ֻ29ज ֻ7௹技 术 经 济Vol 29,No 7 2010୍ 7ᄅ TechnologyEconomicsJuly,2010ࠎႿࢌҭྟࠣш࠽ӮЧ֥ࠏௐყ൲൬ၭܵଆ王 勇,宋国军,李富昌(重庆大学经济与工商管理学院,重庆400030)ᅋ ေ:收益管理是一种新型的经营管理技术,而超订作为收益管理的关键技术之一对提高航班收益具有重要作用b本文在航班存在超订的基础上,建立了考虑交叉弹性及航班向乘客所提供服务的边际成本的机票预售新模型b新模型不仅强调了边际成本对机票预售的重要性,而且充分反映了我国航空公司所面临的激烈市场竞争问题b通过对新模型的进一步分析,得到了存在超订情况下的一系列对现实具有指导意义的最优机票预售策略bܱՍ:收益管理;交叉弹性;边际成本;最优折扣;最优收益ᇏٳোݼ:F562 5 ໓ངѓ്:A ໓ᅣщݼ:1002-980X(2010)07-0056-05ཙbၹՎ,ᇅקିႵིิۚݴϫग़ቖੱaᄹࡆݴϫ൬1 ࣮Мࣟၭᆴ֥ࠏௐყ൲Ҧ,ၘӮູ֒భݴॢग़ᄎਵთ֥20ൗࡀ70୍ս,൬ၭܵቔູ၂ᇕ๙ݖࡹ৫࣮ಣׄbൌൈყҩଆಒקቋࡄཧ൲ࠇڛༀࡎ,۬ၛଔ൬ູԉٳิۚݴϫग़ቖੱaᄹࡆݴϫ൬ၭᆴ,ݓଽೆቋն߄ູଢѓ֥ྍࣜႏܵඌ,൮༵ФૅݓຓၘႵᇙ؟࿐ᆀቔਔնਈ࣮bఃᇏ,Brumelleބݴॢ܄ඳิԛ,ѩᄝෛު࣍40୍֥ؿᅚᇏ,ФܼMcGillקྟٳ༅ਔೂޅࢆ֮ၹӰग़ௐࠇ༂ࠏ֩ႋႨႿࣵaచӚሿਧaၿྛaٖ֩ڛༀྟྛြ,ၹᄯӮ֥ാ[3]bPeterބJohnr๙ݖؓݴॢ܄ٳљ౼֤ਔࢠݺ֥൬ၭིݔbଢభ,൬ၭܵ༢ඳᆭࡗࣩᆚྟ֥ٳ༅,ࡹ৫ਔЇݣӰग़࿊ᄴྛູ֥ၘФಆൗࢸ֥ݴॢ܄ඳᆚཌྷႨ,ѩӮູݴॢ܄ඳٟᆇଆ[4]bSubramanianބStidham۴ऌӰग़֥૫ؓࠗਛ൧ӆࣩᆚൈ֥႔০ఖbູԉٳิۚ൬ௐྛູ,Ⴈஆؒં૭ඍਔቖ໊֥॥ᇅ໙ี[5]bၭ,۲ݴॢ܄ඳᄝ൬ၭܵ༢֥ᆦӻ༯҂؎ࡼކFengބGallego۴ऌིႨ௹ཋ֥҂,࣮ਔթᄝൡඔਈ֥ࠏௐ൲۳ൡކ֥ཨٮಕุ,ѩၛՎ҂؎ิ؟ᇕࡎ۬༯,ࡎ۬э߄֥ቋႪൈࡗ໙ี[6]bDanۚݴϫग़ቖੱbZhangބWilliamL๙ݖӰग़ؓཌ؟