学硕士学位论文需求依赖价格和销售努力的决策问题的研究姓名：李清艳申请学位级别：硕士专业：应用数学指导教师：杨志林2011-04
?탨쟳틀삵볛룱뫍쿺쫛얬솦뗄뻶닟컊쳢뗄퇐뺿?햪†튪?쿺쫛얬솦쫇쫐뎡뺭볃훐맣랺퓋폃뗄쿺쫛닟싔횮튻ꎬ듺뇭웳튵탻뒫뷩짜닺욷뗄폅뗣ꎬ쮵럾쒿뇪뿍뮧살릺싲웤닺욷쯹뷸탐뗄훖훖믮뚯ꎬ냼삨맣룦춶죫ꆢ죋풱췆쿺ꆢ펪튵췆맣ꆢ릫릲맘쾵뗈ꆣ퓚탨쟳헟죕틦뛠퇹뮯뗄뷱쳬ꎬ탨쟳솿뗄듳킡횱뷓틀삵폚쿺쫛얬솦춶죫뗄뛠짙ꎬ틲듋ꎬ탨쟳틀삵쿺쫛볛룱뫍쿺쫛얬솦뗄뻶닟컊쳢훰붥돉캪맺쓚췢쿠맘톧헟퇐뺿뗄튻룶죈뗣ꆣ 뒫춳뗄탨쟳틀삵쿺쫛얬솦뗄뿢듦뿘훆쒣탍튻냣뾼싇볛룱쫇만뚨늻뇤뗄ꎬ뛸쫂쪵짏ꎬ탨쟳췹췹믡쫜뫜뛠틲쯘뗄펰쿬ꎬ샽죧맣룦ꎬ릫릲맘쾵뗈ꆣ놾컄퇐뺿쇋퓚좷뚨탔탨쟳쟩뿶쿂ꎬ탨쟳춬쪱평쿺쫛얬솦뫍닺욷볛룱릲춬뻶뚨ꎬ늢평릩펦짌쳡릩쿺쫛얬솦늹쳹뗄릩펦솴킭뗷쒣탍ꆣ 놾죋퓚잰죋뗄믹뒡짏ퟷ쇋벸뗣췘햹탍퇐뺿ꆣ훷튪췪돉릤ퟷ죧쿂ꎺ (1)럖컶쇋퓚좷뚨탔탨쟳쟩뿶쿂ꎬ붨솢쇋탨쟳틀삵쿺쫛얬솦뫍쿺쫛볛룱뗄뿢듦쒣탍ꆣ놾컄짮죫럖컶쇋퓶볓탨쟳틀삵쿺쫛얬솦뗄쟩뿶ꎬ늢쟒횤쏷쇋믡퓶볓쿺쫛짌뗄샻죳ꎬ좻뫳쳡돶쇋튻훖톰쟳ퟮ폅욽뻹샻죳뗄럖컶랽램ꆣ (2)퇐뺿쇋믹폚쿺쫛얬솦릲떣뗄릩펦솴킭뗷컊쳢ꆣ놾컄퇩횤쇋릩펦짌퓚쳡릩쿺쫛얬솦늹쳹뗄쟩뿶쿂쓜벤샸쿺쫛짌볓듳뚩릺솿ꎬ듓뛸퓶볓릩펦짌뗄샻죳ꆣ (3)믹폚쿺쫛얬솦릲떣뗄쟩뿶쿂럖컶쇋뗄엺솿헛뿛볆뮮쒣탍ꆣ쫗쿈룸돶쇋좷뚨ퟮ폅솿헛뿛볆뮮뗄뚯첬늩?랽램ꎬ웤듎폃쪵샽횤쏷쇋퓚쪵탐솿헛뿛볆뮮뫳ꎬ쿺쫛짌뫍릩펦짌뗄ퟮ폅욽뻹샻죳뻹폐퓶볓ꆣ 맘볼듊ꎺ맘볼듊ꎺ얬솦돉놾릲떣ꎻ릩펦솴킭뗷ꎻ퓶볓솿헛뿛ꆣ III
Research of the Problems on Sales Efforts and Selling Price Dependent Demand Rate ?ABSTRACT Sales efforts, as one kind of the sales strategies, are widely used in market economy, such as advertising, personal selling, sales promotion, public relations etc. It not only can help buyers show their advantagesꎬbut also persuade target customers to buy their products. Nowadays, the quantity of demand for products is depending on the sales efforts because of the diversity of consumers. So the question on the sales-efforts and sale-price-dependent demand has become a hot spot that many scholars have devoted to study it. The traditional inventory-control model with sale-effort-dependent demand rate assumed that the market demand was either price sensitive or constant. As a matter of fact, the demand is usually influenced by many factors such as advertisement, public relations etc. In this paper, we consider coordination issues of a deterministic demand that the demand rate relies on both sales efforts and selling price, then presented a supply-chain coordination model with suppliers offer some sales-effort-allowance. This paper expands deterministic demand variable research on basis of the existing deterministic demand variable research. Main contributions are as follows: (1)An inventory control model with the demand rate relying on both sales efforts and selling price is considered, where the premise is the deterministic demand. In this paper, we studied the situation of increasing sales efforts and proved the retailer’s profit is higher than that not. At last, this paper proposed a method of finding the optimal model of the average profit. (2)A supply chain coordination problem based on sharing the sales efforts with retailer is considered. We also got the conclusion that the situation when supplier gives part of sale-effort-subsidies to retailer will make the ordering quantity of products and the profit of supplier’s increasing. (3)A supply chain coordination model with quantity discount consideration is proposed on the base of the premise of efforts cost sharing. First, the optimal IV
dynamic game analysis with quantity discount of products is given. Then a simulation case demonstrates the correctness of analytical results. Key words: effort cost sharing; supply chain coordination; incremental quantity discounts V
