沈建男，邵曉峰

生產(chǎn)不確定下資金約束供應(yīng)鏈的運(yùn)營(yíng)決策研究

沈建男，邵曉峰

（上海交通大學(xué)安泰經(jīng)濟(jì)與管理學(xué)院，上海 200030）

研究由單一零售商與單一制造商組成的單渠道供應(yīng)鏈，其中資金約束制造商的生產(chǎn)不確定以及生產(chǎn)能力有限，同時(shí)供應(yīng)鏈中企業(yè)雙方交易存在多種付款方式可供選擇。首先以生產(chǎn)確定且不同付款方式下的供應(yīng)鏈最優(yōu)運(yùn)營(yíng)決策與期望收益為基準(zhǔn)；其次討論生產(chǎn)不確定且不同付款方式情形，從而提出資金約束供應(yīng)鏈最優(yōu)付款方式的選擇策略，通過(guò)對(duì)比分析討論生產(chǎn)不確定性、生產(chǎn)能力等因素對(duì)供應(yīng)鏈最優(yōu)決策與最優(yōu)期望利潤(rùn)的影響。研究表明：生產(chǎn)能力較大時(shí)，零售商與制造商有非常相近的最優(yōu)付款選擇；生產(chǎn)能力較小時(shí)，通過(guò)收益共享契約實(shí)現(xiàn)供應(yīng)鏈雙方付款方式上的統(tǒng)一。而且，生產(chǎn)不確定與有限生產(chǎn)能力總體上約束了零售商的訂購(gòu)量，但其中生產(chǎn)能力較少時(shí)，不確定性反而增加了訂購(gòu)量；并且制造商采取了更加保守的運(yùn)營(yíng)策略，同時(shí)減少了雙方的期望收益。最后，通過(guò)算例分析驗(yàn)證了相關(guān)研究結(jié)論。

資金約束；生產(chǎn)不確定；有限生產(chǎn)能力；運(yùn)營(yíng)決策；最優(yōu)付款選擇

0 引言

供應(yīng)鏈運(yùn)營(yíng)中面臨資金約束時(shí)企業(yè)往往不能執(zhí)行最優(yōu)決策，如上游制造商存在資金不足而生產(chǎn)產(chǎn)量出現(xiàn)短缺導(dǎo)致下游零售商會(huì)出現(xiàn)供應(yīng)中斷的風(fēng)險(xiǎn)。資金約束不僅影響到供應(yīng)鏈中一方成員的利潤(rùn)，而且還會(huì)影響到供應(yīng)鏈上游或下游成員的運(yùn)營(yíng)決策，最終導(dǎo)致供應(yīng)鏈各方以及整體供應(yīng)鏈利潤(rùn)的減少。同時(shí)，上游制造商受原材料、自然環(huán)境、生產(chǎn)工藝等因素影響，承擔(dān)著生產(chǎn)不確定性的風(fēng)險(xiǎn)，如中藥飲片的原材料中草藥的種植過(guò)程中就會(huì)受到外界天氣等不確定因素的影響，Health Industry Distributors Association[1]數(shù)據(jù)顯示2004-2005年流感時(shí)節(jié)，疫苗生產(chǎn)企業(yè)Chiron 工廠由于污染減產(chǎn)五百萬(wàn)支疫苗。

在單階段模型中，權(quán)衡庫(kù)存的主要方式有下游企業(yè)觀察到需求之前訂貨，即下游企業(yè)承擔(dān)全部庫(kù)存風(fēng)險(xiǎn)。同時(shí)破解上游企業(yè)資金不足的難題，首先是銀行等金融機(jī)構(gòu)的融資服務(wù)，其次是Petersen和Rajan[2]提出了交易信用的內(nèi)部融資方式在解決企業(yè)資金不足時(shí)就有廣泛的應(yīng)用，交易信用也能夠減少企業(yè)對(duì)銀行外部融資的需求與依賴(lài)。那么，在實(shí)際應(yīng)用交易信用作為供應(yīng)鏈內(nèi)部融資中，最典型的方式有兩類(lèi)：（1）延期付款，為了緩解下游企業(yè)的資金短缺，供應(yīng)鏈采用由下游企業(yè)在產(chǎn)品銷(xiāo)售期末所得收益后向上游企業(yè)支付貨款；（2）提前付款，為了支持資金短缺的上游企業(yè)的生產(chǎn)，下游企業(yè)在產(chǎn)品生產(chǎn)前向上游企業(yè)預(yù)先支付貨款。因此，包括準(zhǔn)時(shí)付款方式，運(yùn)用交易信用的內(nèi)部融資實(shí)際上又豐富了企業(yè)間交易中支付貨款的方式。在實(shí)踐中，沃爾瑪向供應(yīng)商支付貨款的方式有四種：貨到后按賬期結(jié)算、月底結(jié)算、貨到付款、預(yù)付款；物美集團(tuán)對(duì)上游制造商或供應(yīng)商的結(jié)算貨款的方式也有四種：預(yù)付貨款，貨到付款的現(xiàn)結(jié)，按賬期支付的銀行匯款，承兌匯票付款。另外醫(yī)藥零售行業(yè)的雷允上、禮安、海王星辰在采購(gòu)中藥飲片時(shí)也有提前付款，延期付款等多種付款形式，以此保障貨源穩(wěn)定或者充盈的現(xiàn)金流。