Ցݴϫ֥҂Ⴟݓݴॢग़ᄎग़ቖੱ௴ђ҂֥ۚགྷሑ,ॹ࿊ᄴ,ࡹ৫ਔઔغ॓ڏथҦݖӱ֥קࡎଆކֹႄࣉႨ൬ၭܵӮູ၂ᇕсಖ[7]bݓଽ,Ⴕ࿐ᆀ۴ऌݓ֥གྷൌ౦ঃٳ༅ਔݴ൝bऌཌྷܱ࿐ᆀٳ༅,ݓ3նݴॢ܄ඳ֥٦ࠏॢॢ൬ၭܵथҦଢѓ֥ቆӮေބ൬ၭܵ༢ᄝቖੱनູ30%~37 5%[1]bᆭ෮ၛႵೂՎ֥ۚݴॢਵთ֥ൌ࠽ႋႨ֩[8-9]bᄝקਈଆٚ૫,ᇛॢቖ,ੱఃᇏթᄝᇭ؟ჰၹ,ᇭೂิభרௐ֥Ӱग़ᄝ഼ބᅦྖႥ๙ݖؓ҂ݴϫӑר൬ၭ໙ี֥ؓб٦ࠏఏ٦భௐၛࠣํਫ਼ग़ᄎ֥ࣩᆚ֩bၹՎ,ᄝ࣮,ࡹ৫ਔ؟֩ࠩௐࡎଆ[10]b఼ۚބᇫࣁڞ֩թᄝӑקॖି֥౦ঃ༯,ೂݔݴॢ܄ඳ҂Ґ౼ӑק๙ݖႄೆܿ߃,ູࠏௐӑ൲֥ൡൈ॥ᇅิ܂ਔҦ,ପહႮՎᄯӮ֥ാࡼ؟ղ15%[2]bႮႿӰ۷ࡆႵི֥ܵٚم[11]b༜תބౄѡ൮Ցᄝ൬ग़ᄝ٦ࠏఏ٦భࠇఏ٦ൈ൞ڎ౼ཨࠇ٢ఙ֨ࠏ൞၂ၭܵ༢ᇏವೆӰग़აݴॢ܄ඳ֥Ѱᒮྟ,ѩิ۱ෛࠏ൙ࡱ,ၹՎೂݔҐ౼ӑקҦ,ࡼႵॖିؿളԛਔ൬ၭ֥ܵKཌ࣮නམ[12]bᄻཉऊބ፸֨ࠏದඔӑݖݴϫቋնಸਈ֥ॖି,ྟՎൈ߶ؓݴᆽࡔ࣮֩ਔ؎ݴॢ܄ඳௐࡎᅼ२ੱؓࠏௐࡎ۬ॢ܄ඳྐუ؇ބ܄ඳݴϫ൬ၭᄯӮ၂ק֥҂ਅ႕ࠣ܄ඳ൬ၭቋն߄֥႕ཙ໙ี[13]bਗېބӧޡ൬۠ರ௹:2010-03-24ࠎࣁཛଢ:国家自然科学基金资助项目(70872123)ቔᆀࡥࢺ:王勇(1957 ),男,四川内江人,重庆大学经济与工商管理学院教授,博士生导师,研究方向:收益管理a物流管理及优化方法;宋国军(1985 ),男,山东临沂人,重庆大学经济与工商管理学院硕士研究生,研究方向:收益管理a物流管理及优化算法;李富昌(1981 ),男,广东乐昌人,重庆大学经济与工商管理学院博士研究生,研究方向:物流管理及优化算法a收益管理b56
Ⴇ֩:ࠎႿࢌҭྟࠣш࠽ӮЧ֥ࠏௐყ൲൬ၭܵଆ ࣮֩ਔթᄝӁҵၳ߄ൈݴॢ৳ૐ֥קࡎa൬ၭࠒۀੱٳ҃ބӰग़҂ିοൈ֨ࠏ֥ۀੱٳ҃ࣉྛൡႪ൝[14]bႧѯބӧࡴ֩ၛ၂ݴॢ܄ඳ၂ݴ֥֒ӑح൲ௐbႿӰग़ିڎοൈ֨ࠏ൞၂۱ෛࠏཌഈਆ۱҂ൈ؍֥ݴϫູؓའ,ՖӰग़ࠎႿݴϫགྷའ,ࠧӑح൲ԛ֥ௐඔაൎ࠹ඔऌ֤ԛ֥ൈࡗބࠏௐࡎ۬ၹ҂طؓਆ۱ݴϫ෮ቔ֥҂ۀੱٳ҃ཌྷژ,ಯಖႵॖିԛགྷൌ࠽֨ࠏದඔնႿ࿊ᄴԛؿ,࣮ਔݴॢ܄ඳ֥චݴϫ৳ކקࡎݴϫቋնಸਈN֥౦ঃ,၂֊ؿളᆃᇕෛࠏڄག,ଆ[15]bݴॢ܄ඳࣼсྶཟФࠪו֥Ӱग़Ґ౼၂ק֥Ҁӊծ๙ݖؓݴϫ൬ၭٚ૫໓ᅣ֥ؿགྷ,࣐ܵ൬ീbၹՎૌቓԛೂ༯ࡌഡ:ၭܵؓႿݴॢ܄ඳ֥ކᄎႏऎႵᇗေ֥႕ཙቔࡌഡ3:ཌྷؓႿࠏௐࡎَ֥۬э,ࠅӚௐࡎႨ,ಏޓഒႵ࿐ᆀฐษࠎႿ൬ၭ֥ܵࠏௐᄝଖ၂ൈࡗ؍ଽ൞҂э֥bყ൲ҦbՖၛഈ໓ངॖᆩ,ႮႿ໙ี֥گᄖ,ྟၹࡌഡ4:ყרௐ֥ದඔູn,ૄ໊Ӱग़҂οൈ֨Վᇙ؟࿐ᆀ္ᆺ൞Ֆݴॢ܄ඳሱദࠇݴॢ܄ඳࡗ֥ࠏ֥ۀੱູp,ૄ໊Ӱग़൞ڎοൈ֨ࠏ൞ཌྷཌྷܱ༢ԛؿಀ࣮ࠏௐყ൲໙ี,ط૭ඍํਫ਼ग़৫,֥ೂݔႵkದ҂οൈ֨ࠏ,ૌ࠺ູpk,ᄵૄದᄎؓݴॢग़ᄎูսིႋ֥ၹಏӾӾໃିࣉೆࠏௐοൈ֨ࠏ֥ۀੱູ(1-p),࠺ູqbყ൲Ҧ,ᆃ֤܄ඳᄝᇅקҦൈಸၞაग़ᄎ൧ࡌഡ5:ݴॢ܄ඳཟૄ໊ФࠪוӰग़෮ᆦڱ֥ӆຂࢫbૌൈؿགྷᄝࠏௐყ൲Ҧ֥ᇅקݖӱӮЧູӈඔlbᇏ,ႮႿݴϫཟӰग़ิ܂ڛༀ֥ш࠽ӮЧཌྷؓႿݴࡌഡ6:ݴϫఏ٦֥ӮЧູf,ݴϫఏ٦֥ܥקϫܥקӮЧ֥֮б২,ၹՎӈӈФޭbႵඔऌӮЧູb,ݴϫཟૄ໊Ӱग़ิ܂֥֥ш࠽ӮЧູӈཁൕ,2007୍ᇏݓݓଽݴॢ܄ඳ֥ܥקӮЧაш࠽ඔcbӮЧჿӯ4 1֥б২[1],ط؟୍ট၂ᆰԩႿᆃဢ2 2 ࡹ৫ଆ၂۱նุ֥ሑbႮՎ,ᄝݴॢ܄ඳᄎႏݖӱᇏᆰHuntleyބJamesᄝીႵॉ੮ݴϫཟӰग़ิ܂ࢤޭш࠽ӮЧ,҂ࣇ҂০Ⴟݴॢ܄ඳؓݴϫӮЧڛༀ֥ш࠽ӮЧcّࠣ႘൧ӆࣩᆚሑঃ֥ࢌҭྟ֥॥ᇅ,္҂০Ⴟࠏௐࡎ֥۬॥ᇅbၹՎ,Ч໓ᄝ൬EAT֥౦ྙ༯,ഡקਔݴॢ܄ඳࠏௐყ൲֥ଆ[16],ၭܵනམ֥ࠎԤഈ,ࡹ৫ਔЇݣّ႘ग़ᄎ൧ӆࣩѩਈ߄ਔܥקӮЧ༯ݴϫ෮ࠆ֤֥൬ၭᆴ ,Ⴕᆚሑঃ֥ࢌҭྟࠣݴϫཟӰग़ิ܂ڛༀ֥ш࠽ӮЧ֩ၹᄝଽ֥ࠏௐყ൲ྍଆbൈ๙ݖؓଆ (n-k)g-b (n-k!N)=bNg-b-(n-k-N)l (n-k>N)֥࣮ٳ༅ࣉ၂҄ᆣൌྍଆ֥Ⴕིྟބॖྛྟb(1)Ⴟݓږჴখ,ದჴੀࢠն֥གྷሑ,ູਔ2 ଆ֥ࡹ৫ି۷ݺֹّ႘ݴϫሹӮЧࠣग़ᄎ൧ӆ֥ࣩᆚ,ྟ2 1 ໙ี૭ඍૌࡼᄝHuntleyބJames࣮֥ࠎԤഈࣉ၂҄ॉ੮གྷൌᇏ,ૌ҂ؿགྷ৵ࢤਆֹᆭࡗ֥ࢌ๙ᄎݴϫཟӰग़ิ܂ڛༀ֥ш࠽ӮЧcّࠣ႘൧ӆࣩᆚൻٚൔສສႵ؟