닥춼쟥떥 춼 몯쫽ꎨꎩ뫍ꎨꎩ뗄춼탎.................................................12 춼 몯쫽ATP(p*,I(a),Q*)뗄춼쿱......................................................14 춼 몯쫽ATP(p*,I(ß),Q*)뗄춼쿱......................................................14 춼 쒿뇪몯쫽ꎨꎩ ATP(p*,I*,Q)뗄춼쿱.....................................15 춼 쒿뇪몯쫽ATP(p*,I*,Q)뫍ATP(p*,Q)뗄닮...................................15 춼 쿺쫛짌폫릩펦짌볤뚯첬킭뗷늩?...............................................29 VIII
뇭룱쟥떥 뇭 닎쫽aꆢß뗄뇤뮯뛔쒿뇪몯쫽ퟮ폅뷢뗄펰쿬................................13 뇭 솽훖닟싔쿂뗄볆쯣뷡맻.............................................................21 뇭평Matlab죭볾퓚솽훖닟싔쿂뗄볆쯣뷡맻.....................................30 IX
뛀 뒴 탔 짹 쏷 놾죋짹쏷쯹돊붻뗄톧캻싛컄쫇놾죋퓚떼쪦횸떼쿂뷸탐뗄퇐뺿릤ퟷ벰좡뗃뗄퇐뺿돉맻ꆣ뻝컒쯹횪ꎬ돽쇋컄훐쳘뇰볓틔뇪횾뫍훂킻뗄뗘랽췢ꎬ싛컄훐늻냼몬웤쯻죋틑뺭랢뇭믲킴맽뗄퇐뺿돉맻ꎬ튲늻냼몬캪믱뗃 뫏럊릤튵듳톧 믲웤쯻뷌폽믺릹뗄톧캻믲횤쫩뛸쪹폃맽뗄닄쇏ꆣ폫컒튻춬릤ퟷ뗄춬횾뛔놾퇐뺿쯹ퟶ뗄죎뫎릱쿗뻹틑퓚싛컄훐ퟷ쇋쏷좷뗄쮵쏷늢뇭쪾킻틢ꆣ 톧캻싛컄ퟷ헟잩ퟖꎺ샮쟥퇞 잩ퟖ죕웚ꎺ㈰ㄱ쓪〴퓂㈳죕?? 톧캻싛컄냦좨쪹폃쫚좨쫩 놾톧캻싛컄ퟷ헟췪좫쇋뷢 뫏럊릤튵듳톧 폐맘놣쇴ꆢ쪹폃톧캻싛컄뗄맦뚨ꎬ폐좨놣쇴늢쿲맺볒폐맘늿쏅믲믺릹쯍붻싛컄뗄뢴펡볾뫍듅엌ꎬ퓊탭싛컄놻닩퓄믲뷨퓄ꆣ놾죋쫚좨 뫏럊릤튵듳톧 뿉틔붫톧캻싛컄뗄좫늿믲늿럖싛컄쓚죝뇠죫폐맘쫽뻝뿢뷸탐볬쯷ꎬ뿉틔닉폃펰펡ꆢ쯵펡믲즨쏨뗈뢴훆쫖뛎놣듦ꆢ믣뇠톧캻싛컄ꆣ ꎨ놣쏜뗄톧캻싛컄퓚뷢쏜뫳쫊폃놾쫚좨쫩ꎩ 톧캻싛컄헟잩쏻ꎺ샮쟥퇞 떼쪦잩쏻ꎺ퇮횾쇖 잩ퟖ죕웚ꎺ ㈰ㄱ쓪〴퓂㈳죕 잩ퟖ죕웚ꎺ ㈰ㄱ쓪〴퓂㈳죕? 톧캻싛컄ퟷ헟뇏튵뫳좥쿲ꎺ 릤ퟷ떥캻ꎺ 뗧뮰ꎺ 춨톶뗘횷ꎺ 폊뇠ꎺ 춨톶뗘횷ꎺ 폊뇠ꎺ ? II
뗚튻헂 잰 퇔 톡쳢놳뺰뫍퇐뺿틢틥 쿺쫛얬솦ꎬ벴쮵럾쒿뇪맋뿍살릺싲웤닺욷뗄훖훖믮뚯ꎬ냼삨맣룦춶죫ꆢ죋풱췆쿺ꆢ펪튵췆맣ꆢ릫릲맘쾵뗈ꆣ쯦ퟅ싲볒뗄룶탔뮯뫍뛠퇹뮯ꎬ웳튵닺욷뗄짺쏼훜웚훰붥쟷뛌ꎬ헢뻍쪹뗃짌볒퓚쪹폃볛룱룜룋뗄춬쪱튲럗럗뾼싇퓶볓쿺쫛얬솦뛌웚쓚살듌벤싲볒뗄릺싲폻췻ꎬ퓶볓맋뿍탔ꎬ볓듳탨쟳솿ꆣ 뷼쓪살ꎬ쿺쫛볛룱뫍쿺쫛얬솦펰쿬탨쟳뗄컊쳢틽웰쇋웳튵뫍퇐뺿헟쏇뗄맣랺맘힢ꎬ훚뛠퇐뺿헟듓늻춬뷇뛈뛔듋샠쒣탍뷸탐첽뺿ꎬ떫쫇헢킩뛠쫽쫇퓚볙뚨쯦믺탨쟳뗄쟩뿶쿂뷸탐뗄ꎬ뛸퓚쫐뎡뺭볃훐ꎬ쿺쫛얬솦뫍쿺쫛볛룱뗈헢킩틲쯘뛔웳튵살쮵뚼쫇뿉뿘틲쯘ꎬ벴웳튵뿉틔룹뻝쒿뇪쫐뎡뗄탨쟳ꎬ뿉틔ퟔ훷뻶뚨닺욷뗄볛룱뫍듙쿺랽램ꎬ틲듋웳튵믡퓚돤럖ퟶ뫃쒿뇪쫐뎡(뇈죧죋뿚ꎬ릺싲솦뫍릺싲풸췻)럖컶뗄잰쳡쿂ꎬ믡룹뻝좷뚨탨쟳살뷸탐ퟔ벺뗄뚩릺솿뫍쿺쫛얬솦춶죫ꆣ헢쫇평폚웳튵죏쪶떽쇋헢솽룶틲쯘퓚닺욷펪쿺훐뗄훘튪ퟷ폃ꎬ폚쫇탨쟳춬쪱틀삵볛룱뫍쿺쫛얬솦뗄릩펦솴쒣탍훰붥돉캪퓋돯톧ꆢ쫽샭뺭볃톧뫍맜샭뿆톧붻닦퇐뺿뗄튻룶탂쇬폲ꆣ 퓚릩펦짌뫍쿺쫛짌ퟩ돉뗄뛾벶릩펦솴훐ꎬ쿺쫛짌틔ퟔ짭샻틦캪믹뒡뗄쮼뾼폫릩펦솴ퟷ캪튻룶헻쳥뗄ퟮ폅탔횮볤뎣믡랢짺돥춻ꆣ샽죧솽헟횮볤뗄뗘캻닮틬ꎬ닺튵솴훐뗄캻훃뗈틲쯘뚼뿉쓜뛔웤샻틦닺짺펰쿬ꆣ헢쫇틲캪퓚럇뫏ퟷ늩?쟩뿶쿂ꎬ릩펦솴훐뗄돉풱룷ퟔ뛀솢뻶닟ꎬ뻹틔ퟔ짭뗄샻틦캪믹뒡ꎬ틲듋퓚뷸탐뻶닟맽돌훐쿔좻믡틔ퟔ짭샻죳ퟮ듳뮯캪잰쳡ꎬ헢뇘좻쿷죵뛔랽뗄샻죳ꎬ틲듋늻믡듯떽헻쳥ퟮ폅ꎻ퓚뫏ퟷ늩?훐ꎬ릩펦짌뫍쿺쫛짌퓚튻뚨뗄뻶닟듫쪩훐ꎬ폐ퟅ릲춬뗄샻틦쒿뇪ꎬ틲듋뚼믡틔헻쳥ퟮ폅샻죳캪잰쳡ꎬ뷡맻뻹쓜쳡룟ퟔ짭뗄샻죳ꎬ헢뻍믡쪹릩펦솴킭뗷쿔뗃폈캪훘튪ꆣ Abad(1997,2003a)붨솢쇋릩펦짌쳡릩쇙쪱헛뿛볛룱뗄쟩뿶쿂ꎬ쿺쫛짌뗄ퟮ폅뚩릺엺솿뫍쿺쫛볛룱솪뫏뻶닟쒣탍ꆣ퓚쯻뗄컄헂훐ꎬ컒쏇뾴떽떱릩펦짌쳡릩쇙쪱볛룱헛뿛쪱ꎬ쿺쫛짌쫇쓜릻퓚쇙쪱헛볛웚쓚뷸탐쇙쪱뚩믵훐믱뗃샻틦뗄ꆣ헢뻍룸뫏ퟷ늩?쳡릩쇋뗤샽ꎬ쮵쏷릩펦솴튻쳥뮯쓜릻룸돉풱퓶볓샻죳ꆣ 릩펦짌맜샭뿢듦(VMI)쓜릻튻뚨돌뛈짏쿻돽쇋Bullwhip(얣뇞)킧펦ꆣVMI튪쟳헻룶릩펦솴짏뗄룷룶웳튵릲쿭짺닺ꆢ쿺쫛ꆢ탨쟳뗈탅쾢ꎬ뿉틔볓잿릩펦솴짏쿂폎웳튵횮볤뗄뫏ퟷꎬ복짙평폚탅쾢늻뛔돆믲늻췪좫듸살뗄럧쿕ꎬ폅뮯릩펦솴ꆣ탨쟳탅쾢쓜릻헦쪵ꆢ뿬쯙뗘뒫뗝ꎬ탅쾢뗄춸쏷뛈퓶볓ꎬ뿉틔뮺뷢쿂폎웳튵뗄뿢듦톹솦ꎬ뇜쏢Bullwhip킧펦ꆣ헢캪놾컄붨솢떥쿺쫛짌뫍뛠쿺쫛짌뗄릩펦솴킭뗷쒣탍뗬뚨쇋샭싛믹뒡ꆣ 1
맺쓚췢퇐뺿쿖ힴ 쿺쫛볛룱뫍쿺쫛얬솦뗄뫏ퟷ늩?쒣탍퓚릩펦솴훐틑폐맣랺뗄퇐뺿ꎬ늢돉캪늩?싛ꆢ퓋돯톧ꆢ쫽샭뺭볃톧뫍맜샭뿆톧뗄붻닦퇐뺿뗄튻룶탂뗄쇬폲ꆣ뷼죽쪮쓪살ꎬ릩펦솴퇐뺿훐뗄뫏ퟷ늩?럖컶샭싛뗃떽럡뢻랢햹ꎬ늢맣랺펦폃폚짺닺뫍쫐뎡뗄ퟮ폅뮯뻶닟훐ꆣ훷튪퇐뺿뗄랽쏦폐ꎺ (1)뒫춳뗄탨쟳틀삵볛룱쒣탍ꆣ1971쓪Kunreuther뫍Richard쫗듎듓뚨솿뗄뷇뛈붨솢쇋쿺쫛볛룱펰쿬탨쟳뗄뻶닟쒣탍ꆣ벴뾼싇떽쇋퓚뛌웚쿺쫛맽돌훐ꎬ샻폃볛룱룜룋살듌벤탨쟳ꆣ뛸헢킩쒣탍늻뷶캪웳튵뗄쇬떼헟뫍뿢듦맜샭헟뗄뿢듦뻶닟쳡릩쇋샭싛틀뻝ꎬ춬쪱튲췘햹쇋볛룱펰쿬탨쟳뗄뿢듦뿘훆컊쳢뗄퇐뺿쮼슷ꆣ (2)탨쟳틀삵쿺쫛볛룱뫍쿺쫛얬솦뗄뿢듦뿘훆쒣탍ꆣ2007쓪ꎬ뫎폂ꆢ컢쟥쇒뫍헔쇖뛈퓚탨쟳늻좷뚨쟒폫얬솦쮮욽뫍쇣쫛볛룱뻟폐쿠맘탔뗄잰쳡쿂, 붨솢쇋떯탔쫽솿웵풼쒣탍, 늢훘뗣첽쳖틔쿂솽룶훷튪쓚죝ꎬ튻쫇죧뫎좷놣릩펦솴킭ퟷꎬ뛾쫇죧뫎좷뚨ퟮ폅뗄얬솦쮮욽ꆢ쇣쫛볛룱뫍뚩릺솿ꆣ2010쓪ꎬ췴뻾욼ꎬ훜폀컱ꎬ퇮붣늨쳡돶쇋춬쪱뾼싇쇋탨쟳틀삵쿺쫛볛룱뫍쿺쫛얬솦뗄뻶닟쒣탍ꎬ룸돶쇋톰쟳ퟮ폅쿺쫛얬솦춶죫ꆢ쿺쫛볛룱벰뚩믵솿뗄럖컶랽램ꆣ헢쫇퓚볙뚨쯦믺탨쟳뗄잰쳡쿂붨솢뗄뻶닟쒣탍ꎬ늢럖컶쇋탨쟳뗄늻좷뚨탔뛔ퟮ폅쿺쫛볛룱뫍쿺쫛얬솦뗄펰쿬ꆣ (3)쿺쫛얬솦릲떣뗄뫏ퟷ늩?뻶닟쒣탍ꆣ2003쓪ꎬAbad뫍Jaggi퓚볙뚨퇓웚횧뢶뗄쪱볤쫇평릩펦짌살뻶뚨뗄잰쳡쿂ꎬ쳖싛쇋릩펦짌뫍쿺쫛짌뗄솽닣뿢듦컊쳢ꎬ럖뇰붨솢쇋뫏ퟷ늩?뫍럇뫏ퟷ늩?쟩뿶쿂릩펦짌뫍쿺쫛짌뗄ퟮ폅뻶닟쒣탍ꆣ듓ퟮ폅뮯샭싛뷇뛈뾴ꎬ헢캪뫏ퟷ늩?뗄뻶닟컊쳢쳡릩쇋뗤샽ꆣ2006쓪ꎬ뫎폂뫍컢쟥쇒뗈쳡돶쇋쿺쫛얬솦릲떣뗄웵풼쒣탍ꆣ헢튻쒣탍훐ꎬ뾼싇퓚떥릩펦짌뫍떥쿺쫛짌ퟩ돉뗄볲떥릩펦솴쒣쪽훐ꎬ틽죫릩펦짌뫍쿺쫛짌릲춬돐떣얬솦돉놾헢튻듫쪩ꎬ쪹릩펦솴듯떽킭ퟷힴ첬ꆣ (4)엺솿헛뿛ꆣ엺솿헛뿛쫇튻룶웕뇩뗄쫐뎡탐캪ꎬ릩펦짌횮쯹틔풸틢캪쿺쫛짌쳡릩엺솿헛뿛ꎬ폐틔쿂풭틲ꎺ튻쫇듌벤닺욷뗄탨쟳ꎻ뛾쫇복짙릩펦짌뗄짺닺돉놾ꆣAbad(1988a)쫗쿈붫솿헛뿛틽죫떽탨쟳뻟폐볛룱떯탔뗄뿢듦뿘훆뻶닟쒣탍훐ꎬ쳖싛쇋좫떥캻솿헛뿛뛔쿺쫛짌뻶닟컊쳢뗄펰쿬ꆣ뛸Abad(1997ꎬ2003a)퓲뾼싇쇋퓚릩펦짌쳡릩쇙쪱볛룱뗄쟩뿶쿂ꎬ쿺쫛짌뗄ퟮ폅뚩릺엺솿뫍쿺쫛볛룱솪뫏뻶닟컊쳢ꆣ2003쓪ꎬ퇮짆쇖뫍훜폀컱뗈붫볛룱헛뿛틽죫떽솽믵햻뿢듦쒣탍훐ꆣ2006쓪ꎬ췵쪥뚫ꎬ췴뻾욼뗈뾼싇쇋듸폐엺솿헛뿛뗄ퟮ폅뮯컊쳢ꎬ붨솢쇋퓚폐쿞볆뮮웚쓚떥쿺쫛짌뫍뛠릩펦짌뚯첬맦뮮쒣탍ꆣ 믹놾룅쓮 (1)Bullwhip얣뇞킧펦ꎺ릩펦솴훐룷뷚뗣웳튵훮죧릩펦짌ꆢ훆퓬짌ꆢ럖쿺짌뚼폐튻쳗ퟔ벺뗄뿢듦맜샭닟싔ꎬ평폚룷웳튵횮볤뿢듦닟싔뗄닮틬탔ꎬ뇘좻쪹웳 2
튵횮볤탅쾢뗄뒫뗝듦퓚늻좷뚨틲쯘ꎬ틲듋늻뿉뇜쏢뗘믡틽웰탨쟳럅듳뗄쿖쿳ꎬ탨쟳뗄훰벶럅듳붫떼훂릩펦솴훐룷룶뮷뷚뿢듦뗄틬뎣늨뚯ꎬ헢뛔릩펦솴킧싊뫍쿬펦쯙뛈뗄펰쿬쫇늻퇔뛸폷ꆣ헢뻍쫇컒쏇뎣쮵뗄얣뇞킧펦(Bullwhip Effee)ꆣ (2)엁샛췐ퟮ폅(Pareto Optimality)ꎬ튲돆캪엁샛췐킧싊(Pareto Efficiency)ꆣ엁샛췐ퟮ폅쫇횸풴럖엤뗄튻훖샭쿫ힴ첬ꎬ벴볙뚨만폐뗄튻좺죋뫍뿉럖엤뗄풴ꎬ듓튻훖럖엤ힴ첬떽쇭튻훖ힴ첬뗄뇤뮯훐ꎬ퓚쎻폐쪹죎뫎죋뺳뿶뇤뮵뗄잰쳡쿂ꎬ튲늻뿉쓜퓙쪹쒳킩죋뗄뒦뺳뇤뫃ꆣ뮻뻤뮰쮵ꎬ뻍쫇늻뿉쓜퓙룄짆쒳킩죋뗄뺳뿶ꎬ뛸늻쪹죎뫎웤쯻죋쫜쯰ꆣ (3)튻뷗ퟮ폅탔쳵볾ꆣ 짨몯쫽A+IQhcATP(x,I,Q)=x−w(a−bx)− Q2뛔ATP(x,I,Q)쟳맘폚x뗄튻뷗욫떼쫽뗃ꎬ ∂ATP(x,I,)AI(a−bx)−bx−w=− ꎨꎩ Q∂쇮*x캪쪽ꎨꎩ캪쇣쪱뗄뷢ꎬ퓲폐ꎬ *1b(A+I)x=a+bw+ 2bQAT2평폚∂P(x,I,Q)=−2b<0(0<b)뗃몯쫽ATP(x,I,Q)맘폚x쫇낼탎뗄ꎬ벴*x쫇몯2∂x쫽ATP(x,I,Q)뗄횵듯떽ퟮ듳뗄ퟮ폅횵ꆣ (4)좫뻖ퟮ폅ꆣ 볙짨몯쫽f(x,y)듦퓚뛾뷗솬탸욫떼쫽ꎬ쇮*xꎬy*럖뇰캪∂f(x,y)=0ꎬ ∂x∂f(x,y)=0뗄뷢ꎬ쟒싺ퟣ튻뷗ퟮ폅탔쳵볾ꎬ죧맻폐 ∂y∂22f(x,y)∂f(x,y)= ∂xy∂y∂x뫍 ∂2()∂2()∂2()∂2fx,yfx,yfx,yf(x,y)−>0 ∂2y2x∂xy∂y∂x퓲*xꎬy*벴캪몯쫽f(x,y)듯떽좫뻖ퟮ듳뗄ퟮ폅횵ꆣ 놾컄뗄훷튪쓚죝뫍뷡릹낲업 뒫춳뗄탨쟳틀삵볛룱뗄뿢듦뿘훆쒣탍뷶뷶뾼싇쇋볛룱틲쯘ꎬ뛸퓚쪵볊뗄쫐뎡펪쿺훐ꎬ탅쾢뮯틑뺭돉캪튻룶훷튪뗄쟷쫆ꎬ틲듋쿺쫛얬솦튲쫇튻룶펰쿬쿺쫛 3
뗄럇뎣훘튪뗄틲쯘ꆣ놾컄냑쿺쫛얬솦ퟷ캪펰쿬탨쟳뗄뻶닟틲쯘뾼싇퓚놾컄쒣탍횮훐ꆣ훷튪퇐뺿쓚죝죧쿂ꎺ (1)뗚튻헂훷튪뷩짜쇋뛾쪮뛠쓪살ꎬ뾼싇쿺쫛얬솦쿠맘샭싛뫍쪵볹랽쏦뗄펦폃틔벰튻킩믹놾룅쓮ꆣ (2)뗚뛾헂쫗쿈믘맋쇋뒫춳뗄탨쟳틀삵볛룱틔벰탨쟳틀삵쿺쫛얬솦뗄훮뛠쒣탍ꆣ쳡돶쇋탨쟳춬쪱틀삵쿺쫛얬솦뫍쿺쫛볛룱뗄뻶닟쒣탍ꆣ룸돶쇋솪뫏ퟮ폅뚩릺엺솿ꆢퟮ폅쿺쫛얬솦춶죫틔벰ퟮ폅뚨볛쒣탍뗄뻶닟랽램ꎬ늢뷸탐쇋쪵샽럖컶ꆣ (3)뗚죽헂쫗쿈믘맋쇋폐맘쿺쫛얬솦릲떣뗄쿠맘쒣탍ꎬ뷓ퟅ쳡돶쇋튻훖듸폐쿺쫛얬솦늹쳹뗄뚩릺엺솿솪뫏뻶닟쒣탍ꎬ늢뷸탐쇋쪵샽럖컶ꆣ (4)뗚쯄헂퓚믘맋쇋폐맘솿헛뿛뗄뻶닟쒣탍뫳ꎬ쳡돶쇋튻훖탨쟳퓚폫쿺쫛얬솦틔벰쿺쫛볛룱쿠맘뗄쟩탎쿂ꎬ틔릩펦짌캪뻶닟훐탄살짨훃퓶볓솿헛뿛볆뮮뗄쒣탍ꎬ늢뷸탐쇋쪵샽럖컶ꆣ (5)뗚컥헂ꎬ뛔놾컄쯹ퟶ뗄릤ퟷ볓틔ퟜ뷡ꎬ늢뛔뫳탸릤ퟷ뗄퇐뺿랽쿲쳡돶햹췻ꆣ ????????????????????? 4
뗚뛾헂 탨쟳틀삵쿺쫛얬솦뫍쿺쫛볛룱뗄뿢듦쒣탍 룅쫶 쯦ퟅ뺭볃뗄량쯙랢햹ꎬ짌튵뺺헹뗄풽랢벤쇒ꎬ탭뛠웳튵쿠볌볓듳쿺쫛얬솦살듌벤쿻럑헟뗄탨쟳ꆣ룹뻝쏀맺맺볒춳볆뻖쳡릩뗄쫽뻝쿔쪾ꎬ쏀맺웳튵뗄맣룦럑폃춶죫듓1990쓪뗄1300틚쏀풪퓶볓떽2000쓪뗄2360틚쏀풪ꆣ훚뛠퇐뺿헟튲폃쫽뻝횤쏷쇋뺭맽쫊떱뗄듙쿺쫖뛎쓜퓶볓짌튵샻죳ꆣ샽죧컄쿗[1]뫍[2]뛔릩펦짌쳡릩쇙쪱볛룱헛뿛쪱뗄쿺쫛짌뗄ퟮ폅뿢듦뻶닟컊쳢뷸탐쇋퇐뺿ꎬ늢쟒믱뗃쇋튻킩폐볛횵뗄돉맻ꎬ떫웤퇐뺿뻹믹폚죧쿂볙짨ꎺ쇣쫛짌뗄탨쟳쫇만뚨늻뇤뗄ꆣ컄쿗[3]볲쫶쇋탨쟳횻틀삵쿺쫛얬솦뗄쟩뿶쿂쿺쫛짌뗄ퟮ폅뿢듦뻶닟ꎬ컄쿗[4]첽쳖쇋뾼싇얬솦벰볛룱틲쯘뗄틗쫅욷릩펦솴킭뗷컊쳢ꎬ컄쿗[5]퇐뺿쇋쯦믺탨쟳쫇맘폚볛룱뫍맣룦럑폃뗄튻냣몯쫽뗄잰쳡쿂ꎬ쳡돶쇋튻룶튻냣뗄newsboy쒣탍ꎬ룸돶쇋톰쟳ퟮ폅맣룦럑폃ꆢ쿺쫛볛룱벰뚩믵솿뗄럖컶랽램ꆣ 쯤좻쿖폐컄쿗틑붨솢쇋탨쟳틀삵볛룱틔벰맣룦럑폃뗄쒣탍ꎬ떫퓚볙짨좷뚨탔탨쟳뗄잰쳡쿂ꎬ뫜짙폐컄쿗짦벰쿺쫛볛룱뫍쿺쫛얬솦춶죫춬쪱뻶닟뗄컊쳢ꎬ풭틲쫇춬쪱뾼싇헢솽룶틲쯘쓑틔룸돶럖컶뷢ꆣ뛸쪵볊뗄쫐뎡퓋ퟷ떱훐춬쪱닉폃헢솽훖펪쿺쫖뛎뗄짌욷뇈뇈뷔쫇ꆣ뇈죧낮맺헟ꆢ뷰쪿뛙뗈틆뚯직듦엌ꎬ룷샠욷없럾ힰ뗈ꆣ놾컄퓲퓚볙뚨쿺쫛짌뗄탨쟳몯쫽틀삵볛룱뫍쿺쫛얬솦뗄잰쳡쿂ꎬ틔ퟮ폅뗄쿺쫛얬솦살듌벤쿻럑ꎬ냯훺쿺쫛짌훆뚨ퟮ폅뗄ퟮ폅뚩릺솿ꎬ쪵쿖샻죳ퟮ듳뮯ꆣퟮ뫳춨맽쫽횵쪵샽퇩횤쇋쒣탍뗄쟳뷢맽돌늢뗃떽쿠맘웴쪾ꆣ 볇뫅폫볙뚨 놾컄쳡돶뗄쫽톧쒣탍쯹폃뗄볇뫅폫볙짨죧쿂ꎺ?볇뫅 (1)Q뇭쪾쿺쫛짌퓚쿺쫛웚돵뗄뚩릺솿ꆣ (2)w뇭쪾쿺쫛짌뗄떥캻뷸볛ꎬp뇭쪾쿺쫛짌뗄떥캻닺욷뗄쿺쫛볛룱ꆣ (3)A뇭쪾쿺쫛짌쎿듎만뚨뗄뚩믵럑폃ꎬh뇭쪾쿺쫛짌떥캻쪱볤떥캻닺욷뗄뿢듦럑폃햼릺싲뗄냙럖뇈ꆣ (4)I뇭쪾쿺쫛짌퓚쎿룶쿺쫛훜웚쯹ퟷ뗄쿺쫛얬솦춶죫ꆣ 볙뚨 (1)볙짨쾵춳퓋탐퓚컞쿞훜웚쮮욽짏ꎬ늻퓊탭좱믵ꎬ늹믵싊쫇쮲쪱뗄ꎻ (2)릩펦짌폫쿺쫛짌횮볤쪵탐ꆰ엺뛔엺ꆱ닟싔ꎬ틲듋퓚훆퓬짌뒦늻뾼싇뿢듦럑폃ꎻ (3)볙짨탨쟳몯쫽캪D(I,p)=a−bp+abI,b>0,p>a/b,웤훐a>0ꎬ뿉틔샭뷢캪듙쿺춶뗄쏴룐쾵쫽ꎬb쫇춶뗄떯탔ꎬ틲캪쿺쫛얬솦뗄뇟볊킧폃쫇뗝복뗄ꎬ∂D(I,p)틲듋뿉틔볙뚨0<b<1ꆣ싺ퟣꎺꋙp<0∂ꎻꋚ∂D(I,p)≥0∂Iꎬ∂2D(I,p)2<0∂Iꎻ웤훐 5
탔훊ꋙ뇭쪾D(I,p)(틔쿂볲돆D)쫇맘폚쿺쫛볛룱뗄복몯쫽ꎬ탔훊ꋚ뇭쪾D쫇쯦ퟅ쿺쫛얬솦뗄퓶볓뛸퓶볓ꆣ 쒣탍뗄붨솢폫럖컶 룹뻝틔짏볙짨ꎬ놾헂뗄뻶닟컊쳢뇤캪ꎺ퓵퇹춬쪱뻶뚨쿺쫛짌뗄ퟮ폅쿺쫛춶죫ꆢퟮ폅쿺쫛볛룱틔벰ퟮ폅뚩릺엺솿ꎬ쿂쏦놾헂뻝듋붨솢틔쿂쒣탍ꆣ 듸폐쿺쫛얬솦뗄뿢듦뿘훆쒣탍 쇮ATP1(p,I,Q)뇭쪾쿺쫛짌퓚튻룶훜웚쓚뗄욽뻹ퟜ샻죳몯쫽ꎬ 룹뻝짏쏦뗄볇뫅폫볙뚨ꎬ욽뻹ퟜ샻죳뿉뇭쪾캪ꎺ ATP1(p,I,Q)={쿺쫛쫕죫-릺싲돉놾-뿢듦돉놾-뚩릺돉놾-쿺쫛얬솦춶죫} QhcADID=ꎨp−w)D−−− 2QQA+IQhc =p−w−D− ꎨꎩ Q2∂ATP'쇮1(p,I,)ADID=ꎨp−wD' −D'−−I) II∂QQQA+ID=p−w−D'()−=0 ꎨꎩ QIQ벴 AIDpw+−−D' ()= 뗃*I ꎨꎩ QIQ폖틲 ∂2ATPpI'3(,,Q)wA+I=−−DDp"()−2I<0 ∂2QIQ벴횤쏷*I싺ퟣ쪽ꎨꎩ뗄튻뷗ퟮ폅탔쳵볾ꆣ 춬쪱쇮 ATP3(p,I,Q)DA+I=+p−wD'−D'()pp ∂QDA+I=+p−w−(−b)=0 ꎨꎩ Q벴 AIDpw+−−= 뗃p* ꎨꎩ Qb뛸 6
∂2ATP3(p,I,Q)=2DA+I'+" 2pp−w−Dp ∂Q=2D'p=−2b<0 ꎨꎩ 쪽ꎨꎩ쮵쏷p*싺ퟣ쪽2-1뗄튻뷗ퟮ폅탔쳵볾ꆣ 쿂쏦횤쏷뛔폚룸뚨뗄Qꎬ*I뫍p*뿉쪹쪽(1)좡뗃ퟮ듳횵ꆣ ∂2ATP1(p,I,Q)b=D'+ I∂p∂Q∂2ATP1(p,I,Q)Db='+ I∂I∂Q∂2ATPpIQ∂2ATPpIQ2ATPpIQ∂21(,,)1(,,)1(,,)ATP1(p,I,Q)−∂2∂2∂p∂I∂p bDDb24'=I−2bD'×−D'+QIIbQ2bD'2=I−2D×D'−Db'2−QIIQ2 =−2D"−D'b−IIQ =−2DD">0I 벴쮵쏷*I뫍p*쫇몯쫽ATP1(p,I,Q)듯떽좫뻖ퟮ듳뗄ퟮ폅횵ꆣ냑*I뫍p*듺죫쪽ꎨꎩ뫳ꎬ몯쫽뻍돉캪맘폚Q뗄튻캬몯쫽ATPp*(QI*(),(Q),Qꆣ쇮 1)ATP(Q)=ATPp*QI*((),(Q),Qꎬ쿂쏦컒쏇살쟳ퟮ폅뚩릺엺솿Q*ꎬ틔쪹뗃11)ATP1(Q)좡뗃ퟮ듳횵ꆣ 쫗쿈ꎬ평ATP1(Q)뗄튻뷗ퟮ폅탔쳵볾뗃 dATP1(Q)∂ATP1(p,I,Q)∂ATP1(p,I,Q)dp∂ATP1(p,I,Q)dI=d++0pdQIdQ=*=*II(Q),pp(Q)뛸평쪽ꎨꎩ뫍쪽ꎨꎩ횪ꎬ떱*I=I(Q)ꎬQ=Q*(p)쪱폐∂ATP1(p,I,Q)=0뫍∂I∂ATP1(p,I,Q)=0ꎬ틲듋ꎬ폐 ∂pdATPQ*1()∂ATP(p,I,Q)(A+I)D(Q)1hw−=0 ꎨꎩ d∂**2I=I(Q),p=p(Q)2 7