在理論研究中，有關(guān)資金約束供應(yīng)鏈的運(yùn)營(yíng)決策研究。首先是有關(guān)資金約束供應(yīng)鏈在對(duì)外融資中的運(yùn)營(yíng)決策：第一是運(yùn)營(yíng)與銀行融資的聯(lián)合決策，其中企業(yè)利用存貨質(zhì)押，應(yīng)收賬款質(zhì)押進(jìn)行銀行融資下的運(yùn)營(yíng)決策有Dunham[3]，朱文貴，朱道立等[4]，魯其輝等[5]研究了存貨需求隨機(jī)波動(dòng)時(shí)，銀行的最優(yōu)質(zhì)押率決策問(wèn)題。第二是有關(guān)資金約束且銀行融資策略影響下企業(yè)生產(chǎn)、庫(kù)存、訂貨等決策問(wèn)題：Lai, Debo和Sycara[6]研究了當(dāng)供應(yīng)商和零售商都存在資金約束，需要向金融機(jī)構(gòu)借款時(shí)，預(yù)訂模式、寄售模式和組合模式對(duì)供應(yīng)鏈績(jī)效的影響，論文從供應(yīng)商的角度證明了組合模式是最佳；Kouvelis和Zhao[7]研究了當(dāng)存在破產(chǎn)成本時(shí)，資金約束的零售商向銀行貸款，其自有資金和抵押物對(duì)最優(yōu)融資和訂貨決策，以及供應(yīng)商的定價(jià)問(wèn)題。

其次關(guān)于資金約束供應(yīng)鏈在交易信用中的運(yùn)營(yíng)研究，第一，研究了延期付款下供應(yīng)鏈的運(yùn)營(yíng)、激勵(lì)與協(xié)調(diào)等問(wèn)題，如Babich和Tang[8]分析了當(dāng)供應(yīng)商供貨存在產(chǎn)品質(zhì)量風(fēng)險(xiǎn)時(shí)，下游買(mǎi)方利用延期付款方式可有限制約風(fēng)險(xiǎn)，并激勵(lì)供應(yīng)商保證產(chǎn)品質(zhì)量。Zhang et al.[9]分析了在延期付款條件下零售商時(shí)存在破產(chǎn)風(fēng)險(xiǎn)時(shí)，制造商配送量可能會(huì)小于零售商的訂購(gòu)量，而且會(huì)小于供應(yīng)鏈系統(tǒng)最優(yōu)訂購(gòu)量。第二，以延期付款作為內(nèi)生變量與激勵(lì)工具來(lái)研究供應(yīng)鏈協(xié)調(diào)。Luo[10]證明了延期付款信用期激勵(lì)機(jī)制是一種不等價(jià)于數(shù)量折扣的新的供應(yīng)鏈激勵(lì)機(jī)制；陳祥鋒[11]研究了供應(yīng)商為資金約束的零售商提供延期付款貿(mào)易信用的供應(yīng)鏈協(xié)調(diào)問(wèn)題，研究表明當(dāng)零售商存在破產(chǎn)風(fēng)險(xiǎn)且承擔(dān)有限責(zé)任時(shí)，延期付款能有效激勵(lì)零售商增加采購(gòu)量。第三，研究供應(yīng)鏈內(nèi)部延期付款與銀行外部借款的交互問(wèn)題。如Fabbri和Menichini[12]認(rèn)為供應(yīng)商相對(duì)于銀行來(lái)說(shuō)，具有信息優(yōu)勢(shì)和流動(dòng)性?xún)?yōu)勢(shì)，因此供應(yīng)商有動(dòng)機(jī)向具有資金約束的下游企業(yè)提供延期付款信用；Kouvelis和Zhao[13]比較了有資金成本下的供應(yīng)商融資與銀行融資問(wèn)題，設(shè)計(jì)了最優(yōu)兩階段價(jià)格延期付款合同的結(jié)構(gòu)，研究表明在一定假設(shè)下，供應(yīng)商總是應(yīng)該以低于無(wú)風(fēng)險(xiǎn)利率的優(yōu)惠提供延期付款給零售商，最優(yōu)合同下零售商偏好于供應(yīng)商融資；Jing，Chen和Cai[14]，Jing和Seidmann[15]，Chen[16]研究表明制造商的單位生產(chǎn)成本決定了供應(yīng)鏈系統(tǒng)的策略均衡，當(dāng)制造商的單位生產(chǎn)成本較低時(shí)，供應(yīng)鏈系統(tǒng)唯一的均衡為交易信用，反之，供應(yīng)鏈系統(tǒng)唯一的均衡是銀行融資。