ᇕ,ѩ֒ਆֹᆭࡗ֥एղ֞၂ሑঃ֥ࢌҭྟEATؓࠏௐყ൲֥႕ཙbקӱ؇ൈ,ᆰ๙ਆֹ֥ᇶေࢌ๙ᄎൻٚൔᆺႵഒඔ֒ૌᆺॉ੮ܥקӮЧൈ,ॖၛಸၞֹ֤֞ݴࠫᇕbູьႿٳ༅,ૌࡌקࡊၙਆֹᆭࡗᆺթᄝϫ֥ఏ٦ӮЧູf=bb๙ݖؓݴϫཟૄ໊Ӱग़ิ٦ࠏބࠅӚਆᇕᇶေᄎൻٚൔ,ѩႨgսі٦ࠏ֥܂ڛༀ֥ш࠽ӮЧc֥ٳ༅,ॖၛ֤֞ྍྙൔ༯ݴԚࡎ۬,ႨQAaQTٳљսіࡎ۬g༯٦ࠏބࠅӚϫఏ٦֥ӮЧູ֥Ӱग़ਈbࠎႿՎ,ૌቓԛೂ༯ࡌഡ:(n-k)c+b (n-k!N)ࡌഡf=b(2)1:ᄝଖ၂หק֥ൈࡗଽ,Ⴎࡊֹ֞ၙֹ֥Nc+b (n-k>N)Ӱग़ඔਈູQ,֒ࠏௐԚࡎູ۬gൈ,QA+QT!ႮՎ,ૌॖၛ֤֞ࣇॉ੮ш࠽ӮЧcൈݴϫQb෮ࠆ֤֥൬ၭᆴ ∀,ࠧࡌഡ2:٦ࠏ֥ቋնಸਈູN,ࠅӚ֥ቋնಸਈູM (n-k)(g-c)-b (n-k!N)∀=b,N+M!QbN(g-c)-(n-k-N)l-b (n-k>N)ႮႿݴॢ܄ඳҐ౼ყ൲ௐҦ,ၹՎ҆ٳิభ(3)ყרௐ֥Ӱग़ᄝ٦ࠏఏ٦భສສ߶ၹྛӱڿэࠇఃᄝႮࡊֹ๙ສၙֹ֥ݖӱᇏ,૫ؓํਫ਼ग़ᄎ֥҂ಒקၹط֝ᇁௐࠇ༂ࠏ֩ෛࠏགྷའb֒ყཌࣩᆚ,ݴॢ܄ඳေམࠆ֤၂קٺح֥൧ӆ,ླေרௐӰग़ႵॖିӑݖݴϫቋնಸਈNൈ,ݴॢ܄ඳཟӰग़ิ܂ᇉႪࡎ৷֥ग़ᄎڛༀb၇ऌ൧ӆླمູਔႵིิۚൌ࠽ग़ቖ,ੱສສ߶۴ऌӰग़רቖᄵ,ϴෛሢࠏௐࡎ۬g֥э,Ӱቕ٦ࠏ֥ದඔQA57
ඌࣜ࠶ ֻ29ज ֻ7௹ࡼაࡎ۬ӯّཟэbၹՎ,ᄝݴϫᄍྸ֥ቋնಸn-aਈb]pk+∃[a g+(n-a-k)g-(n-k)c-b]pkb(9)Nଽ,ᆺေݴॢ܄ඳ֥ࠏௐࡎ۬҂֮ႿݴϫཟӰk=n-Nग़ิ܂ڛༀ֥ш࠽ӮЧc,߶۳ݴϫջট൬ၭࠇn-aቋཬ߄֥ാb۴ऌࡌഡ1ބ2,֒หקൈࡗଽӰ๙ݖٳ༅ૌᇿၩ֞∃kpk=(n-a)p,ၹՎk=0ग़ඔਈູ၂קӈඔQൈ,QAაQT֤эٚཟཌྷૌॖၛ߄ࡥൔ(9)ູ:,ّࠧQTაࠏௐࡎ۬gཟэbᄵ۴ऌླ (n)=qn(g-c)-(1- -p)ga-cpa-b-ྟn-N-1,ં٦ࠏބࠅӚᆭࡗ֥ࢌҭูսྟॖіൕູ:(g+l-c)∃(n-N-k)pkb(10)k=0E QT g QTgAT=Q=Tg #gQb(4)Tࡼൔ(6)սೆൔ(10),ૌቋᇔॖၛ֤֞ݴϫ֥ఃᇏ,EATіൕ٦ࠏაࠅӚᆭࡗ֥ࢌҭูս௹ຬ൬ၭᆴ (n)ູ:ྟbଖหקൈࡗ؍ଽ,֒๙ສਆֹ֥Ӱग़ඔਈູQ (n)=qn(g-c)-EATQT[(1- 2)g-(1- )ൈn-N-1,ݴॢ܄ඳӰग़ਈQA֥ᄹࡆࡼ߶ႄఏํਫ਼ग़ᄎਈQT֥༯ࢆ,э߄֥ඔᆴཌྷ,֩ૌࡼᆃ۱э߄(g-c)p]-b-(g+l-c)∃(n-N-k)pkb(11)k=0ᆴႨሳଛaս,ูࠧ QA= QT=a,ࡼఃջ(ೆ4)ൔॖ3 ଆٳ༅:֤a= QEATQT gA= QT=b3 1 ቋႪ൬ၭᆴ(5)g๙ݖྍଆ֥ࡹ৫,ૌᄝࠏௐყ൲ݖӱᇏӮႮࡌഡ3ᆩ,֒ࠅӚௐࡎཌྷؓ໗קൈ,ݴॢ܄ඳۿႄೆਔݴϫཟӰग़ิ܂ڛༀ֥ш࠽ӮЧcࠣ൧ӆູิۚग़ቖੱaᄹࡆ൬ၭᆴ,߶ൡൈ֥эࠏௐࡎࣩ۬ᆚࢌҭูսྟEAT,ѩ֤֞ਔھ่ࡱ༯ݴϫ֥gbࡌഡݴॢ܄ඳؓ҆ٳყ൲ࠏௐࡎ֥۬ᅼ२ੱູ௹ຬ൬ၭ (n)bႮႿࣩᆚ༢ඔEAT֥ႄ,ೆၹՎॖ (0! !1), ᄵ҂ࣇࢳਔݴϫҜ໊֥҂ഡၛ֤֞ݴॢ܄ඳᄝ૫ؓࠅӚग़ᄎཌࣩᆚൈିܔҐᇂ,ൈყרௐӰग़൧ӆ္֤ၛ༥ٳ,Ⴎགྷൌॖᆩ,౼֥ቋࡄᅼ२ੱູ:ᅼ२ੱ ᄀն,ᄵࢆࡎږ؇ᄀཬ,ᅼ२ඣᄀ֮b֒ (n)ݴॢ܄ඳᄝԚࡎ۬=-EATQT[2( -1)g+(g-c)p]=0b(12)g֥ࠎԤഈҐ౼ ֥ᅼ२ੱ ൈ,ࠏௐ֥ࡎ۬эնཬູ g=g- g,ࡼఃսೆࠧ:ൔ(3),ॖၛ֤֞ࠅӚӰग़֥ࡨഒඔਈູ: *ppcp(g-c)=1-+=1-b(13)a= QA= QT=EATQT(1- )b22g2g(6)Ⴎൔॖᆩ,ݴॢ܄ඳཧ൲֥ቋႪᅼ२ࠏௐࡎ۬g*:ູ(6)ॖᆩ,ᄝ ֥ᅼ२ੱ༯,჻ၩࢤ൳ࡎ۬ gطᇁݴϫᄹࡆ֥Ӱग़ඔਈູa,ཌྷႋᄹࡆ֥൬g*= *g=g-1p(g-c)b(14)ၭᆴູ2a