붫짏쪽뷸튻늽뮯볲뿉뗃 *(A+I)D(Q)hw= 뗃Q*Q21 2퓲폐 2(A+I)D*(Q Q*) 1= ꎨꎩ hw풤럖컶쪽ꎨꎩ뗄룹뗄쟩뿶ꎬ컒쏇쿈퇐뺿ATP1(Q)뗄뛾뷗떼쫽 d2ATPQ∂2ATPQ∂2ATPQdp∂21()1()1()ATP1(Q)dI=++22d∂pQdQ∂I∂QdQ=**II(Q),p=p(Q) 2A'(I)DA+I=−Dd(A+I)D+DdI+'IQ3Q2pdQQ2dQ 2−2(A+I)(1−b)D+IDb(A+I)=+D'Q32Q4p ꎨꎩ쇮쪽ꎨꎩ캪쇣ꎬ벴폐 2b(A+I)(1−bQ)1=4(A+I)(1−b)D−2ID ꎨꎩ 웤훐D(I,p)=a−bp+aIb 2춨맽쪽ꎨꎩ폐ꎺ떱QdATPQ2)dATPQ<Q1쪱ꎬ1(≥0ꎬ떱Q>Q1쪱1()<0ꆣ dQ2dQ2튲뻍쫇쮵ꎬATP1(Q)쫇맘폚Q뗄낼-춹몯쫽ꆣ듓짏쏦럖컶뿉횪ꎬ쪽(8)펦폐솽룶뷢ꎬ럖뇰볇ퟷQ*1a뫍Q*1bꆣ듓춼훐뿉횪ꎬ쿔좻ퟮ폅뷢캪0뫍Q*1bꆣ쟳ퟮ폅뷢Q*1b볻뢽슼ꋱꆣ 쎻폐쿺쫛얬솦뗄뿢듦뿘훆쒣탍 탨쟳몯쫽D(p)=a−bp,b>0,p<ab?죧맻쎻폐쿺쫛얬솦뗄쟩뿶쿂폐?ꎨAQhcATP(p,Q)=p−w−)D−††††?†?†††?††?ꎨꎩ?Q2뛔p쟳튻뷗욫떼늢쇮웤뗈폚쇣ꎺ?∂ATP(p,Q)A='(p−w−)DP+D=0?∂Q 8
벴평†††††??A−DDp−w−==††?뗃?QD'Pb*1Aap=(w++)††††?†††††??ꎨꎩ?2Qb2평∂ATP(p,Q)=2D'(p*)<0뿉횪p*싺ퟣ몯쫽ATP(p,Q)튻뷗ퟮ폅탔쳵볾ꆣ?2∂p쇮ATP*(p(Q),Q)=ATP2(Q)ꎬ쿂쏦컒쏇살쟳ퟮ폅쿺쫛볛룱Q*?틔쪹뗃ATP2(Q)좡뗃ퟮ듳횵ꆣ?평ATP1(Q)맘폚Q뗄튻뷗ퟮ폅탔쳵볾뗃?dATPQAD*2()(Q)hw=−†††††††††????†?ꎨꎩ?dQQ22쇮짏쪽뗈폚쇣폐?bA2Aa−bw−a=+Q2hw†뗃Q*2††††?††?†† ꎨꎩ?Q뛔쪽ꎨꎩ뷸탐뛾듎쟳떼늢쇮웤뗈폚쇣?d2ATPQ−AbA22()11b=A(a−bw−)+=0††??††††?ꎨꎩ?dQQ3Q2Q4뷢뗃?뗄뷢캪Q3Ab2=ꆣ?2(a−bw)춨맽쪽ꎨꎩ폐틔쿂솽훖쟩뿶ꎺ떱d2QATPQ<Q2쪱ꎬ2()≥0ꎬ떱Q>Q쪱dQ22d2ATP2(Q)<0ꆣ튲뻍쫇쮵ꎬATP2(Q)쫇맘폚Q뗄낼?춹몯쫽ꆣ듓짏쏦럖컶뿉횪ꎬdQ2쪽ꎨꎩ펦폐솽룶뷢ꎬ럖뇰볇ퟷQ*2a뫍Q*2bꆣ듓춼훐뿉횪ꎬ쿔좻ퟮ폅뷢캪?뫍Q*2bꆣ쟳ퟮ폅뷢Q*2b볻뢽슼ꋲꆣ?? 솽쒣탍훐뗄ퟮ폅샻죳몯쫽뗄뇈뷏 캪쇋랽뇣뇈뷏ꎬ놾뷚볙뚨떱뚩릺솿Q쿠춬쟒뚼뗈폚쎻폐퓶볓쿺쫛얬솦춶죫쪱뗄샻죳몯쫽뗄ퟮ폅뚩릺솿Q*1쪱ꎬ솽훖쟩탎쿂샻죳몯쫽뗄듳킡뇈뷏ꆣ 퓶볓쿺쫛얬솦쟩탎쿂샻죳몯쫽캪 **********QhcAD(p1,I1)I1D(p1,IATPpIQ1)=(p*−w)D(p*I*)−1(1,1,1)11,1−−?2QQ2Dp*I*(,)*11=Q−1hw†††??†††††††?†?ꎨꎩ?b2 9
웤훐 †††Dp**1'(1,I)=a−bp1+I=a−bc−(A+I)D+aIbI2?쎻폐퓶볓쿺쫛얬솦쟩탎쿂샻죳몯쫽캪 *****AQhwATP(p,Q)=p−w−(a−bp)−2222?*Q222Dp*()Q*22hw=−††††??†?†††††???ꎨꎩ?b2웤훐††?†††*()=−*1AbDp2abp2=a−bc−?2Q*2쿖좡쪽ꎨꎩ뫍쪽ꎨꎩ훐뚩릺솿Q횵쿠춬ꎬ뻹캪Q*2ꆣ퓲 ATP**************(p1,I1,Q)−ATP(p2,Q)≥ATP(p1,I1,Q2)−ATP(p2,Q2)?Dp*(,I)Q*hwD(p)Q*1=−2−w+2h?bb22D(p*)*,IDp1=()−?bb1{22=Dp*−*(1,I)D(p)}?b쿂쏦횤쏷††††††D(p***,I)−D(p)>0 12횤?†?***Dpb1Ab(1,I)−D(p2)=a−bw−(A+I)+abI−a−bw−Q*?2Q*221Abb(Ab=−+I+aI2Q*)Q*?221=abI−ID'I2?1=abI−abbI2?1=abI(1−b)02>ꎨ평잰쏦볙짨틑횪0<b<1ꎩ?틑횪탨쟳몯쫽Dp*I*(,뫍Dp*11)()뻹캪헽쫽ꎬ평폚Dp**−*,IDp>0ꎬ퓲뗃2(1)(2)돶22D(p*)−p*1,ID()>0ꎬ볌뛸뗃돶솽룶ퟮ폅쒿뇪몯쫽뗄닮횵캪헽횵ꎬ벴? 10
ATP*p*I*Q* −ATP*p*Q*(1,1,)(2,2)>0ꆣ?ퟛ짏쯹쫶ꎬ탨쟳춬쪱틀삵쿺쫛볛룱뫍쿺쫛얬솦뗄ퟮ폅욽뻹샻죳쏷쿔듳폚탨쟳횻틀삵쿺쫛볛룱뗄쟩탎쿂뗄ퟮ폅욽뻹샻죳ꆣ헢뇭쏷퓶볓쿺쫛얬솦뛔쿺쫛짌살쮵쫇럇뎣뇘튪뗄ꎬ죧춼ꎨꎩꆣ?? 뿢듦뿘훆쒣탍뗄ퟮ폅뷢럖컶 쏼쳢1 쒿뇪몯쫽1훐ꎬ떱aꆢb튻뚨쪱ꎬQ횵횻폫I폐맘ꆣ?횤?틑횪탨쟳몯쫽캪D(I,p)=a−bp+abI,,b>0,p>a/b,0<<1ꎬ?맊폐?D'=abIb−1I?평쪽ꎨꎩ뫍쪽ꎨꎩ뗃?b=QD'=QabIb−1I?벴Q횵횻폫I폐맘ꎬ횤뇏ꆣ 쏼쳢2 떱웤쯼닎쫽틑횪쪱ꎬ쒿뇪몯쫽1뗄ퟮ폅횵횻폫aꆢb폐맘ꆣ 횤††평쏼쳢?뗃†††††††Qb=?†††††††††?†ꎨꎩ?D'I평쪽ꎨꎩ뫍쪽ꎨꎩ뗃?D*1'(I)=a−bw−(A+I)D+aIb††††?†††††ꎨꎩ?I2듺죫쪽ꎨꎩ뗃?b2A+ID*()(Q)=?D'hwI솽뇟춬쪱욽랽ꎬ뮯볲뗃?b2(+)(−)−2ab−1hcAIabwAI+Aa1−2bbI+a1−bb+1−2−2b()()II=0 ꎨꎩ?a2b2틲듋ꎬ쪽ꎨꎩ훐볆쯣쯹뗃뗄I횵횻폫aꆢb폐맘ꆣ폖평쪽ꎨꎩ뫍쪽ꎨꎩ횪ꎬpꆢQ횻폫I횵폐맘ꎬ맊헻룶ퟮ폅쒿뇪몯쫽?뗄횵횻폫닎aꆢß폐맘ꎬ횤뇏ꆣ? 쪵샽럖컶 쿂쏦뷡뫏쪵샽룸돶ퟮ폅뷢뗄쫽횵럖컶벰맘폚닎쫽aꆢß뗄쇩쏴뛈럖컶ꆣ 평춼뿉틔뾴돶ꎬ떱p,Q튻뚨쪱ꎬ몯쫽ATP(p,I(a),Q)쯦ퟅa뗄퓶듳뛸퓶듳ꎬ뛸춼뇭쏷쇋떱p,Q튻뚨쪱ꎬ몯쫽ATP(p,I(a),Q)쯦ퟅß뗄퓶듳뛸복킡ꎬ틲듋죧뫎뛔aꎬß좡횵뛔뷡맻폐ퟅ튻뚨뗄펰쿬ꆣ 샽 볙뚨쿺쫛짌쯹쏦쇙뗄탨쟳몯쫽캪D(p)=36000-4000pꎬ쎿듎뚩릺믵컯쯹탨뗄만뚨럑폃캪A=150풪ꎬ릺싲떥캻닺욷뗄돉놾캪w=3풪ꎬ떥캻닺욷퓚 11
떥캻쪱볤쓚욽뻹뿢듦돖폐돉놾햼쿺쫛짌떥캻릺싲돉놾뗄냙럖뇈캪h=ꆣ쫔컊쿺쫛짌죧뫎훆뚨웤뚩릺닟싔틔벰쿺쫛볛룱? 뷢ꎺ쫗쿈샻폃뗼듺쯣램2뿉뗃ퟮ폅뚩릺엺솿Q*=1719ꎨ떥캻ꎩꎬ좻뫳퓙샻폃쪽2-12뗃돶ퟮ폅쿺쫛볛룱p*=ꎨ풪ꎩꎬ붫쯹뗃뗄Q*뫍p*듺죫쪽2-11뿉뗃쿺쫛짌뗄ퟮ폅욽뻹샻죳캪ATP*(p,Q)=33929ꎨ풪ꎩꆣ 샽 볙뚨쿺쫛짌퓚춶죫쿺쫛얬솦틔뫳쯹쏦쇙뗄탨쟳몯쫽캪 D(I,p)=a−bp+aIbꎬaꆢb>0,p>a/b,0<ß<1ꆣ웤쯻닎쫽폫샽2-1쿠춬벴 a=36000ꎬb=4000ꎬw=3ꎬA=150ꎬh=ꎬa=1000ꎬß=ꆣ쫔컊룃쿺쫛짌폖룃죧뫎훆뚨웤뚩릺닟싔틔벰쿺쫛볛룱ꎿ 뷢ꎺ폃짏쫶춬퇹랽램뗃돶*I=1040ꎨ풪ꎩꎬQ*= 5183ꎨ떥캻ꎩꎬp* =ꎨ풪ꎩ, 듺죫쪽2-19뿉뗃쿺쫛짌뗄ퟮ폅욽뻹샻죳캪ATP*p***(1,I1,Q1)=42770ꎨ풪ꎩꆣ 춼 몯쫽ꎨꎩ뫍ꎨꎩ뗄춼탎 평춼뿉틔뾴돶ATP(p*,I*,Q)>ATP (p*,Q)ꆣ?뺭맽뛔뇈벴뿉뾴돶ꎬ볓죫쿺쫛얬솦믡룸쿺쫛짌듸살뷏캪뿉맛뗄쫕틦ꆣ 샽 퓚쒣탍훐ꎬ볙뚨웤쯻쳵볾늻뇤ꎬ쳖싛닎쫽aꆢb뗄뇤뮯뛔ퟮ폅뷢뗄펰쿬ꆣ 12
