ֻ29ज ֻ10௹技 术 经 济Vol 29,No 10 2010୍ 10ᄅ TechnologyEconomicsOct.,2010ඔਈ಼ྟఔჿ༯ڛༀ܂ႋ৽֥ࠗৣࠏᇅ࣮俞海宏1,2(1.浙江大学管理学院,杭州310058;2.宁波大学海运学院,浙江宁波315211)ᅋ ေ:本文研究了数量柔性契约下服务供应链的最优激励机制问题b运用连续工作表现的道德风险模型,构建了服务供应链激励模型,得出最优的激励转移支付,并详细分析了数量柔性契约下供应商需要努力的必要性条件a不同激励程度的机制设计以及不同谈判力要求下的激励机制控制等b研究认为: 在数量柔性契约中,只有特定需求分布的服务供应链才能提供有效的供应商激励机制; 最优激励机制存在一个震荡间断点;!可通过改变参数来调整激励程度并调整成员间的利润分配bܱՍ:服务供应链;数量柔性契约;激励机制;道德风险ᇏٳোݼ:F274 ໓ངѓ്:A ໓ᅣщݼ:1002-980X(2010)10-0085-061 ࣮Мࣟༀ,ၹՎڛༀ܂ႋ৽іགྷԛট֥ѩ҂൞ބӁ܂ႋ৽၂ဢ֥৽ሑࢲܒ,ط൞Ⴎڛༀิ܂അބڛༀ܂ႋڛༀࣜ࠶ၘࣜᄀটᄀӮູಆ౯ࣜ࠶ؿᅚ֥ᇏࡔഅቆӮ֥оߌሙ৽ሑࢲܒቆᆮ,ೂ1a2෮ൕb৯ਈ,ڛༀఒြ๙ݖڛༀຓЇࣉྛࣚ༥߄ٳ۽,ট࿙ނྏࣩᆚႪ൝bෛሢڛༀຓЇ֥҂؎ԛགྷ,ఒြࢸؓڛༀ܂ႋ৽ܵᆩ്֥ླᄀটᄀ௧్bЧ໓࣮֥ނྏ໙ี൞ᄝ၂۱Ⴎڛༀิ܂അބڛༀ܂ႋഅቆӮ֥ਆࠩڛༀ܂ႋ৽֥ᄎቔᇏ,චٚҐႨඔਈ಼ྟఔჿ֥ࢌၞྙൔ༯,ڛༀิ܂അႋ֒1 ڛༀ܂ႋ৽ࢲܒҐ౼હဢ֥ࠏᇅಀࠗৣڛༀ܂ႋഅ୭৯ֹิ܂ڛༀ,֤ڛༀิ܂അބ܂ႋ৽ᆜุ০ၭቋնbᄝࢳᆃ۱໙ีᆭభ,ૌсྶࢳౢԣೂ༯ࠫ۱ၐ໙: ڛༀ܂ႋ৽൞હ,ᄝᄎቔथҦᇏაӁ܂ႋ৽֥Чᇉљᄝଧ; ڛༀ܂ႋ৽ູહླေႮڛༀิ܂അಀࠗৣ܂ႋഅ,طᄝӁ܂ႋ৽ᇏಏ၂Ϯ҂թᄝᆃ۱ေ;!ڛༀ܂ႋ৽ᇏ,܂ႋഅ֥୭৯൞ೂޅᄹࡆᆜ۱܂ႋ৽ၛࠣڛༀิ܂അ֥০2 Ӂ܂ႋ৽ࢲܒၭ֥bᆃᇕᄎቔࢲܒၛࠣڛༀ֥หྟ,֤ڛༀิ܂ڛༀ൞ႵљႿᇉӁ֥၂ᇕഅ,ն҆ٳ࿐അP૫ਢሢ၂۱ྍ֥໙ี,ࠧڛༀิ܂അPمޙᆀಪູڛༀ֥หྟᄝႿ:ݖӱྟaྙྟa҂ॖԥթਈބࡓ॥