ֻ16जֻ3௹۽ြ۽ӱ 2013୍6ᄅJune2013IndustrialEngineeringJournalPractice,2005,25(7):: ֊,ᇛႥༀ,ณധ(ଲ۽ն࿐۽അܵ࿐ჽ,ܼתܼᇜ510640)ᅋေ:๙ݖࡹ৫ݣႵՑੱ֥ಒקྟླEOQ९թ॥ᇅଆ,ฐษਔᄝ؟۱ਬ൲അࢲӮ৳ૐՖ၂܂ႋഅԩ৳ކרࠊӁࣉྛ၂ҩ֥౦ྙ༯,ਬ൲അ৳ૐ֥רࠊҦބ৳ૐ໗קྟ。֤֞ਔ৳ૐ֥ቋႪרࠊҦ,ѩႮ৳ૐ֥Ցॖࡆྟ֤ԛਔࢲӮ৳ૐॖၛࢆ֮ᄎቔӮЧ֥ࢲં。۴ऌކቔѰᒮᇏނაሹุֆטٳࠏᇅ֥ۀิԛਔοб২ؓਬ൲അކቔ৳ૐӮЧࣉྛٳข֥ܿᄵ,ѩᆣૼਔᄝՎܿᄵ༯,ն৳ૐ൞ਬ൲അ৳ૐ֥໗קࢲܒ。๙ݖඔᆴ২ሰؓӮЧٳขܿᄵ֥ކྟࣉྛਔඪૼ。࣮ࢲݔູགྷൌᇏਬ൲അೂޅࣉྛ९թ৳ૐބ৳ૐᆭުೂޅᇅקᄎቔҦิ܂ਔ၂ק֥ҕॉ。ܱՍ:ކቔ৳ૐ;Ցੱ;רࠊਈ;໗קྟᇏٳোݼ: ໓ངѓᆽ:A ໓ᅣщݼ:1007-7375(2013)03-0032-06OnStabilityofRetailers'CoalitionforItemswithImperfectQualityXiaoDan,ZhouYong-wu,TangQin-shen(SchoolofBusinessAdministration,SouthChinaUniversityofTechnology,Guangzhou510640,China)Abstract:Thestabilityofretailers′-retailerorderingfromauniformsupplierviaformingcoalitionisestablishedtoobtainoptimalorderquantityofretailers',,:cooperativecoalition;defectiverate;orderquantity;stability[1] 1915୍,Harrisᄝࡌഡླ൞ӈඔ֥౦ঃ༯֤PorteusࡼՑੱႄೆ֞ࠎЧ֥EOQଆᇏ。Ja-[2]֞ਔׅ֥ࣜEOQ܄ൔ,ھ܄ൔᄝൌ࠽ᇏႋႨܼٗ,mal࣮֩ਔᄝՑੱູӈඔ֥౦ྙ༯,ֆളӁѩ౼֤ਔࢠݺ֥ࣜ࠶ིၭ。൞,ದૌᇯࡶؿགྷᄝࢨ؍ބ؟ളӁࢨ؍֥ቋႪളӁਈ໙ี。Salameh[3]Ⴈھଆൈ൳֞ਔޓ؟ൌ࠽ၹ֥ᇅჿ。২ೂ,ބJaberٳ༅ਔՑੱູෛࠏэਈ֥EOQଆ。[4]ႮႿളӁބᄎൻݖӱᇏᇙ؟ၹ֥ۄಠ,ਬ൲അ෮Papachristos֩ᆷԛਔ໓ང[2]ᇏଆӮ৫֥ԉٳ[5]ࢤ൬֥֞Ӂѩ҂၂קކ۬。