再次，有關(guān)提前付款條件下的供應(yīng)鏈運(yùn)營(yíng)決策與協(xié)調(diào)，如Babich[17]分析了當(dāng)供應(yīng)商出現(xiàn)債務(wù)危機(jī)時(shí)，制造商向供應(yīng)商提供財(cái)務(wù)補(bǔ)貼的融資模式，研究了制造商的聯(lián)合能力預(yù)訂和財(cái)務(wù)補(bǔ)貼決策；Swinney和Netessine[18]研究當(dāng)供應(yīng)商存在破產(chǎn)風(fēng)險(xiǎn)時(shí)，兩階段需求下制造商在第二階段面臨破產(chǎn)的供應(yīng)商時(shí)，在轉(zhuǎn)換供應(yīng)商與向供應(yīng)商提供轉(zhuǎn)移支付融資之間的選擇問(wèn)題；Thangam[19]研究了預(yù)付款和交易信用下供應(yīng)鏈中易逝品的最優(yōu)價(jià)格折扣和批量訂貨策略; Mateut和Zanchettin[20]研究了預(yù)付款和交易信用之間的關(guān)系，研究表明大多數(shù)企業(yè)中二者是替代關(guān)系，但也有些類(lèi)型的企業(yè)中二者是互補(bǔ)關(guān)系。王文利和駱建文[21]研究了零售商提前支付與外部融資的對(duì)比分析，提出了供應(yīng)鏈最優(yōu)生產(chǎn)與融資決策。

在資金約束供應(yīng)鏈運(yùn)營(yíng)策略研究中，大多文獻(xiàn)假設(shè)制造商生產(chǎn)確定以及不考慮其生產(chǎn)能力的限制，而且是單一付款方式下資金約束零售商的運(yùn)營(yíng)決策。較少討論多種付款方式并存，以及生產(chǎn)不確定且生產(chǎn)能力有限下，資金約束制造商如何通過(guò)批發(fā)價(jià)激勵(lì)策略、零售商如何確定最優(yōu)訂購(gòu)量以及供應(yīng)鏈雙方最優(yōu)付款方式的選擇條件、制造商的生產(chǎn)不確定與有限生產(chǎn)能力如何影響供應(yīng)鏈運(yùn)營(yíng)策略。因此，基于企業(yè)實(shí)際交易過(guò)程中普遍存在的多種付款方式、制造商生產(chǎn)不確定與生產(chǎn)能力有限為背景，零售商在銷(xiāo)售期前訂購(gòu)產(chǎn)品，資金約束制造商根據(jù)不同付款方式?jīng)Q策批發(fā)價(jià)折扣或利率等策略。本文基于不同付款方式，首先討論了生產(chǎn)確定且生產(chǎn)能力有限下的運(yùn)營(yíng)決策，其次分析了生產(chǎn)不確定且生產(chǎn)能力有限的情形，從而得到資金約束供應(yīng)鏈最優(yōu)付款方式的選擇條件，得出提前付款有助于資金約束制造商解決生產(chǎn)資金不足的困境。并且以生產(chǎn)確定下運(yùn)營(yíng)決策是基礎(chǔ)，進(jìn)一步分析生產(chǎn)不確定性、生產(chǎn)能力等因素對(duì)供應(yīng)鏈運(yùn)營(yíng)決策的影響。