gbૌࡌקܓઙᅼ२ௐ֥Ӱग़ܓௐࠧڱॻ,҂οࡼ *սೆൔ(4),ॖၛ֤֞ᄝ൧ӆࣩᆚEAT࠻ൈభট֨ࠏᄵࠏௐቔ٬,ᄵ҂ିοൈ֨ࠏ֥Ӱग़ඔקൈݴϫॖ൲ᅼ२ௐ֥ቋႪඔਈa*:ູਈa*=(EATQTp/2)#[(g-c)/g]b(15)kಆ҆টሱܓઙಆࡎௐ֥Ӱग़(n-a)bႮࡌഡ4ބࡌഡ5ॖᆩ,֒ಸਈູN֥ݴϫൌ࠽ყ൲ௐඔ,ࠎႿൔ(11),ૌ֤֞ݴϫ֥ყ௹ቋႪ൬ູၭູ (n*),ࠧ:nൈ,ᄝൔ(3)ࠎԤഈ๙ݖؓᅼ२ੱ ֥ॉ੮,ॖ2ၛ֤֞ݴϫ൬ၭ ∀ູ: (n*)=qnp(g-c)-EATQ2T(g-c)-b-4ga g+(n-a-k)g-(n-k)c-b (n-k!N)n-N-1 ∀=ba g+(N-a)g-(n-k-N)l-Nc-b (n-k>N(g+l-c)∃(n-N-k)pkb(16))k=0(7)3 2 ࢲݔٳ༅ၹູૄ၂۱Ӱग़൞ڎοൈ֨ࠏ൞ཌྷ৫֥,1)ႮႿݴॢग़ᄎބࠅӚग़ᄎᆭࡗู֥սܱ༢,෮ၛ҂οൈট֨ࠏ֥Ӱग़ඔਈkڛՖෛࠏۀੱູPၹՎૌॖၛᆩ֡EAT>0bؓൔ(12)ࣉ၂҄ٳ༅,֥ؽཛٳ҃bఃٳ҃ۀੱ:ູᄵ (n)ܱႿᅼ२ੱ ֥ؽՑ֝ඔ:ູpk=P(K=k)=Ckkn-a-kn-apqb(8) 2 (n)/ 2=-2gEATQT<0b(17)ᄝpk֥ۀੱٳ҃༯,ݴϫ֥௹ຬ൬ၭᆴ (n)ॖᆩݴϫ௹ຬ൬ၭᆴ (n)൞၂۱χݦඔ,๙ݖ:ູؓ ֥טᆜ, (n)߶ෛሢཌྷႋэ߄b֒ %[0,1-n-N-1 (n)=∃[a g+p(g-c)(N-a)g-(n-k-N)l-Nc-]ൈ,ෛሢ ᆴ֥эն, (n)ᆴᄹն, (n)k=02g58
Ⴇ֩:ࠎႿࢌҭྟࠣш࠽ӮЧ֥ࠏௐყ൲൬ၭܵଆ ູֆטᄹݦඔ;,֒ %[1-p(g-c)ग़ᄎ֥Ԋࠌ,္ඪૼਔݴॢ܄ඳაᆜ۱ग़ᄎ൧ӆᆭ,1]ൈ,2gࡗթᄝሢૡ్֥ܱ༢bၹՎ,ᄝᇅקࠏௐყ൲Ҧ (n)ູֆטࡨݦඔb֒౼ᆴູ *ൈ,ॖၛ֤֞ݴൈޭॖูսྟᄎൻ۽ऎ֥႕ཙ,҂০ႿݴϫቋႪϫቋႪ൬ၭᆴູ *(n)b൬ၭᆴ֥ሙಒყҩb๙ݖؓᅼ२ੱ ֥ٳ༅,ૌॖၛᆩ֡ѩ҂൞ᅼ२ੱᄀնݴϫ֥௹ຬ൬ၭᄀն,္ѩ٤ᅼ२ੱᄀ4 ࢲეཬݴϫ֥௹ຬ൬ၭᄀཬ,֒ᅼ२ੱ උႿ[0,1-Ч໓๙ݖؓіགྷ൧ӆࣩᆚ֥ࢌҭྟࠣݴϫཟp(g-c)]ٓຶൈ,ϴෛሢᅼ२ੱ ֥ᄹնݴϫ֥௹Ӱग़ิ܂ڛༀ֥ш࠽ӮЧ֥ॉ੮,ࡹ৫ਔކႵི2g֥ࠏௐყ൲ྍଆ,ѩ๙ݖؓྍଆ֥ࣉ၂҄ٳ༅ຬ൬ၭ (n)ᄹն,֒ᅼ२ੱ උႿp(g-c)[1-,2gࠆ֤ਔྍྙൔ༯ݴॢ܄ඳᄝթᄝӑרॖି౦ঃ༯ႋ1ھҐ౼֥၂༢ਙቋႪҦb࣮ٳ༅іૼ:]ٓຶൈ,ϴෛሢᅼ२ੱ ֥ᄹնݴϫ֥௹ຬ൬ၭ (n)ࡨཬbႮՎ,ॖၛࡆ఼ݴॢ܄ඳᄝൌ࠽ႋႨᇏ1)ࢌҭྟაݴϫ௹ຬ൬ၭᆴӯّཌྷܱܱ༢,ؓᅼ२ੱ֥ൡൈטᆜඪૼݴϫቋႪ௹ຬ൬ၭᆴა൧ӆࣩᆚӱ؇ૡ్ཌྷ,ቋႵᅼ२ੱ֥ਈ߄္ູݴϫҜ໊֥҂֩ࠩഡᇂࠣᅼ२ௐ֥ཧ൲ิ܂ਔགྷൌ၇ܱ,൧ӆࣩᆚᄀࠗਛᄀ҂০Ⴟݴॢ܄ඳ൬ၭᆴ֥ᄹऌbࡆb2)ш࠽ӮЧაቋႪᅼ२ੱӯᆞཌྷܱܱ༢,ႮႿ2)ٳ༅ൔ(13)ॖᆩ,ቋႪᅼ२ੱ *აࢌҭูսྟEATીႵᆰࢤܱ༢bᄝԚࡎ۬ᅼ२ੱ֥ᆴᄀնᅼ२ඣᄀ,֮ၹՎϴෛሢш࠽ӮgބӰग़҂ିοൈ֨ࠏ֥ۀੱpၘᆩ֥౦ྙ༯, *აш࠽ӮЧЧ֥э߄,ᅼ२ඣӯّཌྷܱܱ༢bൈш࠽ӮЧcӯᆞཌྷܱܱ༢,ႻႮႿ *ᆴᄀնᅼ२ඣᄀ֥э߄߶ࣉ၂҄႕ཙݴϫቋႪᅼ२ࡎ۬ބॖ൲ቋႪ,֮ၹՎϴෛሢc֥э߄,ᅼ२ඣӯّཌྷܱܱ༢bш࠽ᅼ२ࠏௐඔਈbӮЧ3)ш࠽ӮЧ֥ކਈ߄Ⴕ০ႿݴϫཟӰग़ิ܂c๙ݖؓቋႪᅼ२ੱ *֥႕ཙ,ࣉطؓቋႪᅼ२ࡎ۬g*aᅼ२ௐ֥ቋႪཧ൲ਈa*ࠣቋႵ௹ຬ൬ၭކ֥ڛༀѓሙ,ၛᄹࡆݴϫ൬ၭᆴb *Ⴎၛഈࢲંॖᆩ,ڿࣉު֥ࠏௐყ൲ྍଆб(n)Ӂള႕ཙbၹՎ,ؓш࠽ӮЧc֥ޭࡼ߶ቅθݴॢ܄ඳᇅק၂༢ਙቋႪҦbᆃᇕਈ߄ܱ༢ჰ֥ࠏௐყ൲ଆ۷ऎགྷൌၩၬbၹՎ,ࠎႿ,Ⴕ০Ⴟݴॢ܄ඳᄝᄎႏݖӱᇏ۷ᆰܴ֥ؓш࠽ӮЧݓږჴখaದჴੀࢠնࠣш࠽ӮЧཌྷؓࢠ֥ۚགྷሑ,҂ିᆰࢤޭ൪ࢌҭྟބш࠽ӮЧؓݴॢ܄cࣉྛႵི॥ᇅbඳ֥႕ཙ,ૌؓݴॢ܄ඳᄝᇅקࠏௐყ൲Ҧ֥3)ٳ༅ൔ(11)ᇏู֥սྟEAT,๙ݖؓః၂Ց֝ॖݖӱᇏऎႵ٤ӈᇗေ֥ቔႨb:֤ႮႿ໙ี֥گᄖྟ,ၹՎЧ໓ࣇॉ੮ਔթᄝݴ (n) E=-QT[(1- 2)g-(1- )(g-c)p]b(18)ATॢग़ᄎބํਫ਼ग़ᄎਆᇕࢌ๙ᄎൻٚൔཌࣩᆚ֥౦ႮႿቋႪᅼ२ੱ *აࢌҭูսྟEATીႵྙ,གྷൌᇏສສ߶թᄝ؟