ၹՎ,ྸ؟࿐ᆀ่ࡱ。ᅦಕ࣮֩ਔಌࠊਈ、ಌཊੱބఃэਈ[6]࣮ਔऎႵՑੱ֥EOQଆ。۴ऌӁ֥ളଁᇛູଆඔ֥९թଆ。Chan֩ॉ੮ਔ၂۱Ї௹ބඋྟ֥҂,ܱႿՑੱ֥࣮ॖၛٳູӈඔওᅼࡎཧ൲、ᇗࡆ۽ބऋधࢤ൬רࠊ౦ྙ֥EPQ໙[7]ಌཊੱ、ෛࠏಌཊੱބଆಌཊੱ3۱ٚ૫。২ೂ,ี。ཬќ֩ษંਔऎႵ҂ಒקՑੱ֥EPQ൬۠ರ௹:2012-05-07ࠎࣁཛଢ:ݓࡅሱಖ॓࿐ࠎࣁሧᇹཛଢ(71131003,71101002)ቔᆀࡥࢺ:֊(1986-),ଳ,Кസದ,Ѱൖ࣮ള,ᇶေ࣮ٚཟູ९թ॥ᇅაႪ߄,܂ႋ৽৳ૐ֥ᄎቔܵ.
ֻ3௹ ֊,ᇛႥༀ,ณധ:ॉ੮Ցੱ֥ਬ൲അ९թ৳ૐרࠊਈა໗קྟٳ༅ 33ଆࠣఃࢳෘم。൞,ഈඍ໓ངࣇॉ੮ਔ၂۱ਬ൲അ९թ৳ૐרࠊҦࠣః໗קྟ໙ี,ѩ֤֞ਬ൲അᇛ௹רࠊ֥౦ࣟ,ѩໃॉ੮؟۱ਬ൲അॖྙਔಒקྟླ༯ݣႵՑ֥ਬ൲അ৳ૐ֥ቋႪרࠊӮ৳ૐ৳ކרࠊҦ,ิԛਔॖྛ֥ӮЧٳขܿᄵ,ᆣૼਔᄝՎٳข。ܿᄵ༯,ն৳ૐ൞৳ૐ֥໗קࢲܒ。གྷᄝ֥അြଆൔၘࣜэӮ܂ႋ৽ა܂ႋ৽ࡗ֥ࣩᆚ,ఒြླေა܂ႋ৽ᇏఃӮჴࢲӮᅞކቔ1 ਬ൲അކቔ৳ૐ֥רࠊਈथҦ৳ૐ,๙ݖ৳ૐႪ൝Ҁ,ࠆ֤ࣩᆚႪ൝,܋ᄹ఼ ژݼაࡌഡ൧ӆࣩᆚ৯。୍࣍ࠫ,ᇏݓ֥҂ഒఒြᄝҐܓ、ᄎQູਬ൲അi(i=1,2,…n)֥רࠊਈ;ൻi、թԥ֩ᄎቔܵٚ૫ࣉྛਔކቔ৳ૐ֥Ӈ൫。২ೂ,2008୍11ᄅ,ᇏݴҋ、ݓଽ۲ݴॢ܄ඳބૅݓcູਬ൲അiרࠊ֥ֆ໊ӮЧ;iކቔࠄϴDູਬ൲അiֆ໊ൈࡗ֥ླਈ;AirlianceMaterials܄ඳ܋ࡹ৫ਔ၂۱ڶiჅݴҋ܋ཚ,ၛܙ、܋ཚ、ט࠴、ཧ൲ູᇶႏြkູҀࠊఓٮႨ;ༀlູֆ۱ਬ൲അ֥ᄎቔӮЧ;,ൌགྷਔᇌݴҋ֥ᇗྍᇂ。2011୍1ᄅ20[1]pູՑੱ;ರ,ն9ࡅґఒြაຖն૫ϰఒြᆞൔదvູਬ൲അi֥Ӂဒੱ;ඇ৳ކҐܓކჿ,ၛղ֞ࢆ֮ҐܓӮЧ֥ଢ֥,۳֮isູӁૄՑဒ֥ӮЧ;֥ґ൧ӆᇿೆਔ၂ܢྍ༷֥࿓၁。hູਬ൲അi֥ֆ໊ᇛ௹ֆ໊Ӂ֥ӻႵӮކቔ৳ૐ֥ྙӮॖၛࢆ֮ఒြ֥ᄎቔӮЧ,ิiЧ;ۚఒြ֥ሸކࣩᆚି৯。൞,ೂޅྙӮކቔ৳ૐ?Tູਬ൲അi৫רࠊൈ֥רࠊᇛ௹;ྙӮ৳ૐᆭު֥ӮЧೂޅٳขၛࠣೂޅЌӻ৳ૐ֥iTູਬ൲അ৳ૐ֥רࠊᇛ௹。໗ק?ؓႿಒק֥९թކቔ໙ี,Meca֩ದؓ؟ࡌഡ(1):ކቔ৳ૐᇏਬ൲അ֥۲ᇕྐ༏൞ປಆ۱ਬ൲അҐႨEPQ/EOQଆרܓ၂ᇕӁ֥९[8]܋ཚ֥;թކቔ໙ีࣉྛਔٳ༅。