캬웕톶 l M句阳’ 닰拆럖分헐招뇪标的뗄릩供펦应商짌数쫽量솿研퇐究뺿??O릨龚탣秀瑾훜周蓉죘?햪摘튪要?탭许多뛠웳企튵业在퓚采닉购릺时쪱，ꎬ뎣常뎣常붫将헻整뇊笔튵业컱务닰拆럖分캪为솽两룶个合뫏同춬ꎺz뷏较듳大的뗄第뗚一?合?同춬和뫍较뷏小킡的뗄第뗚二뛾合뫏同춬，ꎬ춨通맽过?럖分엺批뛾二벶级볛价룱格럢封뇕闭쪽式헐招뇪标살来톡选퓱择늻不춬同뗄的릩供펦应짌商릩供믵货ꆣ。놾本컄文通춨맽过建붨솢立分럖엺批헐招뇪标쒣模탍型分럖컶析了쇋供릩应펦商짌的뗄投춶뇪标策닟싔略?뫍和싲买랽方뗄的닉采릺购닟策싔略ꎬ，뗃得돶出쇋了떱当닎参볓加뗚第튻一뫏合춬同뺺竟뇪标뗄的릩供펦应짌商쫽数쒿目뫍和뗚第뛾二뫏合춬同탂新틽引죫入뗄的릩供펦应짌商쫽数目쒿满싺ퟣ足一튻个룶不늻?뗈等쪽式时쪱ꎬ，닰拆럖分헐招뇪标뗄的닉采릺购돉成놾本킡小폚于헻整쳥体헐招뇪标뗄的닉采릺购돉成놾本ꎬ，늢并쟒且횸指돶出쇋了닰拆럖分뇈比샽例뛔对닰拆럖分헐招뇪标뗄的닉采릺购돉成놾本的뗄影펰?쿬响。ꆣ?맘关볼键词듊닰拆럖分헐招뇪标供릩应펦商짌쫽数目쒿拆닰分럖比뇈샽例中훐标뇪价볛格룱??1ꎮ.닰据럖分헐招뇪标뗄的쒣模탍型??2)?싲买랽方뛔对헻整룶个뫏合同춬的뗄估맀值횵为캪?v.ꎬ?v뇈比돉戚本놾最ퟮ?헐招뇪标닉果폃用럖分批엺二뛾级벶价볛格룱封럢闭뇕式쪽投춶标뇪，ꎬ쒣模型탍包냼?룟高的뗄릩供펦应짌商的뗄戚돉本놾还뮹高룟，ꎬ쯹所틔以싲买랽方늻不뇘必짨设놣保留쇴价볛?삨括죽三个룶阶뷗段뛎ꎺz?룱格:ꎻ?뗚第一튻个룶阶뷗段뛎，ꎬ싲买랽方톡选择퓱出돶?n룶个폐有足ퟣ够릻生짺产닺能쓜??3)?폐有?2룶个以틔上짏风럧险쿕中훐性탔的뗄供릩应펦商짌参닎与폫竟뺺标뇪，ꎬ?솦力的뗄供릩应펦商짌和뫍?m个룶짺生닺产能쓜솦力较뷏킡小的뗄供릩应펦商짌参닎加볓?쎿每룶个릩供应펦짌商쫂事쿈先뚼都知횪道뗀将붫参닎加볓第뗚一튻合뫏同춬竟뺺标뇪和뫍第뗚?뺹뇪ꎬ늢붫헻룶뫏춬닰럖캪튻룶뷏듳뗄뗚튻뫏춬?뛾二뫏合同춬竟뺺标뇪的뗄供릩应펦商짌数쫽目쒿p宽标，并将整个合同拆分为一个较大的第一合同ꎻ?뫍튻룶뷏킡뗄뗚뛾뫏춬ꎬ?ꇝ?ꎯ?캪뗚튻뫏춬햼헻??4)?c?캪为쒳某供릩应펦商짌生짺产닺整헻个룶合뫏同춬的뗄戚돉本놾，ꎬ则퓲他쯻?和一个较小的第二合间，α二三1/2为第一合同占整룶뫏춬뗄뇈샽ꎬ?튻?튻???ꎯ?캪뗚뛾뫏춬쯹햼뗄?짺生닺产뗚第一튻룶个同춬的뗄戚돉本놾为캪α?.ꆤ?c.ꎬ짺生产닺第뗚二뛾合뫏同춬的뗄戚돉?个合同的比例，卢=1-α<1/2为第二合同所占的뇈샽ꎻ?本놾为캪卢슬.ꆤC?;ꎻ? 比例$뗚뛾룶뷗뛎ꎬ?룶폐ퟣ릻짺닺쓜솦뗄릩펦짌?5?)?竟뺺标뇪之횮前잰买싲方랽和뫍供릩应펦商짌都뚼不늻知횪道뗀其웤他쯻供릩应펦?第二个阶段.n个有足够生产能力的供应商쫗쿈닎폫뗚튻뫏춬뗄뺺뇪ꎬ럖뇰톡퓱뗄놨볛쫇?商짌戚돉本놾，ꎬ쎿每룶个릩供펦应짌商짺生닺产헻整룶个뫏合춬同的뗄돉戚本놾均뻹服럾从듓?首先参与第一合同的竟标，分别选择的报价是??ꎬ???튻?ꎬ?ꎬꎬ??ꎬ웤훐놨볛ퟮ뗍뗄릩펦짌틔듎뗍?白??.ꎬ?1J?的뗄均뻹匀퓈分럖布늼，ꎬ룅概싊率럖分布늼函몯数쫽为캪G?(?c?)?。ꆣ?ba,i (i= ..川，其中报价最低的供应商以次低뗄놨볛훐뇪ꎬ훐뇪릩펦짌뗄샻죳캪??ꎻ?2?.ꎮ模쒣型탍的뗄求쟳解뷢?的报价中标，中标供应商的利润为πa;뗚죽룶뷗뛎ꎬ평폚뗚뛾뫏춬뷏킡ꎬ뿉틔틽죫??2?.ꎮ ?1ꎮ.릩供펦应짌商뗄的춶投뇪标策닟略싔?第三个阶段，由于第二合同较小，可以引人m룶탂뗄짺닺쓜솦뷏킡?ퟮ듳뗄짺닺쓜솦뻹캪헻룶?买싲方랽首쫗先쿈进뷸行탐第뗚一튻合뫏间춬的뗄招헐标뇪，ꎬ뛸而对뛔第뗚一튻合뫏?个新的生产能力较小(最大的生产能力均为整个뫏춬뗄튻냫?뗄릩펦짌닎폫뺺뇪ꎬ헢킩탂뗄릩펦짌?同춬进뷸行탐投춶标뇪的뗄供릩应펦商짌的뗄报놨价볛依틀赖삵于폚赢펮得뗃第뗚二뛾合뫏同춬?合间的一半〉的供应商参与竞标，这些新的供应商뫍닎폫뗚튻뫏춬뺺뇪떫캴훐뇪뗄릩펦짌튻웰닎볓?的뗄期웚望췻利샻润죳，ꎬ틲因듋此컒我쏇们닉果用폃逆쓦向쿲倒떹推췆法램，ꎬ쫗首先쿈考뾼虑싇?和参与第一合同竟标但未中标的供应商一起参加뗚뛾뫏춬뷸탐뗄뺺뇪ꎬ럖뇰톡퓱뗄놨볛쫇?뿚ꎬ??튻?参닎与폫第뗚二뛾合뫏同춬的뗄供릩应펦商짌的뗄报놨价볛策닟略싔。ꆣ第뗚二뛾合뫏同춬的뗄?第二合同进行的竞标，分别选择的报价是句，j(j= ?ꎬ?ꎬꎬ???ꆫ??ꎬ웤훐놨볛ퟮ뗍뗄릩펦짌틔듎뗍?招헐标뇪是쫇在퓚没쎻有폐赢펮得뗃第뗚一튻合뫏同춬的뗄(?n一튻1??)룶个릩供펦应짌商以틔?..n+m-口，其中报价最低的供应商以次低뗄놨볛훐뇪ꎬ훐뇪릩펦짌뗄샻죳캪벴ꆣ?及벰m?个룶新탂进뷸入죫的뗄供릩应펦商짌之횮间볤进뷸行탐的뗄。