1 問(wèn)題描述與模型假設(shè)

表1 符號(hào)含義

2 生產(chǎn)確定下的資金約束供應(yīng)鏈運(yùn)營(yíng)決策

本節(jié)在生產(chǎn)確定下分別討論了準(zhǔn)時(shí)付款，提前付款，延期付款下的資金約束供應(yīng)鏈運(yùn)營(yíng)決策。提出了不同生產(chǎn)規(guī)模下的制造商的批發(fā)價(jià)折扣與利率策略，以及零售商的最優(yōu)訂購(gòu)策略，從而得到供應(yīng)鏈雙方的最優(yōu)期望收益。

2.1 提前付款下的運(yùn)營(yíng)決策

根據(jù)決策順序，具體如表2所示。

表2 提前付款且生產(chǎn)確定下的供應(yīng)鏈最優(yōu)運(yùn)營(yíng)策略與期望利潤(rùn)

2.2 準(zhǔn)時(shí)付款下的運(yùn)營(yíng)決策

表3 準(zhǔn)時(shí)付款且生產(chǎn)確定下供應(yīng)鏈最優(yōu)運(yùn)營(yíng)策略與期望利潤(rùn)

2.3 延期付款下的運(yùn)營(yíng)決策

根據(jù)決策順序，采用逆向求解供應(yīng)鏈各方的策略均衡，可得運(yùn)營(yíng)策略與最優(yōu)期望收益如表4、5所示。

表4 延期付款且生產(chǎn)確定下的供應(yīng)鏈最優(yōu)運(yùn)營(yíng)策略

表5 延期付款且生產(chǎn)確定下的供應(yīng)鏈最優(yōu)期望利潤(rùn)

3 生產(chǎn)不確定下的資金約束供應(yīng)鏈運(yùn)營(yíng)決策

本節(jié)分別討論生產(chǎn)不確定且不同付款方式下的資金約束供應(yīng)鏈運(yùn)營(yíng)決策。提出了不同生產(chǎn)規(guī)模下的制造商的批發(fā)價(jià)折扣與利率策略，以及零售商的最優(yōu)訂購(gòu)策略，從而得到供應(yīng)鏈雙方的最優(yōu)期望收益。

3.1 提前付款下的運(yùn)營(yíng)決策

根據(jù)決策順序，采用逆向求解供應(yīng)鏈各方的策略均衡，得如下命題。

表6 提前付款且生產(chǎn)不確定下的供應(yīng)鏈最優(yōu)期望利潤(rùn)

3.2 準(zhǔn)時(shí)付款下的運(yùn)營(yíng)決策

表7 準(zhǔn)時(shí)付款下供應(yīng)鏈最優(yōu)運(yùn)營(yíng)策略與期望利潤(rùn)

3.3 延期付款下的運(yùn)營(yíng)決策

根據(jù)決策順序，采用逆向求解供應(yīng)鏈各方的策略均衡，得如下命題。

命題3：當(dāng)生產(chǎn)不確定且延期付款下，供應(yīng)鏈雙方的最優(yōu)運(yùn)營(yíng)決策為：

其中

表8 延期付款下的供應(yīng)鏈雙方最優(yōu)期望利潤(rùn)