Meca֩ษંਔn۱ਬࡌഡ(2):҂ᄍྸಌࠊ;൲അླྀטרࠊᇛ௹֥९թѰᒮ໙ี,ࡹ৫ਔ९թӮࡌഡ(3):۲۱ਬ൲അҝ९֥թԥି৯ཋ;ЧѰᒮބӻႵӮЧѰᒮਆো९թކቔѰᒮଆ;ᄝ[9]ࡌഡ(4):Ӂᄝਬ൲അᆭࡗ֥ᄎൻӮЧၛࠣൈՎࠎԤഈMeca֩Ⴛॉ੮ਔਬ൲അऎႵಌࠊӮЧࡗູਬ;֥၂Ϯ९թӮЧѰᒮބӻႵӮЧѰᒮ໙ี,ѩᆣૼ[2]ࡌഡ(5):ਬ൲അ෮רܓ֥ӁေࣉྛਔᆃਆᇕѰᒮ൞ປಆޙ֥,ࠧթᄝ၂ᇕٳٚσ[10]ဒ,ဒაཧ൲ൈؿള,൞ဒ؇ჹۚႿླਬ൲അᄝն৳ૐᇏ;ՎຓMeca֩ߎॉ੮ਔ؇。ၹՎ,Ցᄝཧ൲௹ᇏթᄝ֥ൈࡗࢠ؋,҂߶ਬ൲അ৳ކרࠊൈॖࠆ֤ਢൈࡎ۬ᅼ२֥९թކቔФ֒ቓᆞཧ൲ԛಀ。ဒᆭު,෮ႵՑࡼФ၂Ѱᒮ໙ี,ѩࡼఃקၬູpॖࡆѰᒮ。ߎႵ၂ུ࿐Ցྟԩ,҂ॉ੮ԩӮЧࠣҗᆴ。ᆀؓ؟௹ಒק९թކቔ໙ีࣉྛਔ࣮,Van[11] ଆ֥ࡹ৫აࢳdenHeuvel֩ቋᄪՖԮֆ۱ਬ൲അ֥ࣜ࠶ਈm(1≤m≤n)۱ਬ൲അྙӮކቔ৳ૐS(ֆ۱ਬ(ELS)໙ีԛؿ,࣮ਔႵཋ࠹߃௹ଽऎႵಒק[12]൲അॖၛुቔห൹֥“৳ૐ”)ު,ࡼ۲ሱ֥רֆ“յླ֥؟۱ਬ൲അ९թކቔ໙ี;ਾԽਪ֩ၛඹЇ”Ӯ၂۱նרֆཟ܂ႋഅרࠊ,ၛղ֞ࢆ֮ӮЧ֥ࠩਆֆ৽֥ࠢಕൔ܂ႋ৽ູ࣮ؓའ,ᄝਆ۱ֆ৽ଢ֥。ਬ൲അކቔ৳ૐοᅶ၂֥רࠊᇛ௹Tཟ܂ཌྷࣩކ่ࡱ༯,ࡹ৫ਔਆֆ৽ࡗਆਬ൲അॴ৽ࡗႋഅؿԛרֆ,ఃᇏܥקרࠊӮЧູk。ᆭު,ਬ൲९թླྀቔ֥ൈэਗ਼Ͽ॥ᇅ༢ଆ。Guardiola[13]അކቔ৳ૐ൬֞ॖିݣႵՑ֥רֆ,ູਔࢆ֮Ӯ֩ษંਔ၂ো؟௹ಒקླ֥ളӁ-९թކЧ,৳ૐࡼ߶ϜӁթԥᄝӻႵӮЧቋ֥֮ਬ൲അቔ໙ี,ఃކቔ৳ૐӮჴᄝႵཋ࠹߃௹ଽࣉྛളӁҝ९ᇏ,ᄵӻႵӮЧູh=min{h}。ಖު০ႨིੱSii∈Sഡീބҝԥഡീ֥܋ཚ,০Ⴈቋ֥֮ളӁӮЧބӻቋ֥ۚဒඌؓӁࣉྛ၂ဒ,ᄵဒੱႵӮЧࣉྛളӁ、թԥ。൞,ഈඍ໓ངѩીॉ੮ູ֞v=max{v}。ؓႿֆ۱ਬ൲അ৫רࠊটࢃ,ਬSiൌ࠽ᇏ܂ႋഅࢌڱ֥ӁॖିթᄝՑ֥౦ྙ。ಖi∈S൲അiཟ܂ႋഅؿԛרֆ,ႮႿิభ௹ູਬ,ᄵॖ৫طᄝགྷൌ֥ߌᇏ,ྸ؟ਬ൲അ߶৳ކרࠊѩ၂ࠧ൬֞ࠊ。൬֞ࠊᆭު,ၛv֥ဒੱषؓӁࣉྛဒ,ಖުࣉྛӮЧ֥ٳข。ၹՎ,Ч໓iဒ。ၹՎ,ᄝ၂۱רࠊᇛ௹Tଽ,ਬൈख़֥९թᄝഈඍ࣮֥ࠎԤഈ,ॉ੮֞ࠊӁᇏݣႵՑ֥i