ᇕॖูսྟࢌ๙ᄎൻٚൔᆰࢤܱ༢,ၹՎࡼ *ᆴսೆൔ(18܋թ֥౦ྙ,ೂޅࡹ৫؟ᇕࢌ๙ᄎൻٚൔ܋թ౦ྙ)ॖ֤: 2༯֥ࠏௐყ൲ଆ൞༯၂֥࣮҄ٚཟ;ਸ਼ຓႮႿ(n)p=-Q2T(g-c)!0b(19) EAT4gӰग़ௐࠇ༂ࠏ֥ۀੱ൞၂۱ෛࠏඔᆴ,ၹՎݴॢႮൔ(19)ॖᆩ,ϴෛሢEAT֥ᄹն, (n)ᇯࡶ܄ඳ֥ӑ൲Ҧࣼсಖթᄝ၂ק֥ڄག,ೂޅᄝݴࡨཬ,ؽᆀӮّཌྷܱܱ༢bၹՎ,ݴϫ֥௹ຬ൬ၭᆴॢ܄ඳࠏௐყ൲൬ၭܵଆᇏႄೆڄགэਈ,္ა൧ӆ֥ࣩᆚྟૡ్ཌྷ,ܱϴෛሢࣩᆚ֥ࡆखݴϫ൞֒ࣂࠏௐყ൲࣮ݖӱᇏ֥၂۱ಣׄބׄb০߶ཌྷႋֹࡨཬbٳ༅ؿགྷ,๙ݖؓݴϫཟӰग़ิ܂ڛༀ֥ш࠽ҕॉ໓ངӮЧcࠣіགྷࣩᆚࠏᇅ֥ࢌҭྟE[1] ၈౩ ݴॢग़ᄎ֮ࡎႏཧҦ࣮[J] ഈݚࢌ๙ն࿐࿐AT֥ॉ੮,ࠏௐყ൲ྍଆ۷ऎႵགྷൌᆷ֝ၩၬbྍଆᇏш࠽Б,2007(41):109 116 [2] SMITHB,LDIMKUHLERJ,DARROWR,etal YieldӮЧc֥ႄೆ,҂ࣇ఼טਔݴॢ܄ඳླေؓሱദӮmanagementatAmericanairlines[J] Interface,1992(1):ЧࣉྛႵི॥ᇅ,္ඪૼਔݴϫཟӰग़ิ܂ڛༀ֥8 31 [3] BRUMELLESL,MCGILLJI AirlineseatallocationᇉਈႋھЌӻᄝ၂ק֥ѓሙ,ѩ٤ᄀݺ֥ڛༀᄀႵwithmultiplenestedfareclasses[J] OperationsRe ০Ⴟิۚݴϫ൬ၭᆴsearch,1993,41:127 137 ;ྍଆᇏูսྟEATؓݴ[4] BELOBABAPP,WILSONJL Impactsofyieldmanage ϫቋႪ൬ၭᆴ֥႕ཙ,Ⴕ৯ඪૼਔํਫ਼ग़ᄎؓݴॢmentincompetitiveairlinemarkets[J] JournalofAir59
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