܂ႋഅS൞ڎοᅶေ୭৯ֹູग़CྟaၳᇉྟaളӁބཨٮ֥ൈྟaܤग़ҕაྟb֒ิ܂ڛༀ,ၹՎ߶Ӂള֣֡ڄག໙ีbૌᆩ֡,܂၂۱ڛༀิ܂അᄝཟཨٮᆀิ܂ڛༀ֥ݖӱᇏ,ູႋഅ֥୭৯൞Ⴕࡎᆴ֥,߶ᄹࡆᆜ۱܂ႋ৽֥௹ਔิིۚੱބིၭ,ࡼ၂҆ٳڛༀຓЇ۳ڛༀ܂ႋຬ൬ၭ,ၹՎࠗৣ܂ႋഅ൞ླေ֥bބӁ܂ႋഅ,ກఃཟཨٮᆀิ܂ڛༀൈ,ڛༀ܂ႋ৽ьྙӮ৽҂,ڛༀ܂ႋ৽ᇏႮႿ҂թᄝᇏࡗӁ֥־ࢌਔbႮႿڛༀ֥ྙྟaളӁཨٮ֥ൈྟၛࠣܤ໙,ีၹՎPᆺି๙ݖܴҳग़ླ֥э߄ট؎ग़ҕაྟ֩หׄ,ڛༀ܂ႋഅمࡼᇏࡗڛༀӁ܂ႋഅ୭৯აڎ,طᆃᇕэ߄ა܂ႋഅ֥୭৯ᆭࡗሇࢌ۳ڛༀิ܂അ,ၛьႮުᆀ၂ཟग़־ࢌڛ҂൞ಒקݦඔܱ༢,ط൞၂ᇕෛࠏܱ༢,ࠧ܂ႋഅ൬۠ರ௹:2010-07-07ࠎࣁཛଢ:国家社会科学基金项目(09CJY072)资助ቔᆀࡥࢺ:俞海宏(1973∀),男,浙江宁波人,宁波大学海运学院副教授,浙江大学管理学院博士研究生,研究方向:物流管理a供应链管理a服务运营管理b85
ඌࣜ࠶ ֻ29ज ֻ10௹୭৯ਔ,ग़֥ླႵॖିᄹࡆ္Ⴕॖିࢆ֮,ᆺ҂BaimanaFischerބRajanႋႨກսଆ,Ֆଽݖᄹࡆ֥ۀੱэնਔbᆃᇕෛࠏܱ༢֥թᄝ֤ࠗຓ҆ാི֥࢘؇টٳ༅ઙછචٚᆭࡗ֥ఔჿܱৣэ֤۷Ⴕ؇b༢[9]bCorbettބTangิԛਔ҂ؓӫྐ༏༯֥ఔطᄝӁ܂ႋ৽ᇏ,ؓ܂ႋഅ֥֣֡ڄགࠗৣჿٳ༅ॿࡏ[10]bVanMiegham࣮ਔ3ᇕఔჿ༯ࠎЧ൞҂թᄝ֥,ၹູ܂ႋഅ߶ิ܂ु֤ଃ֤ሢᇅᄯഅބٳЇഅᆭࡗ֥ਆࢨ؍ਆ൧ӆᇏડቀෛࠏླطಸၞޙਈ֥ᇉӁ۳ਬ൲അ,ၹՎਬ൲അॖ֥ି৯ބളӁथҦ[11]bCachonބLariviereႨၛ๙ݖᇏࡗӁ֥ᇉਈটሙಒ؎܂ႋഅ୭৯აսଆ࣮ਔෛࠏླ༯ઙછᆭࡗ֥Ӂି࿊ᄴބڎbᆃ္Ӯਔڛༀ܂ႋ৽љႿӁ܂ႋ৽ᄎቔ֥९թٳҦ֥Ӵൌࠏᇅ[12]bނྏ໙ีᆭ၂,ط္҂Ⴟྸ؟࿐ᆀᄝӁ܂ႋ৽ᇏ࣮֥܂ႋഅࠗৣਬ൲അ֥໙,ีჰၹᄝႿభ3 ࠗৣଆܒࡹᆀ൞֣֡ڄག໙,ีطުᆀЧᇉഈ҂൞b3 1 ໙ี૭ඍЧ໓֥࣮නਫ਼ބࢲܒೂ༯:൮༵,ؓཌྷܱ࣮ૌ๙ݖ၂۱২ሰট૭ඍေࢳथ֥ܵ໙ีb໓ངࣉྛඍ;ಖ,ު۴ऌڛༀ܂ႋ৽֥ห,ׄࢲކ၂ࡅ੪ྛഠა၂ࡅڄࣟ੪ܶྙӮਔࠎႿඔਈ಼ྟඔਈ಼ྟఔჿ֥ေ,ႄೆ֣֡ڄགࠗৣଆ,ࡹ৫ఔჿ֥ކቔܱ༢,ᄝ੪Ⴓۚڂ௹ॹটਢൈ,੪ྛഠཟ৵࿃۽ቔіགྷ֥ڛༀ܂ႋ৽ࠗৣଆ;ቋ,ުࢳଆ੪ܶၛࡎ۬wყרٜࡗඔਈq,੪ྛഠ૫ਢֆࡎູp,ѩऎุٳ༅ࠗৣ֥۲ٚ૫ܵ໙ีb֥ෛࠏླd,ླ֥౼ᆴٓຶd#[0,D],ᄵཧ൲ਈs֩ႿMin(q,d)bೂݔླdཬႿყרਈq,ؓႿ2 ཌྷܱ໓ངඍ؟