۽ ြ ۽ ӱֻ16ज 34ඣູQ,ෛሢླ֥ࠒބՑ֥ԩ,ᄝᇛ௹ࢲDcDi1iiTCU(Q)=(k+s)++1∑Q(1-p)(1-p)ඏު,९թඣࢆູ0。طؓႿਬ൲അ৳ૐটඪ,৳1i∈SૐࡼյЇ෮Ⴕרֆཟ܂ႋഅרࠊ,ᆭު၂ࣉྛhDQpDSi1i(1-p)++lS。D2v(1-p)ဒ1S。ᄝ၂֥רࠊᇛ௹ଽ,ਬ൲അ৳ૐᇏਬ൲അi֥2९թඣᄝਬൈख़֥९թඣູQ,ᆭުෛሢླdTCU(Q)2(k+s)Di11Ⴎ=>0ᆩթᄝື၂֥23֥ࠒބՑ֥ԩ,Tൈख़९թࢆູ0。ၹՎ,ֆdQ(1-p)Q11*۱ਬ൲അ৫רࠊࠣਬ൲അ৳ކרࠊ९թඣෛൈQ֤ਬ൲അކቔ৳ૐSᄝֆ໊ൈࡗଽ֥ሹӮЧ1ࡗэ߄ܿੰٳљೂ1ބ2෮ൕ。ቋ֮,ႮሹӮЧܱႿרࠊਈ֥၂ࢨ่ࡱdTCU(Q)(k+s)DhD11Si1-p=-++2∑dQD21(1-p)Qi∈S11pDi=0,v(1-p)S֤2(k+s)v*SQ=D。1122hvD(1-p)+2pDSSii∑1 ਬ൲അ৫רࠊൈ֥९թඣi∈S*** Retailer’sinventorylevelwithindependentlyorderingQQQ1j*1ᄜႮ=ॖ֤Q=D,j=2,3,…,m,jjDDD1j1္ࠧ৳ૐᇏਬ൲അi֥ቋႪרࠊਈაਬ൲അi֥ླӮᆞб,෮Ⴕਬ൲അרࠊਈაླ֥б২ཌྷ֩。*ࡼQսೆTCU(Q)ॖᆩ,ਬ൲അކቔ৳ૐS11ᄝֆ໊ൈࡗ֥ቋ֮ӮЧູ*1TCU(Q)=cD+1∑ii1-pi∈S2 ਬ൲അ৳ކרࠊൈ֥९թඣ Inventorylevelofretailers’coalition2p22(k+s)hD+D+lS。Sii∑2∑i∈Sv(1-p)i∈SS ۴ऌࡌഡ,ਬ൲അ৳ૐᇏਬ൲അi֥רࠊᇛ௹ູ**(2)Q(1-p)QQiijT=T=,i=1,2,…,n,Ֆط=,ఃiDDDiij2 ਬ൲അކቔ৳ૐ֥ӮЧٳขބ໗קྟ**ᇏ,Q、Qٳљіൕކቔ৳ૐSᇏ֥ਬ൲അiބjij ೂݔ෮Ⴕ֥ਬ൲അथקކቔ,ෛᆭطট֥໙֥ቋႪרࠊਈ。ี൞:ሹӮЧೂޅᄝ෮Ⴕਬ൲അᆭࡗࣉྛٳข。ೂၹՎ,ਬ൲അކቔ৳ૐSᄝ၂۱ᇛ௹ଽ֥ሹӮݔ৳ૐᇏ֥၂۱ࠇ؟۱ਬ൲അಪູ࠻ק֥ٳٚσЧູؓሱ࠭҂০,ପࣼॖିष৳ૐ。ၹՎ,ႋھᇅקކTC(Q,Q,…,Q)=k+cQ+s+12mii∑i∈S、܄֥ٳขٚσ֤ਬ൲അ҂ष৳ૐ,ѩ2Q(1-p)TpQiiᄝՎٳขٚσ༯,҂߶ԛགྷ҆ٳਬ൲അቆӮ“ཬ৳h+lS。(1)S∑+i∈S2vSૐ”֥౦ঃ。ൔ(1)ᇏ,ֻ1ཛູ৳ૐרࠊ֥ܥקӮЧ;ֻ2Чࢫ༵ษંਬ൲അ൞ڎႵކቔ֥ࠏ,ࠧކቔཛູ৳ૐרࠊ֥ॖэӮЧ;ֻ3ཛູဒӮЧ;ֻ4ିڎሹӮЧࢆ֮,ᄜษંૄ۱ਬ൲അ෮ٳข֥Ӯ**QQijཛູ৳ૐ֥९թӻႵӮЧ。Ⴎ=ॖࡼൔ(1)Ч൞ڎ֮Ⴟ҂ކቔൈ֥ӮЧ。ᆃ2۱໙ีࣼ൞ކቔDDijѰᒮᇏ෮ษં֥ՑॖࡆྟაކቔѰᒮ֥ࢳ。ڿཿູਬ൲അᆭࡗॖၛྙӮ҂֥ކቔ৳ૐ,ᆃུ৳TC(Q,Q,…,Q) TCR(Q)=k+s+12m1ૐࡼ߶Ӂള҂֥ᄎቔӮЧ。৳ૐ֥ӮЧॖၛႨ၂QpDQ1i1(1-p)TDc+h++lS。iiS∑۱หᆘݦඔख़߂,קၬູc(S)=minTCU(Q)。၂۱D2vD1i∈SS1Qᄵਬ൲അކቔ৳ૐSᄝֆ໊ൈࡗଽ֥ሹӮЧູ۳ק֥ݣՑੱ֥ਬ൲അކቔ౦ॖၛႨ၂۱ჭ
ֻ3௹ ֊,ᇛႥༀ,ณധ:ॉ੮Ցੱ֥ਬ൲അ९թ৳ૐרࠊਈა໗קྟٳ༅ 35ቆ{N,K,{h,D,v,p}}іൕ,קၬః෮ؓႋ֥ކቔiii2p22hD+D+l,k+sSiS∑2i∑Ѱᒮଆູ(N,c),ఃᇏ,Nіൕਬ൲അ֥ࠢކ;cູi∈Sv(1-p)i∈SSކቔ৳ૐ֥ӮЧ。1c(T)=cD+ii∑[12-13]1-pi∈Tקၬ1 ೂݔؓႿၩS,T N,S∩T= ,Ⴕ2p2c(S)+c(T)≥c(S∪T),ᄵӫކቔѰᒮ(N,c)ऎ2hD+D+l,k+sTiiT∑2∑i∈Tv(1-p)i∈TTႵՑॖࡆྟ。 ކቔѰᒮ֥Ցॖࡆྟc(S∪T)=cD+ii∑1-pi∈S∪Tק1 ݣՑ֥९թކቔѰᒮ(N,c)ऎႵՑ2p2ॖࡆྟ。2hD+D+k+sS∪Tii∑2∑i∈S∪Tv(1-p)i∈S∪TS∪Tᆣૼ Ⴎൔ(2)ᆩ,ؓၩS,T N,S∩T= ,l+。ST*1TCU(Q)=cD+1ii∑ႻႮh≤min{h,h},v≥max{v,v}ॖS∪TSTS∪TST1-pi∈Sᆩ,2p22hD+D+l,k+sSi∑2i∑Si∈Sv(1-p)i∈SS1c(S)=cD+ii∑1-pi∈S2p22p2 c(S)+c(T)-c(S∪T)≥2hD+D+2hD+D-k+sSiik+sTii∑2∑∑2∑i∈Sv(1-p)i∈Si∈Tv(1-p)i∈TST2p22hD+D≥k+sS∪Tii∑2∑i∈S∪Tv(1-p)i∈S∪TS∪T2p22p22hD+k+D+2h-sS∪Tk+D+DsS∪Tiiii∑2∑∑2∑i∈Sv(1-p)i∈Si∈Tv(1-p)i∈TS∪TS∪T2p22hD+D=0。k+sS∪Tii∑2∑i∈S∪Tv(1-p)i∈S∪TS∪T ၹՎႵc(S)+c(T)-c(S∪T)≥0Ӯ৫。ࠧv, S N,N≠ }。