ꆣ根룹据뻝Vꋶic?k??的报价中标，中标供应商的利润为吨。쇭췢싲랽탨맦뚨펮뗃뗚튻뫏춬뗄릩펦짌붫늻?r?e?y? (?1?9?6?1? )? [?7?J?的뗄文컄章헂，ꎬ컒我쏇们可뿉知횪(??n?+m?一튻1?)?个룶供릩应펦?另外买方需规定赢得第一合同的供应商将不쓜닎폫뗚뛾룶뫏춬뗄뺺뇪ꎬ캴펮뗃뗚튻뫏춬뗄릩?商짌最ퟮ优폅的뗄报놨价볛策닟略싔都뚼是쫇按내照헕真헦实쪵的뗄戚돉本놾报놨价볛，ꎬ即벴?能垂与第二个合同的竟标，未赢得第一合同的供b?ß뿚(?c?;ꎻa?.ꎬ?n?+m?一튻1?)?=튻c?。ꆣ因틲此듋，ꎬ죧如맻果쒳某튻一个룶供릩应펦商짌?应펦商짌可뿉以틔参닎加볓第뗚二뛾合뫏同춬的뗄竞뺺标뇪zꎻ为캪了쇋避뇜免쏢戚돉本놾最ퟮ?的戚本是c.则他赢得第二合同的惭率为1-G 低뗍的뗄供릩应펦商짌放럅弃웺第뗚一튻合뫏同춬的뗄竟뺹标뇪而뛸参닎与폫第뗚二뛾合뫏同춬?뗄돉놾쫇?ꎬ퓲쯻펮뗃뗚뛾뫏춬뗄룅싊캪?튻??(?c?)?n?+?m?-튻2?ꎬ该룃供릩应펦商짌赢펮得뗃第뗚二뛾合뫏同춬条쳵件볾下쿂来살自ퟔ第뗚?的뗄竟뺺标뇪，ꎬ뮹还탨需맦规뚨定싲买랽方횧支뢶付룸给뗚第뛾二뫏合同춬中훐标뇪供릩应펦?二뛾合뫏同춬的뗄期웚望췻利샻润죳为캪zꎺ?商짌的뗄额뛮外췢费럑用폃也튲要튪支횧付뢶给룸第뗚一튻个룶合뫏同춬的뗄中훐标뇪供릩应펦?π?p뿚(?c?;ꎻα뿚.ꎬ?n?+돰m-튻1?)?튻=(?1?-튻α뿚)? H??( ?$?ꆪ-c?)? ꆤ P?(?$?为캪?商짌，ꎬퟷ作캪为룸给뗚第튻一룶个뫏合춬同뗄的훐中뇪标릩供펦应商짌不늻能쓜赢펮得뗃第뗚?r듎x小킡戚돉本놾I?c?为캪最ퟮ小킡戚돉本놾)?d?$?二뛾个룶合뫏同춬的뗄机믺会믡成돉本놾的뗄补늹偿뎥。ꆣ?ꆣ?=튻(?1?-튻ρ뿚?H? (?$-ꆪc?)? ꆤ (?n+?m?-튻2?)? ? 模쒣型탍假볙设짨2ꎺ?[1 -G($) Jn+m-3 ??싲랽쯹닉릺믵컯캪춬훊쟒뿉럖뗄ꎻ?口뎧?-튻G냕?(c?)J?n十?阳?一2튻"? g(ꆢ$?) d?$? (ꆢ?1)? 1)买方所采购货物为同质且可分的;作ퟷ者헟简볲介뷩:ꎺ龚릨秀탣瑾，ꎬ뢴复쟒旦듳大톧学맜管샭理톧学院풺管맜理샭科뿆学톧系쾵硕쮶士쪿研퇐究뺿生짺，?周훜蓉죘，ꎬ뢴复떩旦大듳学톧管맜理샭学톧院풺管맜理샭科뿆学톧系쾵。ꆣ? ꆤ 5?2? ꆤ?《ꆶ짏上몣海맜曹理샭科뿆学톧)?2?0?0?6?茸쓪第뗚1?期웚?
?캬웕톶 采购管理I 这헢里샯在?是쫇参닎与폫第뗚二뛾合뫏同춬竟뺺标뇪的뗄(??nꎮ?+m?一튻1?)?个룶?合뫏同춬竞뺺争헹的뗄加볓剧뻧，ꎬ살来ퟔ自뗚第뛾二뫏合同춬的뗄期웚望췻利샻润죳腻복少짙?供릩应펦商짌中훐成돉本놾次듎小킡的뗄供릩应펦商짌的뗄成돉本놾，ꎬ也튲就뻍是쫇第뗚二뛾?使쪹得뗃最ퟮ优폅报놨价볛减복小킡。ꆣ?合뫏同춬的뗄均뻹衡뫢价볛格룱。ꆣ赢펮得뗃第뗚二뛾合뫏同춬的뗄供릩应펦商짌应펦该룃是쫇?2?.ꎮ2?.ꎮ买싲方랽的뗄招헐标뇪策닟略싔?(??n?+?m-튻1??)룶个릩供펦应짌商훐中돉成놾本ퟮ最킡小뗄的릩供应펦商짌。ꆣ我컒们쏇?我컒们쏇用폃C?t?(?训?.ꎬC?2? (?n)?分럖别뇰表뇭示쪾参닎与폫第뗚一튻合뫏同춬?假볙设짨G?(?x)?服럾从듓O?到떽1?的뗄均뻹匀퓈分럖布늼函数몯，쫽则ꎬ(퓲1??)?式쪽?竞뺹标뇪的뗄n?个룶供릩应펦商짌中훐成돉本놾最ퟮ低뗍和뫍成돉本놾次듎低뗍的뗄两솽家볒?可뿉化뮯为캪2ꎺ?供릩应펦商짌成돉本놾的뗄期웚望췻值횵，ꎬ웤其훐中돉成놾本最ퟮ低뗍的뗄将붫赢펮得뗃第뗚?????ꎻ?ꎬ??????튻ꆪꆪ?ꎮ??튻??????튻一合뫏同춬。ꆣC?t?(?n?+?m一튻1?)? ꎬ C?2? (? n +? m? -튻1? )?쫇是닎参폫与第뗚二뛾?ß(c;α.n十m一o=-?二立一.c1 -c) (2) n+m一1合同竞标的(n+m-1)个供应商中成本最低，成接뷓下쿂来살考뾼虑싇参닎与폫第뗚→튻合뫏同춬竟뺺标뇪的뗄供릩应펦商짌的뗄期웚?뫏춬뺺뇪뗄???돰튻??룶릩펦짌훐돉놾ퟮ뗍ꎬ돉?本次低两家供应商成本期望值，其中成本最低的望췻利샻润죳。ꆣ令쇮b?.?(?c?)?为캪赢펮得뗃第뗚一튻合뫏同춬的뗄供릩应펦商짌基믹于폚?놾듎뗍솽볒릩펦짌돉놾웚췻횵ꎬ웤훐돉놾ퟮ뗍뗄?将赢得第二合同。Cj(的.C2 (的可以表示为成돉本놾的뗄最ퟮ优폅报놨价볛，ꎬ퓲则룃该릩供펦应짌商살来自ퟔ뗚第一튻合뫏同춬的뗄期웚?붫펮뗃뗚뛾뫏춬ꆣ????ꎬ????뿉틔뇭쪾캪?CI (n) =nf xg(x) [1 -G(x) Jn-I Jdx=nf 望췻利샻润죳为캪Eꎺ?????튻?????????