3.4 最優(yōu)付款方式的選擇

從命題4可以得出，無(wú)論市場(chǎng)批發(fā)價(jià)、生產(chǎn)成本、市場(chǎng)價(jià)格上限之間的關(guān)系如何，以及任意生產(chǎn)不確定參數(shù)的分布函數(shù)，當(dāng)生產(chǎn)能力都較大時(shí)，零售商的最優(yōu)付款方式為提前付款。因?yàn)楫?dāng)生產(chǎn)能力較大，零售商能采購(gòu)到最優(yōu)訂購(gòu)量，通過(guò)提前付款獲得批發(fā)價(jià)折扣，能夠最大化自身收益；而對(duì)于制造商，當(dāng)生產(chǎn)能力較大且訂購(gòu)量較大時(shí)，通過(guò)提前付款交易信用的供應(yīng)鏈內(nèi)部融資能有效緩解生產(chǎn)所需的資金；當(dāng)生產(chǎn)成本與批發(fā)價(jià)相差較小時(shí)，則會(huì)偏向延期付款提高批發(fā)價(jià)。另一方面，當(dāng)生產(chǎn)能力較低時(shí)，零售商的最優(yōu)付款方式為提前付款或準(zhǔn)時(shí)付款，資金約束制造商希望的最優(yōu)付款方式為延期付款。因?yàn)?，生產(chǎn)能力較低時(shí)零售價(jià)會(huì)更高，零售商希望提前付款獲得更多穩(wěn)定的訂購(gòu)量，以此會(huì)獲取更多收益。但生產(chǎn)能力較低時(shí)制造商則不會(huì)提供批發(fā)價(jià)折扣，同準(zhǔn)時(shí)付款的批發(fā)價(jià)相同，那么，零售商會(huì)選擇提前付款或準(zhǔn)時(shí)付款。對(duì)于制造商來(lái)說(shuō)，有限的生產(chǎn)能力能夠最大限度的提升市場(chǎng)批發(fā)價(jià)，資金約束制造商在延期付款下制定批發(fā)價(jià)利率等于融資利率，不僅把增加的邊際生產(chǎn)成本轉(zhuǎn)嫁到零售商，還可以從高批發(fā)價(jià)中獲取更多單位期望收益，因此，制造商會(huì)選擇延期付款。另外，提前付款能為制造商解決生產(chǎn)資金，是制造商次優(yōu)的付款方式。具體見(jiàn)表9。

表9 生產(chǎn)不確定下資金約束供應(yīng)鏈最優(yōu)付款方式

4 生產(chǎn)不確定與容量對(duì)運(yùn)營(yíng)決策的影響

4.1 提起付款下生產(chǎn)不確定的影響

通過(guò)對(duì)比表2與表6可得提前付款下生產(chǎn)不確定的影響。

4.2 準(zhǔn)時(shí)付款下生產(chǎn)不確定的影響

通過(guò)對(duì)比表3與表7可得準(zhǔn)時(shí)付款下生產(chǎn)不確定的影響為：

由于制造商按照市場(chǎng)批發(fā)價(jià)銷(xiāo)售，可以獲得穩(wěn)定的單位收益，通過(guò)對(duì)比生產(chǎn)確定與生產(chǎn)不確定時(shí)的供應(yīng)鏈運(yùn)營(yíng)決策與期望收益，可得：當(dāng)生產(chǎn)能力較大時(shí)，在生產(chǎn)不確定時(shí)的訂購(gòu)量等于生產(chǎn)確定時(shí)，但供應(yīng)鏈雙方的期望收益要小于生產(chǎn)確定時(shí)，生產(chǎn)不確定首先引起了供應(yīng)鏈雙方利潤(rùn)的減少；其次，當(dāng)生產(chǎn)能力較小時(shí)，零售商在生產(chǎn)不確定時(shí)訂購(gòu)量要大于生產(chǎn)確定時(shí)，同時(shí)供應(yīng)鏈雙方期望收益與生產(chǎn)不確定參數(shù)的分布緊密相關(guān)。

4.3 延期付款下生產(chǎn)不確定的影響

通過(guò)對(duì)比表4、5與表8可得提前付款下生產(chǎn)不確定的影響。

4.4 生產(chǎn)能力對(duì)運(yùn)營(yíng)決策的影響

通過(guò)與有限生產(chǎn)能力下運(yùn)營(yíng)決策相比較，可得：當(dāng)準(zhǔn)時(shí)付款下，生產(chǎn)能力有限同樣減少了零售商的訂購(gòu)量、供應(yīng)鏈雙方的期望收益。準(zhǔn)時(shí)付款下，當(dāng)市場(chǎng)批發(fā)價(jià)與生產(chǎn)成本相差較大時(shí)，生產(chǎn)能力的限制同樣使制造商很可能不提供折扣，零售商只能以最低訂購(gòu)量進(jìn)行采購(gòu)，并且都會(huì)降低供應(yīng)鏈雙方的最優(yōu)期望利潤(rùn)；但當(dāng)生產(chǎn)成本與市場(chǎng)批發(fā)價(jià)相差較小時(shí)，生產(chǎn)能力對(duì)制造商的批發(fā)價(jià)折扣沒(méi)有影響，都以最高市場(chǎng)批發(fā)價(jià)出售，但生產(chǎn)能力的下降會(huì)減少零售商的訂購(gòu)量。延期付款下，當(dāng)生產(chǎn)成本與市場(chǎng)批發(fā)價(jià)相差較大或中等時(shí)，生產(chǎn)能力的下降使制造商會(huì)制定最高的延期付款利率，零售商減少訂購(gòu)量，供應(yīng)鏈雙方的期望收益也不斷減少；但當(dāng)生產(chǎn)成本與市場(chǎng)批發(fā)價(jià)相差較小時(shí)，生產(chǎn)能力對(duì)制造商運(yùn)營(yíng)決策沒(méi)有影響，但零售商會(huì)降低訂購(gòu)量。