ר֥ඔਈᇏཬႿ q( #[0,1])҆ٳ,ᄵ੪ܶၛwؓႿڛༀ܂ႋ৽֥࣮նჿ൞2000୍ၛުҌ+cp֥ࡎ۬ཟ੪ྛഠॻ,ೂݔdնႿყרਈq,ᄵष,֥ط࣮ᇶေࠢᇏᄝࠎЧଽݤaࠎԤॿࡏ֩ᆺିӮࢌqb੪ྛഠቔູກದ,ᆦڱ੪ܶٮႨѩۀྟଽಸഈ,ܱႿࠏᇅྟ֥࣮ߎбࢠഒbؓႿກ੪ܶο၂ק୭৯ඣڛༀग़,ಏمሙಒࡓหקఔჿ༯֥ࠗৣࠏᇅ࣮ಯбࢠഒ,აЧ໓໙,ၹՎ߶Ӂള֣֡ڄག໙ีb੪ܶิ܂ڛༀ֥ඣีཌྷܱ֥໓ངᇶေടࠣ֞ڛༀ܂ႋ৽aඔਈ಼ྟఔ(୭৯აڎ)߶႕ཙႳग़֥ડၩ؇,ࡗࢤቔႨႿग़ჿၛࠣࠗৣଆ֩ٚ૫bླb੪ܶ୭৯ླေڱԛӮЧ bູਔࠗৣ੪ܶิEllramaTateaBilinglonಪູڛༀၘӮູಆ౯ࣜۚڛༀඣ,੪ྛഠླေิԛ၂ᇕቋႪࠗৣٚσb࠶֥ᇗေ҆ٳ,ѩิԛਔڛༀ܂ႋ৽֥ۀބଆᆃ۱২ሰࣼ൞ඔਈ಼ྟఔჿߌ༯ڛༀ܂ႋ৽ॿࡏ[1]bDemirkanaChengܒᄯਔႮ၂۱ASP(ap ֥܂ႋഅࠗৣ໙,ีૌ࿙ࢳथ֥൞ڛༀิ܂അplicationserviceprovider,ႋႨڛༀิ܂അ)ބ၂۱ႋ֒ೂޅิ܂၂ᇕࠗৣࠏᇅ,ࠧࠎႿॖܴҳ֥֞൧AIP(applicationinfrastructureprovider,ႋႨഡീӆླࠇൌ࠽Ӯࢌਈྐ༏,۳Ⴭ܂ႋഅ၂ק֥ࠗৣิ܂അ)ቆӮ֥ڛༀ܂ႋ৽ଆ,࣮ਔ۲ᇕླྀטҦᆦڱ,Ќᆣ܂ႋഅ჻ၩ୭৯۽ቔ,ѩൌགྷڛༀิ܂അ֥܂ႋ৽ིࠛ໙ี[2]bBaltaciogluaAdaaKaplan֥০ၭቋն߄b֩ิԛਔ၂۱ڛༀ܂ႋ৽ࢲܒଆ,ѩႋႨႿ၄ਏ3 2 ඌࡌഡЌࡲྛြ[3]bਾ֩ิԛਔࠎႿڛༀӁ֥ڛༀູਔ۷ݺֹܒࡹଆބьႿࢳ,ૌิԛೂ܂ႋ৽ࠢӮ߄ഡ࠹ݖӱ,ᇶေЇওڛༀ܂ႋ৽ܒࡹ༯ࡌഡ:֥ླٳ༅aڛༀӁ֥ഡ࠹aڛༀ܂ႋ৽ো֥ಒ1)୭৯ᆞིႋࡌഡbࠧ܂ႋഅ֥୭৯൞ջটᆞקaڛༀ܂ႋ৽Ӯჴ֥࿊ᄴაಒקaڛༀ܂ႋ৽֥ྙ֥՜ࣉቔႨ,֥߶ิۚڛༀ֥ᇉਈ,ᄹࡆग़֥ડၩӮაᄎྛ֩5۱ٚ૫[4]b؇bॖିᄝགྷൌᇏթᄝห൹֥౦,ྙೂၹڛༀิ܂ᄝඔਈ಼ྟఔჿٚ૫,TsayބLovejoyॉ੮ਔᆀհ༂۽ቔ֝ᇁᄀ୭৯ग़ۋतᄀҵ,ᆃᇕ౦ঃ҂؟