뇭 닎쫽aꆢß뗄뇤뮯뛔쒿뇪몯쫽ퟮ폅뷢뗄펰쿬 a* ß p*IQ*ATP*(Q) ß= 414 3623 46630 a=2500 ß= 34122 33847 80252 ß= 35 —— —— ß= 268 3064 43563 a=2000 ß= 12817 19330 63129 ß= 26 —— —— ß= 162 2602 40741 a=1500 ß= 4100 10355 51077 ß= 17 —— —— ß= 87 2229 38158 a=1000 ß= 1040 5183 42770 ß= —— —— ß= 64 2102 37198 a=800 ß= 554 2348 40261 ß= 6 —— —— ß= 43 1987 36281 a=600 ß= 2325 16447 33120 ß= 3 —— —— ? 13
?춼 몯쫽ATP(p*,I(a),Q*)뗄춼쿱 ?춼 몯쫽ATP(p*,I(ß),Q*)뗄춼쿱 14
춼쒿뇪몯쫽ꎨꎩ ATP(p*,I*,Q)뗄춼쿱 ?뷡싛 웳튵퓚쫐뎡퓋ퟷ맽돌훐춨뎣믡쪹폃볛룱뫍맣룦헢솽룶훘튪쫖뛎ꎬ놾컄횤쏷쇋퓚쫊떱퓶볓쇋쿺쫛얬솦틔뫳웳튵뗄욽뻹샻죳폐쯹퓶듳ꆣ평춼???뿉틔뾴돶웤쫕틦뗄닮뻠늻쫇쳘뇰쏷쿔ꆣ?헢쫇틲캪쪵볊뗄쫐뎡퓋탐훐ꎬ퓶볓쿺쫛얬솦믡춬쪱룸릩펦짌폫쿺쫛짌듸살쫕틦ꎬ튻냣쟩뿶쿂릩펦짌믡춨맽뛔쿺쫛짌뷸탐쿺쫛늹쳹살릲춬럖떣쿺쫛얬솦춶죫ꆣ놾컄뷸튻늽뗄퇐뺿랽쿲쫇ꎬ춨맽훆뚨췪짆뗄쿺쫛웵풼살듙쪹릩펦짌폫떥룶믲뛠룶쿺쫛짌킭뗷럖떣쿺쫛얬솦뗄춶죫ꎬ틔듋살듯떽릩펦솴헻쳥뗄ퟮ폅샻죳ꆣ? 춼 쒿뇪몯쫽ATP(p*,I*,Q)뫍ATP(p*,Q)뗄닮 15
뗚죽헂 쿺쫛얬솦릲떣뗄릩펦솴쒣탍럖컶 ?뻝짏튻헂뿉횪ꎬ죧맻쿺쫛얬솦뷶뷶평릩펦짌살뷸탐쿺쫛얬솦춶죫ꎬ쿺쫛짌뗃떽뗄ퟮ폅욽뻹샻죳퓶솿틔벰뚩릺퓶솿뚼늻쫇쳘뇰쏷쿔ꆣ평폚뚩릺솿퓶솿늻쫇첫듳ꎬ쯦횮릩펦짌튲늻쓜듓쿺쫛짌쓇샯믱좡뫜듳뗄샻죳ꆣ퓚ퟮ뷼벸쪮쓪샯ꎬ탭뛠퇐뺿헟뚼맛달떽ꎬ퓚릩펦짌뫍쿺쫛짌탎돉뗄볲떥릩펦솴샯ꎬ췹췹뫏ퟷ틢캶ퟅ쮫펮ꆣ2010쓪ꎬ뫺놾폂ꎬ샗뚫뫍돂탱퓚믹폚쫕틦릲쿭폫쿺쫛얬솦돉놾릲떣뗄릩펦솴웵풼쒣탍훐ꎬ뛔쿺쫛짌뫍릩펦짌ퟩ돉뗄솽벶릩펦솴,퓚탨쟳캪쯦믺쟒폫얬솦쮮욽쿠맘뗄쫐뎡뮷뺳쿂,붨솢쇋릩펦솴웚좨쿺솿떣놣웵풼쒣탍 ,럖컶쇋얬솦틲쯘릲떣뛔릩펦솴킭뗷뗄펰쿬ꆣ2006쓪ꎬ뫎폂ꎬ컢쟥?뗈퓚뾼싇탨쟳폫쿺쫛얬솦쮮욽쿠맘뗄잰쳡쿂ꎬ횤쏷쇋뒫춳뗄쫽솿죡탔웵풼컞램쪵쿖릩펦솴킭ퟷꎬ늢춨맽퓚뒫춳뗄죡탔웵풼훐틽죫얬솦돉놾릲떣헢튻듫쪩ꎬ쪹릩펦솴믖뢴킭ퟷힴ첬ꆣ춬쪱탭뛠릩펦짌뫍쿺쫛짌쏇튲죏쪶떽쇋떱뇋듋뫏ퟷ쪱ꎬ쮫랽뗄샻죳뻹믡퓶볓ꎬ헢뻍쪹뗃뫏ퟷ돉캪뇘튪ꆣ 뗚뛾헂뾼싇쇋퓶볓쿺쫛얬솦믡퓶볓쿺쫛짌뗄욽뻹ퟜ샻죳ꎬ뛸쎻폐뾼싇떽뫍릩펦짌뗄킭ퟷ컊쳢ꎬ퓚좫쟲뺭볃튻쳥뮯뗄뷱쳬ꎬ탭뛠웳튵튲훰붥죏쪶떽쇋솪뫏웤짏쿂폎웳튵퓶잿웤헻쳥뺺헹솦뗄훘튪탔ꆣ틲듋늻춬뗄뫏ퟷ컊쳢틽웰쇋퇐뺿헟뫍맜샭헟뗄맣랺맘힢ꆣ놾헂붫춨맽릩펦짌쿲쿺쫛짌쳡릩쿺쫛얬솦늹쳹뗄듫쪩ꎬ횤쏷쿺쫛짌퓚듋듫쪩쿂ꎬ웤욽뻹ퟮ폅ퟜ샻죳믡퓶볓ꆣ 볇뫅폫볙뚨 퓚뗚튻헂뗄볇뫅폫볙짨뗄믹뒡짏ꎬ퓶짨볇뫅S캪훆퓬짌뛔쿺쫛짌듙쿺춶뗄늹쳹싊(0<S<1)ꆣ늢쟒늻퓊탭좱믵ꆣ늢볙뚨릩펦짌쳡릩늹쳹쪱폐샻폚쮫랽샻죳퓶볓ꎬ놾컄튲믡횤쏷헢튻뗣ꆣ 쿺쫛얬솦늹쳹뗄뿢듦뿘훆쒣탍뗄붨솢폫럖컶 퓚퇐뺿탨쟳쫜쿺쫛볛룱틔벰쿺쫛얬솦펰쿬뗄뿢듦뿘훆뗄잰쳡쿂ꎬ놾헂쳖싛쇋퓚릩펦짌룸쿺쫛짌쳡릩얬솦춶죫늹쳹뫳ꎬ쿺쫛짌퓚좷뚨ퟮ폅뚩릺엺솿뗄춬쪱ꎬ죧뫎좷뚨ퟮ폅쿺쫛얬솦춶죫뫍ퟮ폅쿺쫛볛룱ꎬ닅쓜쪹ퟔ짭샻죳듯떽ퟮ듳ꎿ늢쟒폫퓚쎻폐퓶볓쿺쫛얬솦춶죫늹쳹뗄쳵볾뇈뷏ꎬ놾쒣탍폐쓇킩룄뷸폫폅쫆ꎿ쿂쏦뻟쳥쳖싛헢룶컊쳢ꆣ ? 퓶볓쿺쫛얬솦늹쳹쪱뗄욽뻹샻죳몯쫽 믹폚잰쏦뗄볙뚨ꎬ쇮ATP3(p,I,Q)뇭쪾쿺쫛짌퓚튻룶훜웚쓚뗄욽뻹ퟜ샻죳몯쫽ꎬ룹뻝뗚튻헂뗄볇뫅폫볙뚨ꎬ퓚퓶볓쇋쿺쫛얬솦늹쳹뫳ꎬ웤욽뻹ퟜ샻죳뿉뇭쪾캪ꎺ 16
ATP3(p,I,Q)={쿺쫛쫕죫-릺싲돉놾-뿢듦돉놾-뚩릺돉놾-쿺쫛얬솦춶죫} ꎨQhcAD(1S)IDp−w)D−=−−− 2QQA+(1−S)IQhc =p−wD− ꎨꎩ Q2 쿂쏦쟳쒿뇪몯쫽ATP(p,I,Q)맘폚쿺쫛볛룱p뫍I뗄욫떼쫽 '쇮∂ATP3(p,I,Q)ꎨAD1−SID=p−wD−D()''I)−− I∂QIQQA+(1−S)I(1−S)D='p−wD−=0 ꎨꎩ QIQ벴 A+(1−S)I(1−S)Dp−wD' = 뗃*I3 ꎨꎩ QIQ∂2ATPpI,Q)A+1−SI1−SD'3(,()"() =2p−wD−2I<0 ∂QIQ벴횤쏷*I3싺ퟣ쪽ꎨꎩ뗄튻뷗ퟮ폅탔쳵볾ꆣ 춬쪱쇮 ∂ATP3(p,I,Q)DASI+p−wD+(1−)=''()p−D ∂QpA+(1−S)I=D+p−w(−b= ꎨꎩ Q)0벴 A+(1−S)IDp−w= 뗃p*Qb3 ꎨꎩ 뛸 ∂2ATPp,I,Q)A+1−SI3(() =2D'+"2pp−w−DQp ∂=2D'p=−2b<0 ꎨꎩ 쪽ꎨꎩ쮵쏷p*3싺ퟣ쪽3-1뗄튻뷗ퟮ폅탔쳵볾ꆣ 쿂쏦횤쏷뛔폚룸뚨뗄뚩릺솿Qꎬퟮ폅쿺쫛얬솦*I뫍ퟮ폅쿺쫛볛룱p*뿉쪹쪽ꎨꎩ좡뗃ퟮ듳횵ꆣ ∂2ATP(p,I,Q)D(1−S)b='+=2D' II∂p∂Q∂2ATP(p,I,Q)(1S)b=D−'+=2D' II∂I∂Q 17
∂2ATPpIQ∂2ATPpIQ∂2ATPpIQ∂23(,,)3(,,)3(,,)ATP3(p,I,Q)−∂2∂2∂p∂I∂p 4b1−SD'()(1SDI)=−2bD'×−4D'2QIQD'II=−2D'+4D'2−4D'2 III=−2DD">0I ꎨꎩ 쪽ꎨꎩ벴쮵쏷*I뫍p*쫇ATP3(p,I,Q)맘폚뚩릺솿Q뗄헻쳥ퟮ폅몯쫽ꎬ냑*I뫍p*듺죫쪽3-1뫳ꎬ몯쫽뻍돉캪맘폚Q뗄튻캬몯쫽ATP3(p*(Q),I*(Q),Q)ꆣ 쿖쇮ATP3(Q)= ATP3(p*(Q),I*(Q),Q)ꎬ늢볙짨웤맘폚Q*뗄ퟮ폅샻죳몯쫽캪3ATP**3(Q)ꎬ퓲쿔좻폐ATP**3(Q)≥ATP3(Q),럖컶맽돌뇭쏷쇋퓶볓쿺쫛얬솦춶죫늹쳹쫇뛔쿺쫛짌폐샻뗄ꆣ 솽훖쒣탍뗄샻죳몯쫽뗄뇈뷏 퓶볓쿺쫛얬솦늹쳹뗄샻죳몯쫽캪 ATP(Q)=ATPp*Q*((),IQ,33(3)Q 3)****(1−S)IQhcAD(p,I=3**333)p3−wD(p3,I3)−− Q2Q2Dp**(,I33)Q=−3hc b2평뗚튻헂횪ꎬ쎻폐퓶볓쿺쫛얬솦늹쳹뗄샻죳몯쫽캪 Q******hcAD(p1,I1)I1D(p1,I)ATP*p*I*Q*(p*c)D(p*I*)11(1,1,1)=1−1,1−−−2QQ?2Dp**(,I)Q*11=−1hcb2††? 캪쇋뇣폚뇈뷏ꎬ쿖쇮ATP3(p*(Q),I*(Q),Q)Q=Q*31ꎬ퓲폐 22Dp***(I)QhcD(p,I)Q*P*Q*−ATP*p*I*Q*3=−311()−+1hcAT3(1,1,1) bb 18
22Dp**I*(,I)D(p,311) =− bb1={22D(p*)−*()1,IDp?b}1=Dp********(1,I)D(p3,I)D(p1,I)+D(p3,I3)?b춬퇹뗘ꎬ쿂쏦횤쏷Dp****(,I)−D(p,I)>0 133*1+****A+(1−S)IDpAI()−()=13**1,IDp3,Ib−b+abI−abIQQ12*3?1**1I(1−S)I=13**bb+abI−abI ꎨꎩ2Q*Q*3111평뗚튻헂컒쏇횪뗀 b=Q*D'=Q*abI*b−111 I1 ꎨꎩ 뛸평쪽ꎨꎩ뫍쪽ꎨꎩ뗃 1−Sb=Q*D'=Q*()abI*b−11 I13 듺죫쪽ꎨꎩ뗃 **I(1−S)I13******bb+abI−abbbbbI31=abI1−abI3+aI3−aI QQ12**112=ab*b−*b−a*b−*b(IIII 13)(13)=a*b−*b(II)(−1>0 13)평틑횪탨쟳몯쫽Dp**(,I뫍Dp*I*(,뻹듳폚쇣ꎬ평폚 11)33)Dp****(,I)−D(p,I>0ꎬ퓲뗃돶22Dp***133)(1,I)−D(p3,I)3>0ꎬ볌뛸뗃돶솽룶ퟮ폅쒿뇪몯쫽뗄닮횵캪헽횵?벴 ATP*Q*−ATP*p*I*()Q*(,,)>0?3111 19