5 數(shù)值分析

圖1 提前付款下的供應(yīng)鏈運(yùn)營(yíng)決策與期望利潤(rùn)對(duì)比分析（）

圖2 提前付款下的供應(yīng)鏈運(yùn)營(yíng)決策與期望利潤(rùn)對(duì)比分析（）

圖3 延期付款下的供應(yīng)鏈運(yùn)營(yíng)決策與期望利潤(rùn)對(duì)比分析（）

圖4 延期付款下的供應(yīng)鏈運(yùn)營(yíng)決策與期望利潤(rùn)對(duì)比分析（）

圖5 延期付款下的供應(yīng)鏈運(yùn)營(yíng)決策與期望利潤(rùn)對(duì)比分析（）

6 總結(jié)

本文分析了單個(gè)制造商與單個(gè)零售商組成的供應(yīng)鏈，其中制造商生產(chǎn)不確定、生產(chǎn)能力有限且存在資金約束；零售商采購(gòu)資金充足，且采取在銷(xiāo)售期來(lái)臨之前向制造商訂購(gòu)并承擔(dān)全部庫(kù)存壓力。同時(shí)，供應(yīng)鏈雙方交易過(guò)程中存在多種付款方式可供協(xié)商選擇（如提前付款；延期付款；準(zhǔn)時(shí)付款），制造商針對(duì)不同的付款方式提出批發(fā)價(jià)激勵(lì)策略：提前付款下的批發(fā)價(jià)折扣、延期付款的批發(fā)價(jià)利率或準(zhǔn)時(shí)付款則按照市場(chǎng)批發(fā)價(jià)銷(xiāo)售；然后零售商在銷(xiāo)售期之前選擇訂購(gòu)量，生產(chǎn)不確定證實(shí)后制造商生產(chǎn)并向零售商進(jìn)行配送；零售商以市場(chǎng)價(jià)格銷(xiāo)售獲取收益。本文基于不同付款方式重點(diǎn)分析了生產(chǎn)確定與生產(chǎn)不確定時(shí)的運(yùn)營(yíng)決策，提出供應(yīng)鏈成員最優(yōu)付款方式的選擇，討論生產(chǎn)不確定、有限生產(chǎn)能力對(duì)運(yùn)營(yíng)決策及期望利潤(rùn)的影響。

研究表明：第一，生產(chǎn)能力較大時(shí)：零售商的最優(yōu)付款方式時(shí)提前付款，制造商的最優(yōu)付款方式很大可能也是提前付款，雙方達(dá)到了統(tǒng)一；而當(dāng)生產(chǎn)能力較小時(shí)：零售商的最優(yōu)付款方式是提前付款或準(zhǔn)時(shí)付款，而制造商的最優(yōu)付款方式是延期付款，次優(yōu)是提前付款，最差時(shí)準(zhǔn)時(shí)付款，雙方在付款方式上存在矛盾，而通過(guò)收益共享契約合同可以實(shí)現(xiàn)生產(chǎn)能力較小時(shí)供應(yīng)鏈雙方付款方式的統(tǒng)一。第二，生產(chǎn)不確定性與有限生產(chǎn)能力減少零售商訂購(gòu)量，制造商執(zhí)行更加保守的批發(fā)價(jià)策略，同時(shí)也減少供應(yīng)鏈雙方的期望利潤(rùn)；

本文有關(guān)制造商的生產(chǎn)能力沒(méi)有考慮成本，而且單階段決策。因此未來(lái)的研究方向：（1）考慮制造商擴(kuò)大生產(chǎn)能力時(shí)需要支付一定的成本；（2）通過(guò)供應(yīng)鏈雙方的契約合同使得在生產(chǎn)容量較小時(shí)，協(xié)調(diào)供應(yīng)鏈雙方付款方式；（3）零售商或供應(yīng)鏈雙方都存在資金約束供時(shí)的最優(yōu)運(yùn)營(yíng)決策與最優(yōu)付款方式的選擇；（4）多階段的資金約束供應(yīng)鏈運(yùn)營(yíng)決策。