튻?????튻???튻???????ꎬ?ꎻ?ꎬ??튻???????튻??ꆤ?튻??ꆤ??x?C?1? -튻x?)?n一I?d?x튻=斗죉~?(?1?0?)? πα(;α.n)=αf1 (b. (伊)-c)'(n一1) [1 nTl 튻-G?(?伊)?J??n~튻2? g?(?伊)? ꆤ ?d伊(3)???C?2? (?n)? =튻n?(?n?一튻1?)?f?ò?x?g?(?x?)?[?1튻-G?(?x)?J?n?~튻2?G?(?工〉?其웤中훐?Z是쫇可뿉能쓜大듳于폚真헦实쪵成돉本놾C?的뗄某쒳个룶值횵，ꎬb?.???쫇닎폫뗚튻뫏춬뺺뇪뗄쇭췢?튻??룶릩펦짌?d?x?一튻쓏ꎬ??2?(?1?1?)? n+l (钊是参与第一合同竞标的另外(n一1)个供应商훐돉놾ퟮ뗍뗄릩펦짌뗄놨볛ꆣ?参닎与폫第뗚二뛾合뫏同춬竞뺺标뇪的뗄(?n?+?m-튻1?)?个룶供릩应펦商짌中中成本最低的供应商的报价。훐?힢틢떽?뿚??ꎻ?ꎬꆱ??튻??쫇펮뗃뗚튻뫏춬뗄?成돉놾本最ퟮ低뗍的뗄供릩应펦商짌以틔成돉本놾次듎低뗍的뗄供릩应펦商짌的뗄成돉本놾中注意到町(c;α.n+m一1)是赢得第一合同的훐?믺믡돉놾ꎬ퓲닎폫뗚튻뫏춬뺺뇪뗄쒳튻릩펦짌뗄?标뇪，ꎬ웤其훐中듎次뗍低돉成놾本뗄的룅慨싊率쏜雷度뛈函몯数쫽fꎬ(?川?是쫇以틔下쿂的机会成本，则参与第一合同竟标的某一供应商的뗄?좫늿웚췻샻죳뿉틔뇭쪾캪ꎺ?四쯄种훖情쟩况뿶下쿂各룷式쪽子ퟓ的뗄总ퟜ和뫍。全部期望利润可以表示为:ꆣ????ꎬ?ꎻ?ꎬ??튻?뿚??ꎬ?ꎻ?ꎬ?????ꆫ??ꆤ?????rr(;)=rr.(工.C;α.n)+(n…1) G(x) 情쟩况뿶?1(?n뻅个룶供릩应펦商짌中훐的뗄成돉本놾次듎小킡的뗄供릩应펦商짌的뗄?ꆤ ?[1? -튻?G(??c)??J?ηt?m-튻2? ꆤ.?叩죕?(c?;ꎻ?α.ꎬ?n?+?m一튻1?)???(4?)?? 成돉놾本为캪?n?+?m一튻?1个룶供릩应펦商짌中훐的뗄次듎小킡成돉本놾)?ꎺ:? ퟜ뗄웚췻샻죳쫇살ퟔ뗚튻뫏춬뗄웚췻샻죳ꎬ?????????2? mn( n-1 )x(?1? 튻-?X )??m+?n?~튻3? 总的期望利润是来自第一合同的期望利润，볓加짏上살来自ퟔ第뗚二뛾合뫏同춬的뗄期웚望췻利샻润죳，ꎬ웤其훐中살来自ퟔ뗚第二뛾合뫏?情쟩况뿶?2?(?m个룶供릩应펦商짌中훐的뗄成돉本놾第뗚三죽小킡的뗄供릩应펦?춬同的뗄期웚望췻利샻润죳是쫇(??1?쪽)式뗄的쳵条볾件웚期췻望샻利죳润돋乘틔以룃该供릩?商짌的뗄成돉本놾为캪?n?+m?튻一1?个룶供릩应펦商짌成돉本놾中훐的뗄次듎小킡成돉?应펦짌商赢펮得뗃第뗚二뛾合뫏同춬的뗄概룅率싊。ꆣ?本놾?hꎺ?뚨定理샭1?닎参与폫뗚第一튻合뫏同춬的뗄供릩应펦商짌的뗄最ퟮ优폅报놨价볛为캪?÷n(n一1)( n -2)x2 c1一工川-3?b?. (?c?;?aꎬ.?n)? 튻=c??+ ?C1?ꎯ/?α)? ꆤ [?1? 튻-?G?( ?c?) ?J? m ꆤ ?좥??튻???튻??ꎮ????튻?????튻? 즺????ꎬ???튻??????쟩情뿶况?3?(?m룶个릩供펦应商짌中훐的뗄成돉本놾最ퟮ小킡的뗄供릩应펦商짌?叩(c;+m-1)(5) 횤쏷쎿룶릩펦짌뚼믡내헕쓜릻쪹ퟔ벺뗄샻?뗄的돉成놾本为캪?n?十?m튻一?1룶个릩供펦应商짌成돉本놾中훐的뗄次듎小킡成돉?证明每个供应商都会按照能够使自己的利죳ퟮ듳뮯뗄춶뇪몯쫽뷸탐춶뇪ꎬ퓲뛔웚췻샻죳몯?놾本)?ꎺ:? 润最大化的投标函数进行投标，则对期望利润函쫽数뷸进行탐求쟳导떼ꎺz?ꇂ÷m?n?(?n튻一?1?时?(??1?-튻工ꎮ?)?，??…튻?3drr( 阳.n)1 =0 (6) 뿚????튻????쟩情뿶况?4?(?m룶个릩供펦应商짌中훐的뗄돉成本놾次듎小킡的뗄供릩应펦商짌?dx ~c ???ꆻ?튻?ꆻ???튻??ꆤ???ꎮ뗄的돉成놾本为캪?n?+m?튻一?1룶个릩供펦应짌商成돉本놾中훐的뗄次듎小킡成돉?车年+(n一1) g(c) ꆪ??ax I I~C ?a?x? ?I .rꎻ~c? ꆰ?놾本)?ꎺ:? ??튻????????튻?ꆤ???????????튻??????2[1 -G(c)]n+m-2 rr{l=O (7) m(m一Onx?c1? 튻-?x)?m??+n?튻-3? ?+m?(?돰m튻一?1)??x?(?1튻-??αꆤ• ?[?b?.?(?c;ꎻa?ꎬ,?n?)튻-c?J? ꆤ ?(n튻 1?)? ꆤ ?[1? 튻-?G?(?c?)?J?n튻-2? ?x?)?m?+??n튻-2? ꆤ ?g(??c?)튻且?(n튻一1?)?ꆤ ?g?(c??) ꆤ ?