i∑i∈Sc(S)+c(T)≥c(S∪T),ק֤ᆣ。Վຓ,ႮႿ৳ૐྙӮݖӱ֥گᄖྟ,ູਔॉ੮҆ק1ඪૼ,ਬ൲അྙӮն৳ૐ(෮Ⴕਬ൲അྙٳ৳ૐྙӮ֥ॖିྟ,҂ࣇླေ૭ඍೂޅٳն৳Ӯ֥৳ૐ)ॖሹӮЧࢆ֮,္ࠧᄝ৳ૐު܋ཚӻࠊૐ֥९թӮЧc(N),ط္ླေ૭ඍೂޅٳ৳ૐӮЧቋ֥֮ҝ९ބቋ֥ۚဒੱॖၛࢆ֮৳ૐ֥NS∈2,{ }֥९թӮЧc(S),۷ླေّ႘ԛૄ۱ӮሹӮЧ。༯૫ҐႨނٳٚσษંӮЧೂޅᄝਬ൲ჴླေٳข֥ӮЧෛ৳ૐ֥ሹุܿଆ֥ᄹࡆطᄹഅࡗࣉྛٳข,֤ਬ൲അႵࡆೆ৳ૐ֥ࠏ。ࡆ。ၹՎႵ࿐ᆀิԛਔሹุֆטٳࠏᇅ֥ۀ。 ކቔ৳ૐᄎቔӮЧ֥ٳข[15]Sקၬ3 ཟਈy={y}൞ӮЧٳขii∈S N,S≠ ނۀႿ20ൗࡀ50୍սᄪ௹ቔູ࣮໗קྟ[13]Ѱᒮ(N,c)֥ሹุֆטٳࠏᇅ(PMAS)֒ࣇ֥၂۱۽ऎФ࿐ᆀิԛ,ෛުShapleyބShubikϜ֒yડቀؿᅚູ၂۱ࢳ֥ۀ。ނٳ൞၂ᇕ܄֥ٳٚSσ,ՎൈીႵޅҕაದ֥ሰࠢՖն৳ૐᇏМஒܒ1)ؓႿ S N,S≠ Ⴕ∑y=c(S);i∈SiSTӮሱ֥࠭৳ૐ߶ቓ֥۷ݺ,ࠧીႵޅ၂۱ሰ৳ૐ2)ؓႿ i∈S,S T NႵy≥y。ii[15]ႵՖն৳ૐᇏٳԛট֥ࠏ。קၬ4 ೂݔؓႿކቔѰᒮ(N,c)֥၂۱ނ[14-15]קၬ2 ડቀೂ༯่ࡱ֥ࠢކӫູކቔѰᇂx=(x,x,…,x),թᄝሹุֆטٳࠏᇅ12nᒮ(N,c)֥ނ。SN(y),ؓၩ֥i∈N,Ⴕy=xӮ৫,ᄵӫ ≠S NiiNC(c)={v∈R|v=c(N)c(S)≥i∑i∈Nᆃ۱ނᇂॖႮሹุֆטٳࠏᇅ֤֞。
۽ ြ ۽ ӱֻ16ज 36ն৳ૐN֥९թӮЧॖοб২ࣉྛೂ༯ٳข:ᄵؓႿၩ֥S N,S≠ Ⴕ,cD2p2iiD+Dp(c)=l++∑ii2ii∈S1-pcDv(1-p)SiiSy=+·i∑∑21-p2p2i∈Si∈S2pDiD+Dii∑2∑2(k+s)hND+i2i∈Sv(1-p)i∈SSv(1-p)N,i=1,2,…,n。22p22pDi2(k+s)hD+D+lS=c(S)。Sii∑2∑∑D+i2i∈Sv(1-p)i∈SSi∈Nv(1-p)Nק2SՎຓ,ؓႿၩ֥i∈S T,Ⴎv≥v,֤y≥TSi1)ٳܿᄵp(c)=(p(c),p(c),…,p(c))12nTS൞ݣՑਬ൲അކቔѰᒮ֥၂۱ނᇂ;y。Ֆطॖᆩ,y={y}iii∈S N,S≠ ൞၂۱ӮЧٳขѰ2)ٳܿᄵp(c)=(p(c),p(c),...,p(c))12nᒮ(N,c)֥ሹุֆטٳࠏᇅ,ѩؓႿၩ֥i∈Nॖၛ๙ݖሹุֆטٳࠏᇅ֤֞。