ླᇛ௹aิభ௹ၛࠣླყҩྩᆞၹ֥ඔਈᄝૌ֥ॉ੮ٓຶb಼ྟఔჿ໙ี[5]bBarnes SchusteraBassokބ2)ڛༀ֥ರӈཨٮྟbग़ؓڛༀ֥ླ҂൞AnupindiՖ۷၂Ϯ֥ࡌഡ่ࡱ༯,ധೆٳ༅ਔֆࢨ၂Ցྟ,֥ࠧթᄝ؟Ցླބཨٮ,طڛༀ൧ӆ൞؍ඔਈ಼ྟఔჿ໙ี[6]bCachonބLariviere࣮ປಆࣩᆚ֥bਔඔਈ಼ྟఔჿაყҩ܋ཚᆭࡗ֥ཌྷ႕ཙ[7]b3)ڄགᇏྟࡌഡbڛༀ܂ႋ৽ᇏ,ڛༀิ܂അY kselބLeeႨधؓᆴսูਔб২ᆴቔູᚐᆴ,ބ܂ႋഅ൞ڄགᇏྟ֥b࣮ਔඔਈ಼ྟఔჿ[8]b4)ླ൞ෛࠏ,ູ֥ၩٳ҃bࠗৣଆᄝ܂ႋ৽ܵᇏ֥ႋႨ࣮Їও:3 3 ଆࡹ৫86
ݚޡ:ඔਈ಼ྟఔჿ༯ڛༀ܂ႋ৽֥ࠗৣࠏᇅ࣮ ᄝభ໓קၬ֥ژݼࠎԤഈ,ૌࡌഡ:ᄝרࠊਈL=थҦູq౦ঃ༯,ڛༀิ܂അ֥ֆ໊ӮЧູcp,܂ႋ[ps-t(s)]f1+ 1[t(s)f1-t(s)f0- f1]അֆ໊ӮЧcsb࠱ࢫଌ؟ר҆ٳᇏ҂ӑݖ q҆ٳ, + 2f1[t(s)+(w-cs-w -cp )q- ],܂ႋഅಆحҀӊ,ࡎູ۬w+cpbཧ൲ਈs֥ૡ؇ݦ0&s&(1- )q;ඔf(s),ఃᇏ܂ႋഅ୭৯ൈ֥ૡ؇ݦඔູf1(s),҂[ps-t(s)-(w+cp)s]f1+ 1{[t(s)-୭৯ൈູf0(s)bڛༀิ܂അູਔࠗৣ,ࠎႿॖܴҳ (w+cp)(1- )q+(w+cp)s](f1-f0)- f1}֥֞ൌ࠽ཧ൲ਈ۳Ⴭ܂ႋഅt(s)֥ሇ၍ᆦڱbڛ+ 2f1[t(s)-cq+(w+cp)s- ],ༀิ܂അބ܂ႋഅनູڄགᇏྟ,ᄵૌࡹ৫ଆ(1- )q<s&qbೂ༯:(6)1)ଢѓݦඔ,ູࠗৣ౦ঃ༯ڛༀิ܂അ০֥০Ⴈঘٚӱॖ֤ቋႪࢳ֥сေ่ࡱ:ቋն߄,ࠧ1)ؓt(s)֝b(1- )qm Lax[∃(ps-t(s)+(w+cp) q)f1(s)ds-=-f1+ 1(f1-f0)+ 2f1(0&s&q)b(7)0 tqൔ(7)ູ0,֤:(cp+w)q+∃(ps-t(s)+(w+cp)(q-(1- )q-f1+ 1(f1-f0)+ 