[1? 튻-?G?(?c?)J?nꆱ?+m?튻-2? ꆤ•탏叼?퓲则싲买랽方뗚第뛾二뫏合同춬닉采릺购돉成놾本的뗄웚期望췻횵值캪为ꎺ2??(?8?) ?E?Pß죕튻且?C2??(?n ?+? m튻一?1?) 튻= ?f? ?xfꎬ ?(?x)? ?d?x? 튻= ?뺭经볆计쯣算뿉可뗃得?(?5?)쪽式。ꆣ?횤证뇏毕?(n+m一1)(3n+2m) +nm (12) 볙짨????럾듓??ꎬ??뗄뻹퓈럖늼ꎬ퓲?욪?(n+?m?튻一?1)?(n?+m??) (?n?+?m?+ ?1)? ꆢꆭꎬ?假设G(x)服从[0，1J的均匀分布，则싲买랽方뗚第튻一뫏合춬同뗄的닉采릺购돉成놾本뗄的웚期望췻횵值为캪ꎺ?z1 -a (1 -c)m+t b. (c ;a.ꎬ?的?튻=c??+?一一旦ꆤ?~~~-1-?(?9?)? ?????훤튻??"αnTm-l ?E?P?.튻=f? b?.?(??cꎻ;?aꎬ.?n?) ꆤ ? nꆤ’ ?(n튻一1?)?ꆤ ?G?(?C?) ꆤ ? 듓从짏上쪽式뿉可볻见ꎬ，닎参폫与뗚第튻一뫏合춬同뗄的릩供펦应짌商뗄的ퟮ最폅优??[?1 튻-?G?(?c?)?Jꎮn?-2? ꆤ ?g?(?C?) ꆤ ?d?c? 놨报볛价쯦随웤其돉成놾本的뗄增퓶加볓而뛸增퓶加볓，ꎬ쯦随릩供펦应짌商쫽数目쒿?nꎬ.?m?틔벰?횵뗄퓶볓뛸폐복킡쟷쫆ꆣ쇭췢ꎬ쯦ퟅ뗚뛾?튻=一?主-:;-튻?+?[?(?1튻-α?)?/ꎯ?α?Jꆤ ? n+1 以及α值的增加而有减小趋势。另外，随着第工ꆤ ?5?3 ꆤ?
?캬웕톶 1 采购f斗胆nꎺ ? (틮n뛾-?1) 웤其훐中훱nꎬ?，m럖分뇰别쫇是닎参볓加뗚第튻一뫏合同춬뺹竟뇪标的뗄릩供应펦??훱?????ꆤ?훱???ꆤ?훱??튻???(?3?)?? (n+m+ 1) (n+m) (n+m一1)짌商죋人쫽数与폫탂新닎参加볓第뗚二뛾合뫏同춬竟뺹标뇪的뗄供릩应펦商짌人죋数쫽。?퓲则싲买랽方헻整룶个뫏合춬同뗄的닉采릺购돉成놾本为캪ꎺ?2???뿚?튻???????튻뿚?ꆤ?????????횤证쏷明若죴令쇮(??1?5 ?)쪽式中훐뿚α뗄的쾵系쫽数??击?ꆣ??一튻?EP(α)=αEPa+O一α) EP卢(14) 뚨定샭理?2헻整룶个뫏合춬同뗄的웚期췻望닉采릺购돉成本놾为캪?n(n뛾一1?)?(훱n?+?m?+ ?1?)? (훱n?+?m)? ?(훱n?+?m튻一1?)??(n一1)?E?P(??α?)?=?[一一一?샶?(n+m+1) (n+m) (n+m一1)(n+m一1)(3n+2m)+nm튻?룍??>0?ꎬ，퓲则웚期췻望采购(n+m一1)(n十m)(n+m+1)十ꎮ?(?훱n?+?m튻一?1?)?(?3?n?+2??m?) ?+n훱?m ?..??훱??튻??훱???훱????ꆭ?ꆧ?튻닉ꎬꆣ튻릺?, ꆣ?(훱n?+?m튻一?1)??(훱n?+?m)? ?(훱n?+?m+?1?)??-’ 成本随α的增大而增大，若令α的系数击???튻?룉?룉????룉????돉놾쯦?뗄퓶듳뛸퓶듳ꎬ죴쇮?뗄쾵쫽??튻?n(n一1)+[一一-n+l (n+m+1)(n+m)(n+m-1) 훱n?(훱n튻-?1?) (n+m+1) (n+m) (n+m-1) ??(?n?+??m-1?)? ?(?3?n?+2?m) +mn .., 튻?훱??(15) 튻(n+m-튻???????l)?(?n훱쪮十?m)??(훱n?+?m??????ꆤ뿚??ꆭ?????十1)-'α(n十m-1)(3n+2m)+nm튻?<0，则期望采购횤쏷싲랽뗄헻룶뫏춬뗄닉릺돉놾캪??(훱n?十?m-튻l?)??(훱n?+?m)?쓴 (?훱n?+?m?+?1) ?ꆭ?ꎬ?퓲웚튻췻?닉튻릺?证明买方的整个合同的采购成本为?????????????튻뿚?ꆤ????돉成本놾随쯦?α뗄的퓶增大듳而뛸减복小킡。ꆣ?횤证뇏毕?EP(α)=αEP+(1-α) EP卢a맛现달黯뚨定理샭?3뿉可以틔发랢现쿖，ꎬ닰拆럖分헐招뇪标뗄的웚期췻望닉采购릺?, 2 ?. ?1一α_N<___"-一·ꆤ?~'n+lα 돉成놾本폫与헻整쳥体招헐标뇪的뗄期웚望췻采닉购릺成돉本놾的뗄相쿠对뛔大듳小킡，ꎬ与폫?잧???(?n룉?一1?)??????ꆫ??ꆤ??α뗄的듳大킡小컞无맘关，ꎬ벴即내按뫎何훖种뇈比샽例닰拆럖分헻整룶个뫏合同춬并늢不늻??(훱n?十?m+?1?)??(훱n?+?m)? ?(훱n?+?m튻一:?o?ꆫ}+oꆭ-α)? 会믡影펰响쿬到떽拆닰分럖招헐标뇪与폫整헻体쳥招헐标뇪的뗄选톡择퓱。ꆣ究뺿竟뺹是쫇拆닰?(nꇀ+?m뛾一?1)(3nꇀ+?2m)ꇀ十?n틮m??훱??튻???훱????훱???????럖分헐招뇪标뛔对买싲方랽有폐利샻还뮹是쫇整헻体쳥招헐标뇪对뛔买싲方랽有폐利샻，ꎬ只횻?(n+m一1)(n+m)(n+m+1) 뺭볆쯣뗃????쪽?폫与뗚第뛾二뫏舍同춬新탂引틽人죫的뗄供릩应펦商짌数쫽目쒿有폐关맘，ꎬ即벴싲买方랽究뺿?经计算得(15)式뚨샭?볙짨릩펦짌뗄돉놾럾듓??ꎬ??샛볆럖?竞뺹选톡择퓱拆닰分럖招헐标뇪还뮹是쫇选톡择퓱整헻体쳥招헐标뇪，ꎬ只횻要튪看뾴훱n뫍和?定理3假设供应商的成本服从[0，1J累计分늼몯쫽캪????뗄뻹퓈럖늼ꎬ닰럖헐뇪뗄웚췻닉릺?m뗄的大듳小킡，ꎬ将붫훱nꎬ，?m듸带入죫?(?6?)?쪽式，ꎬ죧如맻果룃该늻不뗈等式쪽成돉?布函数为G(c)的均匀分布，拆分招标的期望采购돉놾킡폚헻쳥헐뇪뗄웚췻닉릺돉놾ꎬ죧맻?ꎬ훱싺?솢立퓲则톡选퓱择닰拆分럖招헐标뇪，ꎬ죧如맻果룃该늻不뗈等쪽式늻不돉成솢立퓲则选톡择퓱?成本小于整体招标的期望采购成本，如果m，n满ퟣ?整헻体쳥招헐标뇪。ꆣ?足뇈比뷏较뚨定理샭3?和뫍뚨定理샭4?뿉可以틔发랢现쿖，ꎬ떱当닰拆分럖招헐标뇪?m>?.布ꇌ뫅?ζ?-훱튻f뫅?(?16?)? 的뗄닉采购릺돉成놾本小킡于폚整헻体쳥招헐标뇪的뗄采닉购릺成돉本놾时쪱，ꎬ采닉购릺成돉?웤훐훱ꎬ?럖뇰쫇닎볓뗚튻뫏춬뺹뇪뗄릩펦?本놾随쯦α?뗄的增퓶大듳而뛸增퓶大듳。ꆣ因틲此듋，ꎬ캪为쇋了쪹使期웚望췻价볛格룱变뇤?其中n，m分别是参加第一合同竟标的供应짌죋쫽폫탂닎볓뗚뛾뫏춬뺺뇪뗄릩펦짌죋쫽ꆣ?小킡，ꎬ퓲则α?值횵尽뺡可뿉能쓜选톡择퓱小킡。ꆣ也튲就뻍是쫇说쮵，ꎬ놣保证횤拆닰分럖招헐?商人数与新参加第工合同竞标的供应商人数。횤쏷싲랽톡퓱닰럖헐뇪퓲쯻튪뢶돶뇈헻쳥?标뇪的뗄第뗚-튻合뫏同춬大듳于폚第뗚二뛾合뫏同춬的뗄前잰提쳡下쿂，ꎬ第뗚一튻合뫏同춬?证明买方选择拆分招标则他要付出比整体헐뇪뛮췢뗄럑폃?尽뺡量솿小킡-튻些킩，ꎬ뗚第뛾二뫏合同춬尽뺡量솿大듳一튻些킩。ꆣ另쇭外췢，ꎬ탂新引틽入죫?招标额外的费用ꇷLJ?a뿚，ꎬ的훱?=?E?P?(?a뿚?)튻-E?P?(?1?)??(?1?7?)?? 供릩应펦商짌数쫽目쒿?m越풽大듳，ꎬ则퓲α?的뗄系쾵数쫽1ꆪ??丁???튻?웤훐?????튻???훱?ꎬ죴닰럖헐뇪폅폚헻쳥헐?nil 其中EP(1)=C2 (川，若拆分招标优于整体招뇪ꎬ퓲탨ꇷ?뿚ꎬ훱???ꎬ벴?n쮿?(쮿n뛾-?1) 标，则需6(a，n)<0，即(?n훱+??m+?1?)? (?n훱+?m?)? (?n훱?+?m튻-1?)? ?α뿚 {? 击?훱ꆪ?맧??+?[?(ω?t?卜튻-丁α川뿚讪ω?ꎯ〉뿚?ꆤ?(n+m-1) (3n+2m) +nm 튻?(?n훱슳+?m튻-1?) (?n훱+?m룰)? (n훱+?m+? 1?)?越풽大듳，ꎬꆯ?헢这쪱时增퓶大듳?샶?훱??????(훱n?一?1υ>??훱샶??튻??}ꆫ??+O튻??一튻?αꆫ)? 第뗚二뛾合뫏同춬减복小킡第뗚一튻合뫏同춬，ꆣ붵降뗍低웚期望췻价볛格룱的뗄效킧果맻会믡?(n+m+ 1) (n+m) (n+m-1) 룟?훱?튻??훱???훱?????ꆢ?훱??ꋨꆭ?更룼明쏷显쿔。ꆣ因틲此듋如죧果맻因틲拆닰分럖引틽入죫了쇋比뇈较뷏多뛠的뗄生짺产닺能쓜?(n+m-1) (3n+2m) +nm (18) (n+m一1)(n+m) (n+m+ 1) -"""n+ i 力솦较뷏小킡供릩应펦商짌时쪱，ꎬ뿉可以틔考뾼虑싇选톡择퓱α?值횵接뷓近뷼1/?ꎯ2?，ꎬ벴即?经뺭计볆算쯣得뗃(1??6?)?式쪽。ꆣ?证횤毕뇏?第뗚一튻合뫏同춬和뫍第뗚工뛾合뫏同춬大듳小킡相쿠近뷼。ꆣ另쇭外췢，ꎬ如죧果맻买싲方랽?定뚨理샭4?假볙设짨供릩应펦商짌的뗄戚돉本놾服럾从듓[?0?，ꎬ1?J?累샛计볆分럖?从듓降붵低뗍供릩货믵成돉本놾等뗈方랽面쏦考뾼虑싇，ꎬ在퓚?m和뫍n훱的뗄数쫽目쒿不늻?布늼函몯数쫽为캪G?(?c?)?的뗄均뻹匀퓈分럖布늼，ꎬ?满싺足ퟣ(?6??)?式쪽的뗄情쟩况뿶下쿂依틀然좻选톡择퓱拆닰分럖招헐标뇪，ꎬ则퓲此듋时쪱??01ꆣ期웚望췻采닉购릺成돉本놾随쯦α?的뗄增퓶大듳而뛸增퓶大듳，ꎬ如죧果맻?m，ꎬ?拆닰分럖招헐标뇪的뗄采닉购릺成돉本놾高룟于폚整헻体쳥招헐标뇪的뗄采닉购릺戚돉本놾，ꎬ?n满싺足ퟣ?并늢且쟒期웚望췻采닉购릺戚돉本놾随쯦α?的뗄增퓶大듳而뛸减복小킡，ꎬ也튲就뻍是쫇在퓚??ꇌ뫅훱??훱튻뫅????这헢种훖情쟩况뿶下쿂买싲方랽应펦该룃尽뺡量솿使쪹第뗚一튻合뫏同춬所쯹占햼比뇈例샽大듳?m>~!n2工7-f(16) 来살降붵低뗍采닉购릺戚돉本놾。ꆣ??02ꆣ否럱则퓲，ꎬ웚期췻望닉采购릺成돉本놾随쯦α?的뗄增퓶大듳而뛸瞄복小킡?3?.ꎮ模쒣拟쓢计볆算쯣?ꆤ S?4? ꆤ?《ꆶ짏上몣海雷맜理샭科뿆学톧}?2?0?0?6?茸쓪第뗚1?期웚?