헢뻍쮵쏷ꎬ퓶볓쿺쫛얬솦늹쳹쪱럇뎣폐뇘튪뗄ꆣ ퟮ폅뷢럖컶 뚨샭1 퓚퓶볓쿺쫛얬솦춶죫늹쳹S뫳ꎬ쿺쫛짌뗄ퟮ폅욽뻹샻죳몯쫽듳폚쎻폐퓶볓늹쳹쪱뗄ퟮ폅욽뻹샻죳ꎬ벴 ATP*Q*−ATP*p*()I*Q*(,,)>0 3111횤 닎볻뷚럖컶맽돌ꆣ 뚨샭2퓚뗃떽늹쳹뫳ꎬ쿺쫛짌튻랽뗄ퟮ폅뚩릺솿룟폚쎻폐뗃떽늹쳹잰뗄ퟮ폅뚩릺솿ꆣ 횤 평뗚뛾헂횪ꎬ퓚쿺쫛짌쎻폐퓶볓쿺쫛얬솦춶죫늹쳹쪱뗄쒿뇪몯쫽캪 A+IQhcATP1(p,I,Q)=p−w−D− Q2A+IQhc=p−w−a−bp+aIbQ− ꎨꎩ 2평폚0<S<1ꎬ퓲평쒿뇪몯쫽ꎨꎩ뗃 A+(1−S)IQhcATP3(p,I,Q)=p−wD− Q2A+(1−S)IQhc=p−wa−bp+aIb()− Q2A+(1−S)IQhc≥p−wa−bpabb(1S)IQ+−− 2A+(1−S)IQhc=p−wabpabSIbQ−+(1−)− 2=ATP1(p,(1−S)I,Q) 평쪽ꎨꎩ횪ꎬ쒿뇪몯쫽ATP1(p,(1-S)I,Q)뇭쪾퓚쎻폐퓶볓쿺쫛얬솦춶죫늹쳹쪱뗄욽뻹샻죳몯쫽ꎬ쟒쿺쫛얬솦춶죫캪(1-S)Iꆣ 평뗚뛾헂맘폚쒿뇪몯쫽ATP1(p,I,Q)맘폚Q뗄ퟮ폅뷢럖컶횪ꎬ볙짨Q3싺ퟣATP3(p,I,Q)뗄튻뷗ퟮ폅탔쳵볾ꎬ퓲폐 2[A+(1−)]2[A+(1−S)]a−bp+aIbQ*I*SD3(1)== ꎨꎩ hwhw평뗚뛾헂쪽ꎨꎩ뗃 b2A+(1−S)ID2A+(1−S)Ia−bp+a(1−S)IbQ*21== ꎨꎩ hwhw 20
샠쯆뗘ꎬ폐 *b[A+(1−S)I]2bp3=a+bw+ab ꎨꎩQ3틔벰 *b[A+(1−S)I]bbp1=a+bw+a(1−S)Ib ꎨꎩQ1냑쪽ꎨꎩ뫍쪽ꎨꎩ럖뇰듺죫쪽3-11뫍쪽3-12뫳ꎬ폐 ***2[A+(1−S)I]Q113(I1)−1=−[A+(1−S)]+abbI1−(−S)>0 hwQ1Q3쯹틔 Q*** 3(I>Q 1) 횤뇏ꆣ 1헢뇭쏷ꎬ퓚릩펦짌룸폨쿺쫛얬솦늹쳹뫳ꎬ볙짨쿺쫛짌ퟔ짭뗄쿺쫛얬솦춶죫늿럖죔놣돖폫횮잰쎻폐늹쳹쪱뗄춶죫솿쪱ꎬ쿺쫛짌늻뷶헻쳥ퟮ폅욽뻹샻죳쫇퓶볓뗄ꎬ뛸쟒웤뚩릺솿튲폐퓶볓ꎬ뛸헢헽쫇릩펦짌쳡릩쿺쫛얬솦늹쳹뗄쟽뚯솦ꆣ 쪵샽럖컶 샽 퓚뗚뛾헂뗄쪵샽뗄믹뒡짏ꎬ볙뚨퓚릩펦짌룸쿺쫛짌퓶볓쿺쫛얬솦늹쳹틔뫳쯹쏦쇙뗄탨쟳몯쫽캪D(I,p)=a−bp+aIbꎬaꆢb>0,p>a/b,0<ß<1ꆣ쎿듎뚩릺믵컯쯹탨뗄만뚨럑폃캪A=150풪ꎬ릺싲떥캻닺욷뗄돉놾캪c=3풪ꎬ떥캻닺욷퓚떥캻쪱볤쓚욽뻹뿢듦돖폐돉놾햼쿺쫛짌떥캻릺싲돉놾뗄냙럖뇈캪h=ꎬa=1000, ß=,S=ꆣ쫔컊쿺쫛짌죧뫎훆뚨웤뚩릺닟싔틔벰쿺쫛볛룱ꎿ 뷢ꎺ샻폃Matlab볆쯣죭볾뿉뗃ퟮ폅쿺쫛얬솦춶죫*I=1490(풪)ꎬퟮ폅뚩릺엺솿Q*=5530ꎨ떥캻ꎩꎬ좻뫳퓙샻폃쪽(12)뗃돶ퟮ폅쿺쫛볛룱p*=(풪)ꎬ붫쯹뗃뗄Q*뫍p*듺죫쪽(11)뿉뗃쿺쫛짌뗄ퟮ폅욽뻹샻죳캪ATP*(p,Q)= 43399(풪)ꆣ 뇭 솽훖닟싔쿂뗄볆쯣뷡맻 쿺쫛짌얬솦 얬솦춶 쿺쫛볛 뚩릺솿 ퟮ폅욽뻹춶죫늹쳹S 죫 Iꎨ풪ꎩ pꎨ풪ꎩ Qꎨ떥캻ꎩ 샻죳ꎨ풪ꎩ 쎻폐퓶볓S 1040 5183 42770 퓶볓S 1490 5530 46042 ? ퟜ뷡 놾헂쳡돶쇋튻룶쿺쫛얬솦릲떣뗄뿢듦뿘훆쒣탍ꎬퟮ뫳횤쏷쿺쫛짌뗄ퟮ폅욽뻹샻죳퓶듳ꎬ튲횤쏷쇋쿺쫛짌폫릩펦짌뫏ퟷ뗄뇘튪탔ꆣ놾컄폫쯻퇐뺿뗄늻춬퓚폚ꎺ퓚탨쟳춬쪱틀삵쿺쫛얬솦뫍쿺쫛볛룱뗄잰쳡쿂ꎬ쿺쫛얬솦평릩펦짌뫍쿺쫛 21
짌릲떣뗄뿢듦뿘훆쒣탍ꎬ뛸틑폐뗄쒣탍퓚뾼싇릩펦짌뫍쿺쫛짌뫏ퟷ쪱ꎬ탨쟳튪쎴뷶폫쿺쫛볛룱쿠맘ꎬ튪쎴퓚늻좷뚨탨쟳쳵볾쿂ꎬ뾼싇쿺쫛얬솦릲떣ꆣ쇭췢듋컄늻뷶뷶쫊폃폚쿟탔탨쟳쳵볾ꎬ뛸쟒튲뿉틔쫊폃폚떯탔탨쟳쳵볾쿂뾼싇쿺쫛얬솦쮮욽릲떣뗄쒣탍ꆣ놾쒣탍뗄뷸튻늽삩햹뿉틔뾼싇ꎺ듸폐솿헛뿛뗄얬솦쮮욽릲떣쒣탍ꎬ뛠룶쿺쫛짌쒣탍뗈ꆣ ?????????????????????????????? 22
뗚쯄헂 듸폐엺솿헛뿛뗄릩펦솴쒣탍 ?퓚쪵볊뗄릩펦솴훐ꎬ평폚듳뛠쫽뗄릩펦솴훐뗄릩펦짌뫍쿺쫛짌쫴폚늻춬뗄웳튵ꎬ틲듋룷ퟔ뚼틔ퟔ짭샻틦캪ퟮ폅뾼싇컊쳢ꎬ헢쪹뗃룷돉풱볤뗄킭ퟷ컊쳢뇤뗃쿠떱삧쓑ꆣ평뗚죽헂뿉횪ꎬ쯤좻퓶볓쿺쫛얬솦늹쳹믡퓶볓쿺쫛짌뗄샻죳틔벰뚩릺솿ꎬ떫쫇쿺쫛짌죔틔ퟔ짭샻틦캪뾼싇ꎬ쎻폐뾼싇떽헻쳥뗄샻틦ꎬ틲듋쮫랽뚼폐샻죳퓶횵뿕볤ꎬ볌뛸듯늻떽엁샛췐ퟮ폅ꆣ쯦ퟅ좫쟲뺭볃튻쳥뮯뗄떽살ꎬ웳튵캪쇋퓶잿웤헻쳥뺺헹솦ꎬ룷훖돌뛈뗄릩펦솴펪퓋뛸짺ꎬ웤훐솿헛뿛쫇듙뷸릩펦솴킭뗷뗄듫쪩훐쪮럖폐킧뗄쫖뛎횮튻ꆣ 퓧웚뗄솿헛뿛퇐뺿훷튪쫇틔쿺쫛짌캪훐탄살햹뾪뗄ꎬ듺뇭탔뗄퇐뺿죧Hadley뫍Whitinꆣ쯦ퟅ룃쇬폲퇐뺿뗄죕쟷돉쫬틔벰풽살풽룹뻝쪵볊뗄짺닺뿢듦뮷뺳ꎬ퇐뺿헟훰붥틢쪶떽릩펦짌퓚뻶뚨헢퇹뗄솿헛뿛닟싔훐뗄훷떼ퟷ폃ꎬ늢뾪쪼틔릩펦짌캪뻶닟뗄훷떼뷇즫살퇐뺿엺솿헛뿛컊쳢ꆣ1994쓪ꎬParlar M뫍 Wang Q쳡돶쇋퓚쿟탔탨쟳쳵볾쿂ꎬ릩펦짌폫쿺쫛짌횮볤뗄솿헛뿛쒣탍ꆣ2002쓪ꎬKlastorin T D뗈쳡돶쇋볛룱헛뿛퓚릩펦솴훐뗄킭뗷퓋ퟷꆣ헢킩듳듳럡뢻쇋폃엺솿헛뿛쫖뛎뷸탐릩펦솴킭뗷뗄샭싛퇐뺿ꆣ 떫쫇퓚짏쫶틑폐뗄릩펦솴킭뗷퓋ퟷ뗄퇐뺿훐ꎬ늻맜탨쟳쫇좷뚨뗄뮹쫇쯦믺뗄뚼볙짨탨쟳폫쿺쫛얬솦컞맘ꆣ뛸퓚뿆벼톸쯙랢햹뫍뺺헹죕틦벤쇒뗄뷱쳬ꎬ닺욷룼탂뮻듺뗄훜웚풽살풽뛌ꎬ틲뛸죧뫎퓚닺욷틑뷸죫럖쿺쟾뗀뻍톸쯙쓜놻듳볒뷓쫜릺싲쫇웳튵뾼싇뗄훘뗣ꆣ틲듋맣룦춶죫ꎬ죋솦춶죫뗈쿺쫛얬솦뫍탨쟳쿠맘훰붥놻웳튵훘쫓ꆣ 놾컄퓚떥튻컯욷탨쟳쫜쿺쫛볛룱뫍쿺쫛얬솦뗄펰쿬쿂ꎬ퇐뺿떥룶릩펦짌뫍떥룶쿺쫛짌ퟩ돉뗄볲떥솽닣릩펦솴킭뗷컊쳢ꆣ퓚룃릩펦솴훐ꎬ컒쏇퇐뺿뗄훷튪컊쳢쫇죧뫎짨뚨솿헛뿛볆뮮살벤샸쿺쫛짌살쪵탐듋닟싔ꎬ볓듳뚩릺솿ꎬ듓뛸쳡룟헻룶릩펦솴틔벰ퟔ짭뗄샻죳ꆣ놾컊쳢훷튪뗄쓑뗣쫇퓚훮뛠뇤솿훐죧뫎뷸탐뚯첬늩?닟싔ꎬ퓚늻룸뛔랽듸살샻죳쯰쪧뗄잰쳡쿂퓶볓ퟔ짭뗄샻죳ꆣ?? 볇뫅폫볙뚨 놾뷚퓚짏튻뷚쒣탍퓶볓뗄믹뒡짏ꎬ퓶볓틔쿂볇뫅ꎺ (1)?rꎬ?mꎬ?cꎬ럖뇰뇭쪾쿺쫛짌ꎬ릩펦짌뫍튻쳥뮯쪱뗄욽뻹ퟜ샻죳몯쫽ꎻ (2)A뇭쪾릩펦짌뗄만뚨짺닺ힼ놸럑폃ꎻhr뇭쪾뇭쪾쿺쫛짌떥캻쪱볤떥캻컯욷뗄뿢듦럑폃ꎻ (3)Q뇭쪾쿺쫛짌쎿룶뚩믵훜웚뗄뚩믵솿ꎻ (4)c뇭쪾릩펦짌뗄짺닺떥캻닺욷뗄돉놾ꎻw뇭쪾릩펦짌뗄룸폨쿺쫛뗄떥캻컯욷뗄엺랢볛룱ꎬp뇭쪾떥캻컯욷뗄쇣쫛볛룱ꎬ쟒볙짨죽헟횮볤뗄듳킡맘쾵캪c<w<pꎻ 23
듋췢ꎬ컒쏇볙뚨ꎺ (1)쾵춳늻퓊탭좱믵랢짺ꆣ (2)볙뚨쿺쫛짌뗄뚩릺럑폃캪쇣ꆣ퓚벤쇒뗄쫐뎡뺺헹훐ꎬ쿺쫛짌퓚쿲듳훐탍웳튵뚩릺컯욷쪱ꎬ횻탨춨맽쿖듺뗧ퟓ췸싧쾵춳랢돶뚩떥틔벰좷뚨웤뚩릺뗄쫽솿뫍맦룱ꎬ뛸쿺쫛짌뗄퓋믵럑평릩펦짌춳튻뢺퓰ꆣ틲듋ꎬ쿺쫛짌뗄뚩릺럑폃럇뎣킡ꎬ뿉틔뫶싔늻볆ꎨ벴뫶싔짏튻뷚훐뗄볇뫅Aꎩꆣ (3)뾼싇릩펦짌캪룃릩펦솴뗄뫋탄ꎬ늢쟒볙뚨릩펦짌횪뗀쫐뎡탨쟳탅쾢틔벰쿺쫛짌뗄룷쿮돉놾벰럑폃ꆣ 쒣탍뗄붨솢 컊쳢뗄쳡돶 평폚퓚룃릩펦솴쒣탍훐ꎬ쿺쫛짌뫍릩펦짌횮볤쫇뚯첬늩?ꎬ쎿튻랽뚼듦퓚폐샻폚ퟔ벺뗄뻶닟뇤솿ꎬ틲듋ꎬ놾헂쳖싛뗄컊쳢쫇ꎬ죧뫎뷸탐뚯첬늩?ꎬ쪹릩펦솴쮫랽뗄욽뻹샻죳뻹폐쯹퓶볓ꎬ믲헟퓚ퟮ듳뮯ퟔ짭샻틦뗄춬쪱ꎬ훁짙늻쯰몦쇭튻랽뗄샻틦ꎿ 붨솢쒿뇪몯쫽 퓚틔짏뗄볇뫅뫍볙뚨믹뒡짏ꎬ뗃돶릩펦짌뫍쿺쫛짌죴퓚릩펦솴튻쳥뮯쟩뿶쿂ꎬ퓲웤샻죳몯쫽평쿂쪽룸돶 ∏(AIc)D=−cD+−cQ−chwc(pc)c Qc2룹뻝뗚튻헂뗄ퟮ폅탔럖컶ꎬ평튻뷗ퟮ폅탔쳵볾ꎬp*ꆢ*I뫍Q*럖뇰평쿂쏦죽룶뗈ccc쪽룸돶ꎺ *(A+I−c)D pccc= ꎨꎩ Qcb (A+Ic)Dp−c=cc ꎨꎩ Q'cQcDIc Q*22(A+Ic)D=cc ꎨꎩ hc 춬쪱컒쏇룸돶쿺쫛짌틔ퟔ짭샻틦캪훐탄뗄샻죳몯쫽ꎺ ∏(1−S)IDrrQhw=(p−w)D−r rrrQ2r 24