2f1=0(0&s&q)b(8)s))f1(s)ds]b(1)ᆜ2)ؓ 1֝b,ު֩ࡎႿ: L(1- )qqmax[∃(ps- =1t(s))f1(s)ds+0∃(ps-(1- )qt(s)f1-t(s)f0- f1,0&s&(1- )q;t(s)-(w+cp)s)f1(s)ds]b(2)2)܂ႋഅࠗৣཌྷಸჿඏ,ࠧ܂ႋഅ୭৯ൈ֥࣪[t(s)-(w+cp)(1- )q+(w+cp)s](9)൬ၭ҂ཬႿ҂୭৯ൈ֥࣪൬ၭ (f1-f0)- f1,(1- )q<s&qb:ႮႿჿඏູ҂֩ൔ,ၹՎႋડቀ:(1- )q∃(t(s)+(w-cs)q-(w+cp) q-0 L1; 1%0b(10) =01q )f1(s)ds+∃(t(s)+(w-cs)q-(w+cp)(q(1- ࠧ:)q(1- )q 1[t(s)f1-t(s)f0- f1]=0,0&s&(1- )q;-s)- )f1(s)ds-∃(t(s)+(w-cs)q-(w+0 1{[t(s)-(w+cp)(1- )q+(w+cp)s]q(f1-f0)- f1}=0,(1- )q<s&qbcp) q)f0(s)ds-∃(t(s)+(w-cs)q-(w+(1- )q(11)cp)(q-s))f0(s)ds%0b(3)߄ࡥު3)ؓ 2֝b:֤ L(1- )q(1- )q∃(t(s)- )f1(s)ds-∃t(s)f0(s)ds+ =200f1[t(s)+(w-cs-w -cp )q- ],0&s&(1- )q;q∃(t(s)-(w+cp)(1- )q+(w+cp)s-f1[t(s)-cq+(w+cp)s- )],(1- )q<s&qb(1- )qq(12) )f1(s)ds-∃(t(s)-(w+cp)(1- )q+(w+(1- )qႮႿჿඏ္ູ҂֩ൔ,ၹՎႋડቀ:cp)s)f0(s)ds%0b(4)3)܂ႋഅҕაჿඏ,ࠧ܂ႋഅ୭৯ൈ֥࣪൬ၭ L(s,t)2=0; 2%0b(13) 2҂ູڵbࠧ(1- )q 2[f1(t(s)+(w-cs-w -cp )q- )]=0,0&s&(1- )q;∃(t(s)+(w-cs)q-(w+cp) q-0 2[f1(t(s)-cq+(w+cp)s- )]=0,(1- )q<s&qbq (14))f1(s)ds+∃(t(s)+(w-cs)q-(w+cp)(q(1- )q4)ሸކഈඍൔ(8)aൔ(11)aൔ(14),ѩಀԢ҂ડ-s)- )f1(s)ds%0b(5)3 4 ଆࢳቀჿඏ֥ࢳ,֤֞:ܒᄯঘ۬ರФࠒݦඔ(ູਔཿٚь,༯໓ᇏf1іൕf1(s),f0іൕf0(s)):87