?캬웕톶 采购管理| 볙假짨设쒳某企웳业튵进뷸行탐招헐标뇪采닉购릺，ꎬ뫲候톡选的뗄供릩应펦商짌中훐?쯼它们쏇分럖别뇰代듺表뇭?4个룶能쓜够릻参닎与폫第뗚一튻合뫏同춬竞뺺标뇪的뗄有폐足ퟣ?有폐4?个룶是쫇有폐足ퟣ够릻生짺产닺能쓜力솦的뗄供릩应펦商짌，ꎬ另쇭外췢?m个룶是쫇?릻够生짺产닺能쓜力솦的뗄供릩应펦商짌的뗄成돉本놾，ꎬ这헢4?个룶供릩应펦商짌先쿈对뛔?生짺产닺能쓜솦力뷏较小킡的뗄供릩应펦商짌(?ퟮ最듳大뗄的짺生닺产쓜能솦力均뻹为캪整헻?第뗚一튻合뫏同춬进뷸行탐竟뺺标뇪，ꎬ룹根뻝据쎿每룶个릩供펦应짌商的뗄成돉本놾计볆算쯣?个룶合뫏同춬的뗄一튻半냫)?ꆣ。룹根뻝据쏼命题쳢四쯄，ꎬm?<?3?时쪱采닉用폃整헻体쳥?出돶쯼它쏇们룷各自ퟔ的뗄놨报价볛，ꎬ웤其훐中놨报볛价ퟮ最뗍低뗄的릩供펦应짌商以틔次듎?招헐뇪标的뗄采닉购릺成돉本놾较뷏低뗍，ꎬ늢并쟒且웚期췻堕价볛格룱将붫随쯦?α的뗄增퓶?低뗍的뗄报놨价볛?P"中훐标뇪;ꎻ뷓接ퟅ着짺生成돉m?룶个服럾从듓?[?Oꎬ，l?J?均뻹匀퓈?大듳而뛸增퓶大듳ꎻ;?m:ꎺ?二3?쪱时采닉用폃닰拆分럖招헐标뇪的뗄采닉购릺成돉本놾较뷏?럖分布늼的뗄随쯦机믺数쫽，ꎬ뗚第튻一뫏合춬同未캴中훐标뇪的뗄3?个룶供릩应펦商짌连솬?뗍低，ꎬ늢并쟒且웚期췻望볛价룱格붫将随쯦?α的뗄增퓶大듳而뛸增퓶大듳。ꆣ?同춬쇭另췢外탂新틽引죫人뗄的짺生닺产能쓜力솦较뷏小킡的뗄m?个룶供릩应펦商짌共릲?쿂下쏦面춨通맽过쒣模拟쓢计볆算쯣分럖别뇰分럖析컶?m=?2?，ꎬ?m=튻3?ꎬ，m??同춬닎参폫与뗚第뛾二뫏舍同춬的뗄竞뺺标뇪，ꎬ웤其훐中돉成놾本ퟮ最뗍低的뗄供릩应펦商짌?=튻4?ꎬ，죽三훖种쟩情뿶况쿂下ꎬ，늻不춬同닰拆럖分뇈比샽例뗄的닰拆럖分헐招뇪标的뗄采닉?以틔돉成놾本듎次뗍低뗄的릩供펦应짌商的뗄成돉本놾?Pp中훐标뇪oꆣ最ퟮ后뫳计볆算쯣?购릺돉成놾本。ꆣ쒣模拟쓢过맽程돌如죧下쿂:ꎺ붫将헻整룶个뫏合춬同닰拆럖分为캪两솽个룶?出돶닰拆럖分헐招标뇪后뫳整헻룶个合뫏同춬的뗄中훐标뇪价볛格룱P?。ꆣ붫将该룃拆닰分럖?合뫏同춬，ꎬ뗚第튻一뫏合춬同쯹所햼占뗄的比뇈例샽为캪?a(??1!ꎯ?2?<α?至ꇜ1?)?，ꎬ，ꎬ뗚第?招헐标뇪过맽程돌模쒣拟쓢5?0?次듎，ꎬ뗃得到떽?5?0组ퟩ拆닰分럖招헐标뇪的뗄采닉购릺?二뛾뫏合同춬所쯹占햼的뗄比뇈例샽为캪1?튻-?a，ꎬ쫗首先쿈通춨过맽计볆算쯣机믺生짺成돉?成돉本놾，ꎬ볆计쯣算出돶5?0?듎次模쒣拟쓢的뗄均뻹值횵和뫍方랽差닮oꆣ??4个룶服럾从듓[?O?，ꎬ?lJ?뻹均匀퓈分럖布늼的뗄随쯦机믺数쫽?nl?ꎬ，n?2?'ꎬ町?ꎯ?，ꎬ?n4?,ꎬ? 襄쮥1??不늻同춬拆닰分럖比뇈例샽的뗄采닉购릺成돉本놾的뗄均뻹值횵和뫍方랽差닮??m=?2?? ?m=?3?? 폅m=?4?? α뗄的取좡值횵?5?0?次듎쒣模쓢拟的뗄均뻹值횵??50?듎次模쒣拟쓢的뗄方랽差닮?α?的뗄좡取值횵??50?次듎쒣模拟쓢的뗄均뻹值횵?5?0?次듎模쒣拟쓢的뗄方랽差닮?α뗄的取좡值횵??50?듎次模쒣拟쓢的뗄均뻹值횵??50?듎次쒣模拟쓢的뗄方랽差닮?1?? ?0ꎮ.4?1?5?8?8?5?? 0ꆾ?.ꎮ1?8?1?3?6?0?? ???ꎮ????????ꎮ??????????ꎮ???????ꆾꆿꎮ???????1 O. 181360 1 ?ꎮ????ꎮ???????ꆾꆿꎮ????????ꎮ????ꎮ????????ꎮ????????ꎮ?????ꎮ?????????ꎮ??????? 。. 0?ꎮ.9?? ?0ꎮ.4?2?0?0?3?3?? 0??.ꎮ1?6?7?7?4?9?? ?0ꎮ.9?? 0?.ꎮ4?1?5?8?7?3?? ?0ꎮ.1?6?9?5?2?1? ?0?ꎮ.9?? 0?ꎮ.4?0?9?6?8?7?? O?.ꎮ ?1?6?54?0?7?? ?ꎮ????ꎮ????????ꎮ????????ꎮ????ꎮ????????ꎮ????????ꎮ????ꎮ????????ꎮ??????? O. 162422 ?ꎮ???ꎮ????????ꎮ????????ꎮ???ꎮ????????ꎮ????????ꎮ???ꎮ????????ꎮ??????? O. 155522 O. 159324 O. 152561 O?.ꎮ 7?5? ??0ꎮ.4?2?6?2?5?4?? O?ꆿ.ꎮ 1?5?0?0?3?5?? ?Oꎮ. ?75? ?0?.