N,Ⴕy=xӮ৫。ၹՎ,ᆃ۱ނٳܿᄵॖႮሹiiᆣૼ ุֆטٳࠏᇅ֤֞。ᆣи。1)൮༵ၞᆩ,p(c)=c(N)Ӯ৫。ק2ඪૼ,ᄝοӮЧб২ٳขܿᄵᇏ,ն৳ૐi∑i∈Nᇏਬ൲അٳข֥ӮЧࡼ֮Ⴟఃޅ৳ૐ(ЇওఃՑ,2ሱרࠊ)ᇏ෮ٳք֥ӮЧ,္ࠧඪૼؓႿ৳ૐᇏ၂cDiiDi2pp(c)=+·iD+∑∑i∑∑2ਬ൲അটඪ,ીႵஒฦ֥ࠏ,္ࣼ҂ॖିྙӮԢ(1-p)i∈Si∈Svi∈SNi∈S(1-p)ਔն৳ૐᆭຓ֥ޅྙൔ֥৳ૐ。ၹՎ,ն৳ૐ൞12h+lS≤ݣႵՑੱ֥ਬ൲അ৳ૐ֥໗קࢲܒ。2p2k+sND+Di∑2i∑i∈Nv(1-p)i∈ ඔᆴෘ২2cDiiDi2p๙ݖඔᆴෘ২ؓ෮ิԛ֥ٳٚσࣉྛඪૼ。+·D+∑i∑∑21-pi∈Svi∈SNi∈S(1-p)ࡌഡ෮ॉ੮֥܂ႋ৽༢ᇏࣇႵ3۱ਬ൲അࣉ1ྛླྀטרࠊ,3۱ਬ൲അ֥ҕඔೂі1෮ൕ。2(k+s)h+lS≤N2p2D+Dii∑2∑i∈Sv(1-p)i∈і1 3۱ਬ൲അ֥ҕඔ ParametersofthreeretailerscDii+∑1-pi∈ f2(k+s)hD+D+lS≤Sii∑2∑i∈Sv(1-p)i∈ f+∑1-pi∈S ๙ݖ෮ܒᄯԛ֥ٳܿᄵ,Ч໓ॖקၬ఼൝֥2p22(k+s)hD+D+lS=Sii∑2∑i∈Sv(1-p)i∈SSਬ൲അູఃֆ໊רࠊӮЧაླ֥Ӱࠒᄝ෮Ⴕਬ൲c(S)。അᇏࢠ֮,ၹՎ,֒ਬ൲അ఼൝ൈ,ః෮ٳข֥ӮЧሸഈॖᆩٳܿᄵp(c)=(p(c),p(c),…,12ႋࢠ֮。ᄝഈඍ২ሰᇏH=cD=7500,H=1112p(c))ᄝਬ൲അކቔѰᒮ֥ނᇏ。ncD=6600,H=cD=6300,ఃᇏ,H>H>2233312S2)ᄜࡌഡٳٚσູy={y}ii∈S N,S≠ ,ఃᇏ:H,ඪૼਬ൲അ3ቋ఼ູ൝,طਬ൲അ2ཌྷ఼ؓ൝,32p2D+Dਬ൲അ1ቋູ൝。๙ݖ࠹ෘ,ॖᆩ൝֥ਬ൲അ1ii2cDv(1-p)SiiSy=+i෮ٳข֥ӮЧູ,ཌྷ఼ؓ൝֥ਬ൲അ2෮1-p2p2D+D∑i2∑ii∈Sv(1-p)i∈Sٳข֥ӮЧູ,طቋ఼ູ൝֥ਬ൲അ3෮Sٳข֥ӮЧቋູ֮,ՖطඪૼਔЧ໓෮ิ2p22(k+s)hD+D+l,Sii∑2∑i∈Sv(1-p)i∈SSԛٳขܿᄵ֥ކྟ。
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