ඌࣜ࠶ ֻ29ज ֻ10௹ f1t(s)=,0&s&(1- )q;f1-f0 f1t(s)=-(w+cp)[s-(1- )q],(1- )q<s&qbf1-f0(15)Чࠗৣ໙ีᇏ,ႮႿڛༀิ܂അ҂ॖି๙ݖࠗৣཋᇅֹᄹնყ௹൬ၭ,ၹՎᄝགྷൌᇏсקթᄝ၂۱ଢѓིႨ֥ቋնᆴ,طଆࢳᆺ֤֞၂۱3 ླૡ؇ݦඔf0af1ॖྛࢳ,۴ऌۚ֩ඔ࿐ቋႪં,ھࢳсູቋնᆴࢳ,ط൞ಆअቋႪࢳb๙ݖٳ༅,ૌؿགྷ:1)ᄝҐႨඔਈ಼ྟఔჿ֥ڛༀ܂ႋ৽ᇏ,ڛༀิ܂അླေؓ܂ႋഅࣉྛࠗৣ,ൌགྷᆜ۱܂ႋ৽֥০ᄹࡆbቋႪࠗৣࠏᇅ൞ิ܂ࠗৣሇ၍ᆦڱ,ೂൔ(15)෮ൕb۴ऌൌ࠽Ӯࢌਈsઋᄝ҂֥ٓຶ,࿊ᄴ҂֥ᆦڱܿᄵ4 ླٳ҃ݦඔF0aF1,֒s=(1- )qൈ,ਆ۱ᆦڱܿᄵ֥ᆦڱਈېݺཌྷ֩bൕ௹ຬཧ൲ਈb2)ᄝሇ၍ᆦڱݦඔᇏ,(1- )q<s&qൈ,ᆦႮႿൌ࠽ཧ൲ਈູרࠊਈބླਈᆭࡗ֥ཬڱݦඔᇏࡨಀਔ(w+cp)(s-(1- )q),൞ၹູᆀ,ࠧMin(q,n),ၹՎ௹ຬ֥ൌ࠽ཧ൲ਈS(q)֥ f1ᇏၘЇݣਔࠗৣၹ,Ϝޅ؟Ⴥ֥ᆦڱ࠹ෘೂ༯(F൞ᆷླ֥ٳ҃ݦඔ):f1-f0q۳२Ԣ,ၛൌགྷڛༀิ܂അ֥০ၭቋն߄bS(q)=q[1-F(q)]+∃yf(y)dy=q-03)֤ഈඍሇ၍ᆦڱൈ,܂ႋഅ֥ࠗৣཌྷಸჿqඏ൞ࣅ,֥ࠧ܂ႋഅ֥୭৯࣪൬ၭېݺູਬbၩ∃F(y)dyb(17)0ሢࠗৣ൞ቋ֮ӱ؇֥,ؓႿࠗৣ৯؇֥טࢫ,ᄝ4 3Ⴕ:ࢫऎุٳ༅bq!∀(q)=p∃[F0(y)-F1(y)]dy- b(18)40)ᆃ၂ࠗৣࠏᇅթᄝ၂۱ห൹ׄ(f1=f0ൈ),ླေห൹ԩ,ᄝ4 2ࢫऎุٳ༅bᆺေ୭৯ջট֥௹ຬ࣪൬ၭູᆞ,ᄵؓ୭৯֥ࠗৣࣼႵсေbࠧડቀ:4 ࠗৣࠏᇅٳ༅q!