ꎮ4?1?5?8?5?4?? ?ꎮ????????ꎮ????ꎮ???ꎮ??????ꎮ??????? O. 75 O. 146726 O?.ꎮ 7?? ?0ꎮ.4?2?8?3?2?8?? ?O?.ꎮ 1?4?5?0?2?9?? ?O.ꎮ ?7? 0?ꎮ.4?1?5?8?4?8?? ?O.ꎮ 1??51??0?9?9? O?.ꎮ 7?? 0?ꎮ.4?0?0?3?9?0?? O?.ꎮ ?1?41?3?4?8?? 0?ꎮ.6?5?? ?0ꎮ.4?3?0?4?0?1?? O?.ꎮ ?1?40?5?6?6?? ?0ꎮ.6?5?? ?0ꎮ.4?1?5?8?4?2?? O?ꎮ. 1??4?7?8?3?3? 0?ꎮ.6?5?? 3?9?4?1?9?1?? ?O.ꎮ ?1?3?64?8?3?? 0?ꎮ.6?? ?ꎮ????????ꎮ????????ꎮ???ꎮ????????ꎮ????????ꎮ???ꎮ?????????ꎮ??????? O. 145184 0??.ꎮ5?5?? ?0ꎮ.4?3?4?5?4?9?? 0?.ꎮ1?3?3?4?1?8?? ?0.ꎮ5?5?? 0?.ꎮ5?1?8?8?2?9?? ?0.ꎮ1?4?3?1?8?7?? 0?ꎮ.5?5?? 0?ꎮ.3?8?7?9?9?3?? O?.ꎮ 1?2?8?5?1?4?? ?0.ꎮ5?? 0?ꎮ.4?3?6?6?2?2?? ?0.ꎮ1?3?0?8?5?2?? 0?ꎮ.5?? 0?.ꎮ4?1?5?8?2?3? ??ꎮ????????ꎮ???ꎮ????????ꎮ??????? O. 125523 평뇭?뿉볻ꎬ?튻?쪱닰럖헐뇪뗄닉릺돉놾뗄??Jo?u?r?n?a?l? o?f? ?Ec?o?n?o??mi?c ?S?u?r?v?e??ys?,ꎬ 1??9?9?9.ꎬ ?Vo?l?.ꎮ1?3?,ꎬ ?No?v? ?3?.ꎬ ?2?2?7~?2?8?5?.? 由表1可见，m=2时拆分招标的采购成本的均뻹值횵大듳于폚整헻体쳥招헐标뇪的뗄采닉购릺成돉本놾的뗄均뻹值횵，ꎬ쟒且拆닰分럖招헐?뇪뗄닉릺돉놾뗄뻹횵쯦?횵뗄복킡뛸퓶듳ꎬ쇭췢??R?es??e?a?r?c?h? ?o?n? ?th?e?? ?nu?r?n?b?e?r? ?o?f? s?u??pp?l??i?er?s?? 标的采购成本的均值随α值的减小而增大，另外닉릺돉놾뗄랽닮쯦?뗄복킡뛸복킡ꎬ헢쮵쏷닰럖?i?n?? s?p??l?it?-??a?w?a?r?d? ?au??ct?i?o?ns?? 来购成本的方差随α的陆小而减小，这说明拆分招헐标뇪能쓜够릻降붵뗍低采닉购릺成돉本놾的뗄风럧险쿕;ꎻ?m튻=3?ꎬ，?m=튻4?时쪱拆닰??Go?n?g?? ?Xi?u?ji?n ??Z?h?ou?? ?R?on??g? 分럖招헐뇪标的뗄采닉릺购돉成놾本的뗄均뻹值횵小킡于폚整헻体쳥招헐标뇪的뗄采닉购릺成돉??A?b?s?t?r?a?c?tꎺ,? I??n? m?a?n?y?? ?pr??oc?u??re?m?e?n??t? p??ra?c?t?i?c?e?s.ꎬ ?th?e?? ?bu?y??e?r? 本놾的뗄뻹均值횵，ꎬ쟒且닰拆럖分헐招뇪标뗄的닉采릺购돉成놾本的뗄뻹均值횵随쯦?α值횵??????????????????????????????????????????????????????????splits h s requirement into two contracts and awards them to 뗄的减복킡小而뛸복睹킡小，ꎬ쇭另췢外닉采릺购돉成놾本뗄的랽方닮差也튲随쯦α?的뗄减복??di?f?f?e?r?e?n?t ?su?p?p?l?i?er?s?.ꎮ T?h?e?? ?pr?i?m??ar?y?? c??o?n?tr??a?c?t? a?n??d? t?h??e? ?se?c??o?nd??a?ry?? 小킡而뛸减복킡小，ꎬ헢这쮵说쏷明닰拆럖分헐招뇪标붵降뗍低닉采릺购돉成놾本的뗄同춬时쪱???????????????????????????????????????????????????????ꆪ?contract are awarded sequentiaIIy by using second-price auc›能쓜够릻붵降뗍低닉采릺购成돉本놾的뗄风럧险쿕，ꎬ틲因듋此此듋时쪱应펦该룃选톡用폃拆닰?t?i?on?.ꎮ T?h?e?r?e?? a?r?e? ??su?p?p?l?i?e?r?s? w?h?o?? p??a?rt?i?c?ip??a?t?e? t?h??e? a?u?c??t?io??n? ?of? ?pr?i?