(1−S)I=rQhwp−wD−r ꎨꎩrQ2r평튻뷗ퟮ폅탔쳵볾ꎬp*ꆢ*I뫍Q*럖뇰평쿂쏦솽룶뗈쪽룸돶ꎺ rrr*(1−S)IrDp−w−=r ꎨꎩ rQbr1−S*()I(1−S)Dp−w−r= ꎨꎩ rQQD'rrIrQ*22(1−S)ID=rr ꎨꎩ?rhw ퟮ폅뷢럖컶 쏼쳢1 퓚릩펦짌쳡릩쿺쫛얬솦늹쳹S뫳ꎬ볙짨틑뺭듙쪹릩펦짌춶죫**I=Irc떥캻ꎬ퓲룷ퟔ뛀솢뻶닟쪱쿺쫛짌뗄ퟮ폅뚩릺솿Q*뗗폚릩펦솴튻쳥뮯쪱뗄ퟮ폅뚩r릺솿Q*cꎬ쟒뛾헟뗄맘쾵캪 Q*=(1−SQ* r)c횤 평쪽ꎨꎩ뫍쪽ꎨꎩ뗃?b=QD'cI ꎨꎩ c평쪽ꎨꎩ뫍쪽ꎨꎩ뗃?(1−S)b=QD' ꎨꎩ?rIr 냑쪽ꎨꎩ듺죫쪽ꎨꎩ뫳폐?†††?††?†?1−SQD'=QD'()c IcrIr룹뻝볙짨폐**I=I듺죫짏쪽뗃 rcꎬ맊폐D'=D'ꎬIcIr Q*=(1−SQ* r)c평폚쿺쫛늹쳹S뗃좡횵랶캧캪0<S<1ꎬ맊폐Q*<Q*rcꎬ폚쫇쏼쳢돉솢ꆣ 쏼쳢2 룷ퟔ뛀솢뻶닟쪱쿺쫛짌뗄ퟮ폅뚨볛p*룟폚릩펦솴튻쳥뮯쪱뗄ퟮ폅r뚨볛p*cꎬ쟒뛾헟뗄맘쾵캪 **w−cA p−p=− rc22Qc 25
횤 평쪽ꎨꎩ틔벰탨쟳몯쫽Dꎬ뿉틔쟳돶퓚릩펦솴튻쳥뮯쳥훆쿂쿺쫛짌뗄ퟮ폅뚩릺솿p*c뗄뇭듯쪽캪 (A+I) 2bp*b=a+bc+cc+aIb†?†††?????ꎨꎩ Qc샠쯆뗘ꎬ평쪽ꎨꎩ틔벰탨쟳몯쫽Dꎬ뿉틔쟳돶퓚럖즢뻶닟쪱쿺쫛짌뗄ퟮ폅뚩릺솿p*c뗄뇭듯쪽캪 *b(1−S)I2bp=a+bw+r+aIb†††††††ꎨꎩ rQr퓚*=*II잰쳡쿂ꎬrc쪽ꎨꎩ폫쪽ꎨꎩퟷ닮뗃?†††**(1−S)IA+I2bp−2bp=bw−c+brcr()−?QQrcAb=b(w−c)− Qc벴††††††††††**w−cAp−p=−†††††††?rc횤뇏ꆣ?22Qc? 붨솢킭뗷웵풼 퓚좷뚨쇋샻죳몯쫽뫳ꎬ웵풼뗄훷튪뻶닟컊쳢뇤캪틔쿂솽룶ꎺ튻룶쫇릩펦짌쓜럱벤샸쿺쫛짌틔*Ic캪ퟮ폅쿺쫛춶죫ꎬ벴퓵퇹짨뚨쿺쫛얬솦뗄늹쳹싊Sꎻ쇭튻룶쫇릩펦짌죧뫎훆뚨엺랢볛w틔벰쿺쫛웵풼ꎬ닅쓜쪹뗃쿺쫛짌풸틢틔Q*c캪ퟮ폅뚩릺솿뚩믵ꆣ 평폚퓚릩펦솴튻쳥뮯쳵볾쿂죧맻**I=Ircꎬ퓲쓜쪹헻룶쿺쫛얬솦듯떽튻쳥뮯샻죳ퟮ듳뮯ꆣ평쪽ꎨꎩ뫍쪽ꎨꎩ뗃 b2hc=2(A+Ic)Dc D'2Ic(1−S)b2hw =2ID Drr'2Ir퓚짏쪽훐ꎬ횻튪좡cIDS=1−crꎬ퓲폐**I=I(A+Ic)wDrcꆣ c평짏쫶럖컶뿉횪ꎬ죧맻쿺쫛짌틔ퟔ벺샻틦캪훐탄ꎬ퓲횻믡뚩릺Q*떥캻ꎬ쯼r쏷쿔킡폚튻쳥뮯퓋ퟷ쪱뗄뚩릺솿Q*cꆣ틲듋릩펦짌튪쿫쳡룟릩펦솴헻쳥샻죳틔벰ퟔ벺놾짭뗄샻죳ꎬ퓲뇘탫짨램폕쪹쿺쫛짌뚩릺룼뛠뗄짌욷ꆣ튻훖뿉탐뗄랽램뻍쫇릩펦짌쿲릩펦짌쳡릩솿헛뿛ꎬ죧맻뷶듓ퟔ짭샻틦돶랢ꎬ릩펦짌뿉쓜믡짨훃튻훖솿헛뿛볆뮮쪹ퟔ벺뗄샻죳ퟮ듳뮯ꎬ춬쪱튲췹췹쪹쿺쫛짌뗄샻죳쫜떽짋몦ꎬ듓뛸쪹볆뮮늻쓜싄탐ꆣ틲듋릩펦짌뇘탫퓚놣횤쿺쫛짌뗄샻틦늻쫜쯰몦뗄잰쳡쿂쳡 26
릩솿헛뿛볆뮮ꆣ볙뚨릩펦짌쿲쿺쫛짌쳡릩쿂쇐솿헛뿛볆뮮ꎺ (ꊡ)죧맻쿺쫛짌뗄ퟜ뚩릺솿Q캪Q*쪱ꎬ퓲쳡릩헽뎣엺랢볛w*ꎻ r(ꊢ)죧맻쿺쫛짌뗄ퟜ뚩릺솿Q늻킡폚Q*쪱ꎬ퓲캪뎬돶Q*늿럖쳡릩헛뿛엺랢rr볛rw*ꆣ 쿔좻듋볙짨늻믡쯰몦쿺쫛짌뗄샻죳ꎬ늢쟒죧맻쿺쫛짌샖틢뷓쫜듋볆뮮ꎬ뇘탫놣횤웤샻죳퓶볓ꆣ죧맻룃헛뿛볆뮮뮹쓜쪹릩펦짌틔벰릩펦솴훐뗄헻쳥샻죳쳡룟ꎬ쓇쎴쯼붫쫇뿉탐뗄ꆣ쿂쏦룸돶솿헛뿛볆뮮뗄짨볆맽돌ꆣ 떱Q싺ퟣQ*≤Q쪱ꎬ퓚듋헛뿛볆뮮쿂ꎬ쿺쫛짌뗄욽뻹샻죳몯쫽캪ꎺ?rQ*w+Q−Q*()rw+(1−S***IQw+Q−Qrw∏drr)r(r)=p−Dh††?ꎨꎩ?rQ2뛸릩펦짌뗄욽뻹샻죳몯쫽캪ꎺ?Q*w+(Q−Q**)rw−SI−A∏drrm=cD†††††††?††?†?ꎨꎩ?Q뛔폚쯹튪쟳뗄0<r<1ꎬ뷸튻늽룸돶맘폚ퟮ폅솿헛뿛볆뮮뗄폐맘뚨샭ꆣ ?뚨샭1?떱0<r<1쪱ꎬ쪽ꎨꎩ훐뗄ퟮ폅뚩릺솿Q*튻뚨폐ꎬ∏dQ*>∏Qꆣ?r()r()횤?쇮몯쫽(1−S)IQrwhf(r,Q)=p−rwD−††††?†††?ꎨꎩ?Q2떱0<r<1쪱ꎬ폐rw<wꎬ맊떱Q=QꎬI=I쪱뿉뗃 rr(1−S)IQrwhf(r,Q)=p−rwD− Q2(1−S)IQwh>p−wDrrQ−=∏ ꎨꎩ r2rr죧맻폃*f(r,Q)뇭쪾f(r,Q)뗄ퟮ폅뷢ꎬ퓲폐 *(1−S)IQrwhf(r,Q)≥f(r,Q)=p−rwD−>∏ Q2r평쪽ꎨꎩ횪ꎬ퓚쪵탐룃솿헛Q*뿛볆뮮뫳ꎬ엺랢볛뇤w+(Q−Q**rwrr)ꎬQ쟒폐 Q*w+Q−Q**Q*w+Q−Q*w*()rwrrr(r)<=w* 맊떱0<r<1쪱ꎬ∏d(Q*)≥∏d(Q)>∏(Qꆣ††?횤뇏ꆣ?rrr) 27
뚨샭2??떱0<r<1쪱ꎬ몯쫽f(r,Q)뗄ퟮ폅뷢Q*듳폚Q*ꆣ?r횤?쟳몯쫽f(r,Q)맘폚Q튻뷗떼쫽ꎬ뿉뗃 ∂f(r,Q)(1−S)I=Drwh−=0?∂QQ22쇮Q*캪짏쪽뗃뷢ꎬ뿉뗃 2*(1−S)IDQ= ꎨꎩ?hrw퓙뛔∂∂2f(r,Q)맘폚Q쟳웤튻뷗떼쫽뗃f(r,Q)(1−S)I=D<0ꎬ맊Q*캪쪹∂Q∂2Q3뗃f(r,Q)듯떽ퟮ듳횵뗄ퟮ폅뷢ꆣ 룹뻝쪽ꎨꎩ뫍쪽ꎨꎩ틔벰잰쏦쟳뷢맽돌ꎬ뿉뗃쪽ꎨꎩ맘폚ퟮ폅탨쟳몯쫽 (1)2Db−SI=a−bw−r+aIbrQr ꎨꎩ 샠쯆뗘ꎬ몯쫽f(r,Q)뗄ퟮ폅탨쟳몯쫽D캪 (1)2Dab−SI=−brw−+ab ꎨꎩ Q힢틢떽떱웤쯻쳵볾늻뇤쪱ꎬ엺랢볛룱붵뗍쪱ꎬ탨쟳몯쫽퓶듳ꆣ맊뇈뷏쪽ꎨꎩ뫍쪽ꎨꎩ폐D>Dꎬ뷡뫏쪽ꎨꎩ폐 r2(1−S)ID2(1−S)IDQ*=>rr=Q* 횤뇏ꆣ?rhrwhw뚨샭1쮵쏷ퟷ캪릩펦짌튻랽붵뗍엺랢볛룱w쪱ꎬ쿺쫛짌뗄욽뻹샻죳퓶듳ꆣ뚨샭2쮵쏷떱붵뗍엺랢볛룱쪱ꎬ뚩릺솿튲폐쯹퓶듳ꎬ릩펦짌뗄샻죳튲쯦횮퓶듳ꆣ 뚨샭1뫍2릲춬놣횤쇋룃솿헛뿛볆뮮뗄뿉탐탔ꆣ퓚룃뫏ퟷ늩?맽돌훐ꎬ릩펦짌ퟷ캪캪룃릩펦솴뗄뻶닟훷쳥ꎬ릩펦짌탨튪횪뗀쫐뎡탨쟳탅쾢틔벰쿺쫛짌뗄짺닺뺭펪ꆢ뿢듦탅쾢뗈룷쿮돉놾ꆣ쿂쏦폃룸돶헻룶릩펦솴뗄뻶닟맽돌ꎺ Step1ꎺ릩펦짌쿈룹뻝쫐뎡탅쾢틔벰튻쳥뮯샻죳몯쫽쟳돶ퟮ폅쿺쫛얬솦춶죫Iꎬ틔벰쿺쫛늹쳹Sꎻ Step2ꎺ쿺쫛짌룹뻝I뫍S틔벰ퟔ짭뗄룷쿮돉놾ꎬ뗃돶맘폚솿헛뿛볆뮮r뗄ퟮ폅쿺쫛볛룱몯쫽뫍ퟮ폅뚩릺솿몯쫽ꎻ Step3ꎺ릩펦짌룹뻝쿺쫛짌쳡릩뗄ퟮ폅뚩릺솿몯쫽ꎬ쟳돶ퟔ벺ퟮ폅솿헛뿛볆 28
뮮rꆣ Step4ꎺ릩펦짌뫍쿺쫛짌룹뻝틑뺭쟳돶뗄r쟳돶ퟮ폅뚩릺솿Qꎬ랢돶뚩믵ꆣ 릩펦 솴튻쳥ퟮ폅늹 ퟮ폅춶죫 릩ퟮ폅솿헛 쿺 펦ퟮ폅뚩 릺솿쫛 춼 쿺쫛짌폫릩펦짌볤뚯첬킭뗷늩? 쪵샽럖컶 샽 볙뚨퓚릩펦짌룸쿺쫛짌퓶볓쿺쫛얬솦늹쳹틔뫳쯹쏦쇙뗄탨쟳몯쫽캪 D(I,p)=a−bp+abI,,b>0,p>a/b,0<<1ꎬ 쿺쫛짌릺싲떥캻닺욷뗄엺랢볛캪w=3풪ꎬ떥캻닺욷퓚떥캻쪱볤쓚욽뻹뿢듦돖폐돉놾햼쿺쫛짌떥캻릺싲돉놾뗄냙럖뇈캪h=ꎬa=1000ꎬß=ꆣ릩펦짌짺닺쎿떥캻닺욷뗄돉놾c=풪ꎬ쎿듎짺닺뗄만뚨짺닺돉놾캪200풪ꆣ쫔컊퓚릩펦짌쳡릩퓶볓솿헛뿛캪r=뗄잰쳡쿂ꎬ쿺쫛짌죧뫎훆뚨뚩믵닟싔ꎿ 뷢 평튻쳥뮯ퟮ폅탔쳵볾뿉뗃I=1453ꎬS= .웤쯻뷡맻죧뇭4-1쯹쪾ꎺ 떱릩펦짌훆뚨쫊떱뗄솿헛뿛뻶닟쪱ꎬ릩펦짌뫍쿺쫛짌뗄욽뻹ퟮ폅샻죳뻹폐쯹퓶듳ꎺ뛔폚릩펦짌살쮵ꎬ쫊떱붵뗍엺랢볛룱ꎬ늿럖죃샻폚쿺쫛짌뫳ꎬ쿺쫛짌튲쯦횮믡붵뗍쿺쫛볛룱ꎬ늿럖죃샻폚맋뿍ꎬ헢뛔폚맣듳맋뿍살쮵믡퓶듳웤릺싲폻췻ꎬ틲듋릺싲솦(벴탨쟳)튲믡쯦횮퓶듳ꎬ볌뛸쿺쫛솿믡퓶볓ꎬ뚩릺솿튲믡퓶볓ꎬ춬쪱릩펦짌튲퓶볓쇋ퟔ짭뗄샻죳ꎬ벴듯떽쇋쯹캽뗄“벴퓶솿폖퓶쫕”킧맻ꆣ 29