∀(q)=p∃[F0(y)-F1(y)]dy- %0b04 1 ࠗৣ֥ᄹᆴބсေྟٳ༅ᄝభ໓֥ٳ༅ᇏ,ૌࡌഡ܂ႋഅ୭৯߶ᄹࡆ(19)ᆜ۱܂ႋ৽֥൬ၭ,طൌ࠽ഈؓႿ҂֥൧ӆߌaॖၛ֤:֞qڛༀӁ,ᆃ۱ࡌഡѩ҂၂קડቀbᆃ,টٳ༅܂∃[F0(y)-F1(y)]dy% b(20)0pႋഅ୭৯ؓ܂ႋ৽֥ᄹᆴ,ၛ֤ࠣᄹᆴູᆞ֥ડ๙ݖٳ༅ॖᆩ,ᄝڛༀ܂ႋ৽ᇏ,൞ڎؓ܂ႋഅቀ่ࡱ,Ֆطॖၛ֤ԛླေؓ܂ႋഅิ܂ࠗৣ่֥ࠗৣ֥؎่ࡱ൞ൔ(20),ః႕ཙၹႵ4۱:܂ႋࡱbഅ֥୭৯ӮЧa൧ӆཧ൲ࡎ۬aרܓਈၛࠣᆃোڛༀ܂ႋഅ֥୭৯,Ӂള֥ࢲݔ൞ग़ླ(ࠇડၩ֥ླٳ҃หྟbڛༀิ܂അרܓਈᄀն,ᄵᄀླ؇)֥௹ຬᆴᄹࡆ,ࠧԛགྷۚླ֥ۀੱᄹࡆ,طԛགྷ֮ླ֥ۀੱࢆ֮,ླԛགྷ֥ٓຶ҂эေؓ܂ႋഅ֥ࠗৣ,ѩࡆնࠗৣӱ؇(ᄝ4 3ཬࢫ,ೂ3෮ൕbࡼ߶ٳ༅ࠗৣӱ؇טࢫ)b֒ڛༀ֥൧ӆࡎ۬ഈᅨૌॖၛ֤ԛᄝרࠊਈູq֥౦ঃ༯,܂ႋഅൈ,۷ေॉ੮ࠗৣѩࡆնࠗৣӱ؇b֒܂ႋഅ֥ᄎ୭৯ջট֥܂ႋ৽௹ຬ࣪൬ၭݦඔቔིੱิۚa୭৯ӮЧ༯ࢆൈ,ࡆնࠗৣ္൞Ⴕၭ:֥bਸ਼ຓ,F0(y)-F1(y)؇ਈਔหקڛༀؓ܂ႋ!∀(q)=∀1(q)-∀0(q)=pS1(q)-pS0(q)- bഅ୭৯֥ૹۋ(ྟࠇӫ∋ླ-୭৯ૹۋྟ(),ؓႿ(16)ఃᇏ,༯ѓૹۋྟն֥ڛༀྛြ,۷ླေᇿᇗࠗৣ໙ีb1іൕ୭৯,0іൕ҂୭৯,S(q)і88
ݚޡ:ඔਈ಼ྟఔჿ༯ڛༀ܂ႋ৽֥ࠗৣࠏᇅ࣮ 4 2 ࠗৣ֥ᆑ֕ࡗ؎ׄࠗৣᄀ,ሇ၍ᆦڱᄀնbܴҳሇ၍ᆦڱ֥ݦඔྙ,ೂ5෮ൕ,թᄝ၂4 3 ࠗৣӱ؇ٳ༅۱ࡗ؎ׄZ,ࠧf1=f0ൈ֥ླ,ׄᄝZׄቐш(Ӯࠗৣሇ၍ᆦڱൔ(15)൞ؓ܂ႋഅቋ֮ӱ؇֥ࠗࢌਈཬႿZ),ሇ၍ᆦڱູڵ,ࠧླေӲـ܂ႋഅ;ᄝৣ,ၹູࠗৣཌྷಸჿඏ൞ࣅ,֥ࠧ۳Ⴭ֥ࠗৣሇ၍ᆦZׄႷш(ӮࢌਈնႿZ),۳Ⴭ܂ႋഅᆞ֥ࠗৣᆦڱېݺҀ܂ႋഅၹ୭৯Ӂള֥ӮЧbؓ܂ႋഅطڱbՖቐᇀႷࣜݖZׄൈ,ሇ၍ᆦڱՖ-)๋ሇູ+,୭৯֥࣪൬ၭა҂୭৯֥࣪൬ၭཌྷ֩bᄝᆦڱ)bᆃ൞ႮႿ୭৯ᄝᆃ၂ׄഈؓླ҂Ӂളޅ႕ݦඔᇏ္ॖၛؿགྷЇݣਔ၂ཛ-(w+cp)(s-(1-ཙ,ၹՎᄝZׄഈ,܂ႋഅ࿊ᄴ҂୭৯,ࠇᆀඪೂݔ၂ )q),ၩሢϜඔਈ಼ྟఔჿᇏჰ༵۳Ⴭ܂ႋഅ֥קေࠗৣ܂ႋഅ୭৯֥߅,ླေ۳Ⴭ౫ն֥ሇ၍ᆦ҆ٳᆦڱ۳ַཨਔ,ଢ֥ᄝႿ۳Ⴭቋ֮ӱ؇֥ࠗৣbڱbᆃᄝൌ࠽Ҡቔᇏ൞҂གྷൌ,֥ᆃࣉྛ࣍රࡥ߄ೂݔᄝଖᇕགྷൌ౦ঃ༯,ླေࡆնؓ܂ႋഅ֥ԩ,ؓႿሇ၍ᆦڱࣉྛٓຶࢸק:|t(s)|& bࠗৣ৯؇,ࠧ܂ႋഅ୭৯֥࣪൬ၭေնႿ҂୭৯֥࣪൬ၭ,ᄵॖၛ๙ݖטᆜሇ၍ᆦڱ֥ݦඔটൌགྷbᆃิ܂ਆᇕٚൔ: f1+#,0&s&(1- )q;f1-f0t(s)= f1+#(22)-(w+cp)(s-(1- )q),f1-f0(1- )q<s&qbࠇ: f1∃,0&s&(1- )q;f1-f05 ࠗৣሇᆦڱݦඔt(s)t(s)= f1∃-(w(23)+cp)(s-(1- )q),f1-f0(1- )q<s&qbఃᇏ,#ބ∃ӫູӱ؇॥ᇅҕඔbҕඔ∃֥॥ᇅ۷఼ਛb#ࠏᇅൌགྷི֥ݔೂ༯:܂ႋഅ୭৯֥൬ၭ-҂୭৯֥൬ၭ,ࠧ:qq∃ f1+#f1+#f1(s)ds-0f1-f0∃ f0(s)ds-0f1-f06qq ࣍රࡥ߄ު֥ሇ၍ᆦڱݦඔt(s) =∃ f1(s)ds+0∃#ds- = +q#- =q#b0,ᄝOׄބD,ׄဢႮႿf1=f0,ၹՎ∃ࠏᇅ༯,܂ႋഅ୭৯֥൬ၭ-҂୭৯֥טᆜሇ၍ᆦڱູ ,ؓࠗৣࠏᇅྩᆞೂ༯:൬ၭ=(∃-1) b෮ၛ,#ބ∃ࠏᇅࡼڿэࠗৣӱ f1؇b,0&s&(1- )q;f1-f0ؓ#ބ∃֥౼ᆴٓຶቔ၂ٳ༅b๙ݖ#ބ∃֥t(s)= f1-ڿэটᄹնࠗৣӱ؇,ൈ္ႄఏචٚᆭࡗ֥০(w+cp)(s-(1- )q)f1-f0ٳэ,ഈཋ#ބ∃ېݺ֤ڛༀิ܂അ০ູ(1- )q<s&qbਬbࠧ(21)qఃᇏ,|t(s)|& ,෮ၛᄝൌҠቔൈ,ॖၛࡼඔ∃ f1+#ps-f1(s)ds-(cp+w)q+(w+0f1-f0ਈ಼ྟఔჿڛༀ܂ႋ৽֥ࠗৣࠏᇅטᆜູൔ(21),cp) q=0b(24)ᆦڱ֥ഈཋູ ;ᄝࡗ؎ׄf1(s)=f0(s)֥ቐш,ॖ:֤ླေӲـ܂ႋഅ,ᄝႷш۳Ⴭᆞ֥ࠗৣᆦڱ;ೂݔଖ#=Dোڛༀླؓ୭৯ૹۋྟᄀն,ࠧ∃q|f1(y)- f10[∃ps-f1(s)ds-(cp+w)q+(w+0f1-f0f0(y)|dyᄀն,ᄵؓ܂ႋഅ֥ࠗৣࣼᄀಸၞ,नqf1ሇ၍ᆦڱ္߶ᄀ֮(ၹt(s)& ֥ཋᇅ)bّᆭᄵcp) q]/∃dsb(25)0f1-f089
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