ꆪ›?分럖헐招뇪标并늢且쟒拆닰分럖比뇈例샽α?应펦尽뺡可뿉能쓜小킡。ꆣ??????????????ꎮ?????????????????????????????????????ꆪ?mary contract. The existing of secondary contract can in›닎?뾼?컄?쿗??c?r?e?a?se?? ?ne?w?? s?u??pp?l?i?e?rs?? o??f? l?o?w? c?a?p??ac??i?ty?? t?o?? p??ar?t?i?c?i?p?a?t?e? ?t.ꎮ ?W?e? 参考立献?A?n??to?n.ꎬ J?.ꎮ ?an?d?? ?D.ꎮ Y??3 0?.ꎮ S?e?c?o?n?d?? S??o?u?rc??in?g?? a?n?d? ??th?e?? E?x?p?e?r?i?en?c?e? ???????????????????????????????????????????????????????formulate a model of sequential split-award auction and prove C?u?r?v?e?,ꎺ P?r?i?ce? ?C??o?m?p?e?ti?ti?o?n? ?in ?D??ef?en?s?e? ?P?r?o?c??u?re?m?e?n?t? [?J?]?.ꎮ R?A?N?D? ??t?ha?t? w??he?n?? ?a?nd?? s?a?t?i?sf? ?ed?? ?a ?c?e?r??ta??in?? ?in?e?qu??a?ti?o?n,ꎬ t?h??e? e?x??pe?c?t?e?d?? ?????????????????ꎬ????ꎬ?????ꎮ??????Journal of Ec()nomics. 1987. 18( 1). 57~76 ?????????????????????????????????????????????????????????procurement cost of sp!it-award auctions is less than that of ?2? ?A?n?to?n?,ꎬ J?.ꎮ ?an?d?? D?.ꎮ Y??ao?.ꎮ ?Sp?l?it? ?A?w?ar?d?s?.ꎬ ?Pr?o?c?u?r?e?m?e?n??t ?3n?d? ?l?nn?o?v??a›ꆪ??so??le?ꆪ-s??ou?r?c?e?? a?u?c?t? ?on?.ꎮ ?Fu??rt?h??er? m?o?r?e?,ꎬ ?th?e?? o??pt?i?m??a?l s?t?r?a?t?e?g?y?? o?n?? t?io?n? [?J?J?.ꎮ R??AN?D? ?J?(?)?ur?n?a?l? ?of? ?E?co?n?o?m??ic?s.ꎬ ?1?9?8?9.ꎬ 2??0?(?4?).ꎮ ?5?3?8ꆫ~ ????????????????????????????????????????????????????????????ꆪ?how to split the contract is discussed to help the buyer bene›?5?5?2? ???????ꎮ?fit more. ??䅮??ꎬ?ꎮ?????ꎮ奡?ꎮ???????????????????????䅵??????3 Ant()n, J. and D. Yao. Coordination in Split Award Auctions ?????????ꎺ??????????????????ꎬ???????????????????ꆪ????ꎮ??????????????????????????ꎬ????ꎬ???ꎬ???ꆫ???ꎮ?Key words, split-award auct on. the number of suppli›[JJ. Quarterly J()urnal of Economics, 1992. 107. 681~708 ????????????????????????????ꎺ?????????????????????????ꎮ????ꎬ????????????????ꎬ???????????????????ers, primary contract. secondary contract 4 Klemperer Paul. Auction Th四ry，A Guide ωthe Literature [JJ. .ꆤ s?s? .ꆤ?