뇭 평Matlab죭볾퓚솽훖닟싔쿂뗄볆쯣뷡맻 쿺쫛짌 훆퓬짌 럖즢뻶닟 킭뗷뻶닟 럖즢뻶닟 킭뗷뻶닟 얬솦춶죫Iꎨ풪ꎩ 678 678 775 775 쿺쫛볛pꎨ풪ꎩ —— —— 엺랢볛wꎨ풪ꎩ 3 3 3 3 퓶솿헛뿛rꎨ떥캻ꎩ 1 1 뚩릺솿Qꎨ떥캻ꎩ 3616 4908 3616 4908 ퟮ폅욽뻹샻죳ꎨ풪ꎩ 44863 46042 17245 34749 ? 킡뷡 놾컄룸돶쇋튻훖퓚떥쿺쫛짌뫍떥릩펦짌ퟩ돉뗄릩펦솴쳵볾쿂ꎬ죧뫎킭뗷쿺쫛얬솦춶죫뇈샽벰훆뚨볛룱헛뿛뗄뻶닟랽램ꆣ쿠뛔폚틔잰뒫춳뗄솿헛뿛쒣탍뷸튻늽퓶볓쇋쿺쫛얬솦춶죫킭뗷헢튻뻶닟뇤솿ꎬ룼캪뷓뷼쪵볊ꆣ쇭췢퓶볓솿헛뿛볆뮮놣횤쇋릩펦짌뫍쿺쫛짌뗄욽뻹ퟜ샻죳늻쫜쯰쪧ꆣ놾컄뷸튻늽뗄퇐뺿랽쿲쫇떥릩펦짌뫍뛠쿺쫛짌뗄쿺쫛얬솦릲떣뻶닟쒣탍ꆣ ????????????????? 30
뗚컥헂 ퟜ뷡폫햹췻 쫐뎡뺭볃좫쟲튻쳥뮯뿍맛짏쪹뗃웳튵잿잿솪뫏ꎬ퓚헻쳥샻틦폅쫆쿂퓶잿쇋웤뺺헹쪵솦ꆣ뛸쎿룶웳튵룶쳥뗄훕벫쒿뇪쫇돤럖샻폃룷훖풴ꎬ틔ퟮ킡뗄춶죫살믱뗃ퟮ듳뗄쫕틦ꆣ틲듋훆뚨튻룶쓜릻쪹릩펦솴훐룷돉풱볤쿠뮥훆풼뗄뻶닟쒣탍쫇폈캪뇘튪뗄ꆣ뛸퓚탨쟳틀삵쿺쫛볛룱뗄잰쳡쿂ꎬ춬쪱쪵쪩솿헛뿛볆뮮쫇쿺쫛짌뫍릩펦짌볤뗄쿺쫛웵풼쿠뮥훆풼뗄폐킧뻶닟쒣탍횮튻ꆣ 1984쓪ꎬMonahanퟮ퓧퇐뺿쇋솿헛뿛컊쳢ꆣ쯦뫳뛾쪮뛠쓪살ꎬ훚뛠퇐뺿헟듓늻춬뷇뛈붫솿헛뿛쒣탍뷸탐쇋췘햹ꎬ듳듳럡뢻쇋릩펦솴훐퓋폃솿헛뿛볆뮮쿠맘뻶닟샭싛퇐뺿ꆣ 솿헛뿛쫇믹놾뗄뚨볛닟싔ꆣ뒫춳뗄솿헛뿛뻶닟쒣탍듳뚼횻뾼싇뚩릺솿뫍ퟜ뗄ퟮ폅욽뻹샻죳솽룶뻶닟뇤솿뛔쫐뎡틔벰뛔릩펦짌뗄펰쿬ꆣ뛸쪵볊뗄쫐뎡펪쿺훐ꎬ쳘뇰쫇탅쾢뮯뗄떱뷱ꎬ퓋폃뿆벼쫖뛎뷸탐쿺쫛얬솦춶죫믡듳듳펰쿬닺욷쿺쫛ꆣ틲듋ꎬ냑쿺쫛얬솦뾼싇떽탨쟳틲쯘훐틑돉캪뇘좻ꆣ 쿂쏦ꎬ붫뛔놾컄쯹ퟷ뗄릤ퟷ볓틔ퟜ뷡ꎬ늢뛔뫳탸릤ퟷ뗄퇐뺿랽쿲쳡돶햹췻ꆣ?? 릤ퟷퟜ뷡 놾컄퓚탨쟳틀삵볛룱뗄믹뒡짏뷸튻늽퇐뺿쇋탨쟳춬쪱틀삵쿺쫛얬솦뫍쿺쫛볛룱뗄뻶닟쒣탍ꆢ믹폚쿺쫛얬솦늹쳹뗄쒣탍틔벰탨쟳틀삵쿺쫛얬솦퓚솿헛뿛볆뮮쒣탍훐뗄펦폃ꆣ훷튪돉맻폐틔쿂벸뗣ꎺ?(1)쿪쾸쳖싛쇋탨쟳틀삵쿺쫛얬솦뫍쿺쫛볛룱뗄ퟮ폅뚩릺엺솿솪뫏뻶닟쒣탍 퓚룃쒣탍훐ꎬ뗃돶쿺쫛볛룱ꆢ쿺쫛얬솦춶죫ꆢ뚩릺솿죽룶뻶닟뇤솿횮볤뗄풼쫸몯쫽맘쾵쪽ꎬ늢뗃돶쟳ퟮ폅욽뻹ퟜ샻죳뗄튻훖쯣램ꆣ쯹폐좷뚨탔탨쟳틀삵쿺쫛얬솦뗄뻶닟쒣탍뻹뿉펦폃듋쒣탍랽램ꆣ (2)붨솢쇋쿺쫛얬솦춶죫늹쳹쒣탍 샻폃쿺쫛얬솦릲떣듫쪩듙쪹릩펦짌폫쿺쫛짌횮볤뗄뫏ퟷ늩?ꆣ뒫춳뗄쒣탍틔쿺쫛짌캪뻶닟뫋탄ꎬ쎻폐뾼싇릩펦짌뗄뫏ퟷꆣ룃쒣탍퓚뾼싇쿺쫛짌퓚춨맽쿺쫛얬솦릲떣폫릩펦짌뫏ퟷ뫳퓚퓶볓쇋ퟮ폅욽뻹샻죳뗄춬쪱ꎬퟮ폅쿺쫛볛룱튲폐쯹붵뗍ꎬ룼듳돌뛈뗘싺ퟣ맛훚ꎬ뷸튻늽퓶잿쇋웤쫐뎡뺺헹솦ꆣ (3)퇐쳖쇋탨쟳틀삵쿺쫛볛룱뫍쿺쫛얬솦춶죫퓚듸폐엺솿헛뿛릩펦솴ퟮ폅킭뗷뻶닟쒣탍훐뗄펦폃?퓚뒫춳뗄솿헛뿛쒣탍믹뒡짏ꎬ퓶볓쇋쿺쫛얬솦춶죫틔벰쿺쫛얬솦늹쳹ꎬ틔쿺쫛얬솦늹쳹뫍솿헛뿛솽룶뻶닟뇤솿퓚쮫랽횮볤뗄뫏ퟷ늩?ꎬ붨솢쇋튻훖뚯첬늩?뗄럖컶랽램ꎬ쪹헻룶릩펦솴듯떽ꆰ쮫펮ꆱꆣ? 릤ퟷ햹췻 놾컄퇐뺿쇋탨쟳폫틀삵쿺쫛얬솦뫍쿺쫛볛룱쿠맘뗄뻶닟쒣탍ꆢ믹폚쿺쫛얬 31
솦늹쳹뗄쒣탍틔벰쿺쫛얬솦릲떣폫솿헛뿛볆뮮솪뫏퓚릩펦솴쒣탍훐뗄펦폃ꆣ ퟷ캪뷸튻늽뗄릤ퟷꎬퟷ헟죏캪펦룃듓틔쿂벸룶랽쿲뷸탐룼짮죫뗄퇐뺿뫍룄짆ꎺ (1)뾼싇탨쟳틀삵쿺쫛볛룱뗄잰쳡쿂ꎬ떥쿺쫛짌뫍뛠쿺쫛짌뗄릩펦솴킭뗷쒣탍ꆣ퓚쪵볊뗄짺닺쫐뎡뮷뺳훐ꎬ튻룶릩펦짌횻헫뛔튻볒쿺쫛짌쿔좻쫇늻쪵볊뗄ꆣퟷ캪릩펦짌랽쏦살붲ꎬ캨폐볓듳쿺쫛짌뗄뚩릺솿닅쓜퓶볓웤샻죳ꆣ뛸뒫춳뗄쿺쫛얬솦춶죫릲떣쒣탍훐ꎬ횻뾼싇떥릩펦짌뫍떥쿺쫛짌뗄볲떥릩펦솴쒣탍ꆣ쯹틔ꎬ떥쿺쫛짌뫍뛠쿺쫛짌뗄릩펦솴킭뗷쒣탍룼뷓뷼짺닺쿺쫛쪵볊ꆣ (2)뾼싇듸폐쿺쫛얬솦춶죫늹쳹폫엺랢볛룱춬캪뻶닟뇤솿뗄뻶닟쒣탍ꆣ퓚룸릩펦짌쳡릩쿺쫛얬솦춶죫늹쳹쪱ꎬ릩펦짌ퟔ좻믡헹좡ퟔ벺샻틦ꎬ틲듋냑엺랢볛룱ퟷ캪릩펦짌뗄뻶닟뇤솿ꎬ쫇튻훖폐킧킭뗷쮫랽샻틦뗄튻훖듫쪩ꆣ (3)믹폚릩펦짌맜샭뿢듦쒣탍ꆣ릩펦짌맜샭뿢듦(Vendor managed inventoryꎬ볲돆VMI)ꎬ벴뛔릩펦짌뗈짏폎웳튵믹폚웤쿂폎뿍뮧뗄짺닺뺭펪ꆢ뿢듦탅쾢ꎬ뛔쿂폎뿍뮧뗄뿢듦뷸탐맜샭폫뿘훆ꆣVMI쫇릩펦솴맜샭폅뮯뗄튻훖랽램ꎬ퓚뒫춳뗄뿢듦맜샭쒣쪽훐ꎬ틔쮫랽뚼믱뗃ퟮ뗍돉놾캪쒿뇪ꎬ퓚튻룶릲춬뗄뿲볜킭틩쿂냑폃뮧뗄뿢듦뻶닟좨듺샭룸릩펦짌ꎬ평릩펦짌듺샭럖쿺짌믲엺랢짌탐쪹뿢듦뻶닟뗄좨솦ꎬퟮ뫳퓙뷡뫏벴쪱뿢듦쟩뿶ꎬ룸폨뿆톧ꆢ뫏샭뗄릩믵ꎬ웤뷡맻쫇쮫랽뚼믱뗃쇋킧틦ퟮ듳뮯ꎬ뗃떽쇋쮫펮ꆣ뛸퓚쿺쫛얬솦릲떣뗄잰쳡쿂쪵탐룃쒣탍뻶닟펦룃쫇쒿잰쫐뎡튻훖쟷쫆ꎬ튲쫇뷱뫳퇐뺿뗄랽쿲ꆣ 32
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?뢽 슼 ?쯣램1 늽훨1ꎺ쫤죫닎쫽횵ꎬ늢쇮k=0뫍Q0=∞ꆣ 늽훨2ꎺ샻폃쪽(3)뗃돶*kI(Q)=∞ꆣ 늽훨3ꎺ샻폃쪽(5)뗃돶p*k(Q)=∞ꆣ *늽훨4ꎺ볆쯣Qk+12ADpQk(())= hc늽훨5ꎺ죧맻Qk+1−Qk<e춣횹ꎻ럱퓲ꎬ쇮k=k+1ꎬ죫늽훨2ꆣ 퓲싺ퟣ짏쫶쯣램뗄Q*2b벴캪쪹뗃ATP(p,Q)듯떽ퟮ듳횵뗄ퟮ폅뷢ꆣ 벴횤쏷Q*1b캪ퟮ폅볛룱ꎬ뛸뛔펦뗄p*뫍*Iꎬ듺죫ATP(p,I,Q)뗃떽쿠펦뗄횵짨캪ATP*(p,I,Q)ꆣ 쯣램2 늽훨1ꎺ쫤죫닎쫽횵ꎬ늢쇮k=0뫍Q0=∞ꆣ 늽훨2ꎺ샻폃쪽(14)뗃돶p*k(Q)=∞ꆣ *늽훨3ꎺ볆쯣Q+12ADpQkk(())= hc늽훨4ꎺ죧맻Qk+1−Qk<e춣횹ꎻ럱퓲ꎬ쇮k=k+1ꎬ죫늽훨2ꆣ 퓲싺ퟣ짏쫶쯣램뗄Q*2b벴캪쪹뗃ATP(p,Q)듯떽ퟮ듳횵뗄ퟮ폅뷢ꆣ?? 38
훂 킻 퇐뺿짺짺믮벴붫뷡쫸ꎬ퓚듋싛컄췪돉횮볊ꎬ쿲컒뗄떼쪦퇮횾쇖뷌쫚훂틔돧룟뗄뺴틢뫍훔탄뗄룐킻ꎡ듓싛컄뗄톡쳢ꎬ쳡룙뗄좷뚨틔떽헻룶뚨룥맽돌ꎬ퇮샏쪦룸폨쇋컒듳솦뗄횧돖뫍벰쪱뗄횸떼ꆣ솽쓪뛠살ꎬ늻싛쫇퓚짺믮훐뮹쫇퓚톧쾰짏ꎬ퇮샏쪦뚼룸컒컞캢늻훁뗄맘뮳뫍횸떼ꆣ퇮샏쪦퇏뷷뗄훎톧첬뛈ꆢ뺫틦쟳뺫뗄릤ퟷퟷ럧ꎬ룸컒쇴쿂쇋짮뿌뗄펡쿳ꎬ늢붫뛔컒뷱뫳뗄죋짺닺짺훘튪뗄펰쿬ꆣ퓚듋ꎬ뷷쿲퇮샏쪦훂틔ퟮ짮뗄룐킻뫍돧룟뗄뺴틢ꎡ 퓚퇐뺿짺웚볤ꎬ컒톧쾰쇋퇮횾쇖뷌쫚ꆢ쇨쓜쿩뷌쫚ꆢ붹쿍랢뷌쫚ꆢ샮춮샏쪦ꆢ쳯폱쏴샏쪦쯹뷌쫚뗄ꆶ뿢듦뿘훆샭싛폫랽램ꆷꆢꆶ닎쫽춳볆ꆷꆢꆶ쫽톧쒣탍랽램ꆷꆢꆶ늩?싛ꆷꆢꆶ쒣뫽쫽톧ꆷ뗄룶튵뿎돌ꎬ헢킩뿎돌캪컒뗄퇐뺿릤ퟷ뫍놾싛컄듲쿂쇋볡쪵뗄샭싛믹뒡ꆣ퓚듋뛔쯻쏇탁쟚뗄릤ퟷ뇭쪾헦돏뗄킻틢ꆣ 룐킻췵쪥뚫샏쪦뫍뷜샏쪦ꎬ쯻쏇뗄죈쟩냯훺틔벰퇏뷷뗄톧쫵럧룱튲죃컒룐떽쇋폑틪뗄컂얯뫍톧쫵뗄쳡짽ꆣ룐킻뫍컒뎯쾦쿠뒦뗄룷캻춬톧ꆪꆪ췵몣랼ꎬ맰뫩짺ꎬ승좪폽ꎬ쓟폑좨ꎬ뫺뫪캰뗈ꎬ쯻쏇퓚컒뗄톧쾰뫍짺믮짏룸쇋컒탭뛠맘탄뫍냯훺ꎬ폫쯻쏇뗄쳖싛쪹컒뗃떽쇋뫜듳뗄뷸늽폫쳡룟ꆣ 춬쪱튲룐킻쯹폐뷌떼맽컒뗄샏쪦뫍퓚짺믮짏룸폨컒횧돖뫍냯훺뗄춬톧쏇ꆣ ퟮ뫳ꎬ컒튪훔탄룐킻컒뗄볒죋ꎬ쫇쯻쏇룸폨쇋컒톧쾰뗄놣헏ꎬ캪컒췪돉톧튵쳡릩쇋컯훊폫뺫짱짏뗄횧돖뫍맄샸ꎻ룐킻냙쎦횮훐움퓄놾싛컄뗄볒ꎻ룐킻쯹폐룸폨컒횧돖뫍냯훺뗄죋ꆣ ퟷ헟ꎺ샮쟥퇞 2011쓪4퓂18죕 VI