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Research on operational strategies for capital-constrained supply chains with yield random

SHEN Jiannan, SHAO Xiaofeng

(Antai College of Management, Shanghai Jiao Tong University, Shanghai, 200030)

The manufacturer’s financial constraint may lead to unsmooth production. Thus, the downstream firm will face the risk of supply shortages or supply disruption in the supply chain operation, which the firms cannot make optimal decisions, and their profit decrease rapidly. Especially the manufacturer produces under limited production capacity, and the actual output is subject to a random production yield, which further restricts the firms’ decisions. Bank financing and trade credit are commonly used to release financial constraint. As being lack of full business information and avoiding financial risks, the bank may afford a finite credit size. Trade credit, mainly including advance payment and delayed payment, is the business credit between supply chain enterprises or between supply chain enterprises and their customers. Besides punctual payment, trade credit enriches the payment terms between firms. But recently, many studies about the capital-constrained supply chain mainly discussed the optimal decision-making under one payment term and analyzed how to choose the optimal financial channel to solve the limited capital for the retailer. Little research considered that the capital-constrained manufacturer had limited production capacity and random yield under different payment terms.

Under stochastic yield and appropriate financial services, a capital-constrained manufacturer with a traditional partner (i.e., a retailer) sold her products with an exogenously fixed wholesale price. The basic model was classical single-period make-to-order framework under different payments. So the retailer prebooked quantity before the period of selling, and retailer price was a linear function of demand. Without loss of generality, the manufacturer’s initial capital was zero. To keep a successful operation in the supply chain, the manufacturer had a strong incentive as wholesale price discount to advanced payment. But if the retailer implemented delay payment, the manufacturer must be a borrower and announced interest rate of per unit wholesale price to the retailer. Also, because of limited production capacity, the optimal order could not always be satisfied. From the percept of maximizing the profit of enterprises, the model of the operational decision was constructed with different payments. First, this paper took the bench of optimal operational decision and profits under deterministic yield and analyzed them under random yield. Second, according to comparative results under different scenarios, the influences of random yield and limited capacity were proposed.

In the first part, we respectively discuss the optimal strategy and expected revenue under deterministic yield or random yield. So we study the advanced payment scenario that retailer orders quantity and pays the money before producing, and then manufacturer executes a wholesale price discount. Furthermore, we discuss the punctual payment scenario, which product delivering, and financial transactions take place simultaneously. The third scenario, which the manufacturer announces wholesale price with an interest rate replying to delay payment, is analyzed. Using Stackelberg model and backward approach, we respectively show the retailer’s optimal preorder quantity and manufacturer’s optimal discount rate or interest rate under limited production capacity. Calculation formulas of optimal profits are also given. Main results show that the manufacturer will make a heavy discount when capacity and wholesale price is all high so that the retailer will order more quantity, but the discount will be always zero when the wholesale price is low, and whatever capacity is. Also, the rate will be zero when capacity and wholesale price are all high, and the rate will ascend when the wholesale price is intermediate, but the rate will be the highest when the wholesale price is low and whatever capacity is.

In the second part, this study separately compares the retailer’s optimal profits, and manufacturer’s under different payment terms. The result shows that the retailer will choose advanced payment or punctual payment under stochastic yield. Also, we establish the conditions that the manufacturer chooses the optimal payment terms based on production capacity. So when the capacity is high, the manufacturer chooses advanced payment. When the capacity is low, the manufacturer chooses delay payment. The optimal payment between retailer and manufacturer is partly identical under the same conditions. When a coordination contract is designed under low capacity, revenue sharing not only partly coordinates optimal payment terms between retailer and manufacturer under lower capacity but also can improve their profit performance.

In the third part, we further explore the influence of random yield or limited production capacity on operational strategy. The results show that yield random or limited capacity restricts retailer’s ordering. The manufacturer takes a more conservative operating strategy, such as a lower discount or higher rate of the wholesale price. These strategies can reduce their expected revenue. Finally, a numerical example is used to verify the results.

In summary, a manufacturer can use internal financing (i.e., advanced payment) to ease capital pressure when capacity is high. The retailer has the incentive to provide financing to the manufacturer. This conclusion is consistent with prior research. Further, the study under low capacity complements the existing research, and the interesting result is that the capital-constrained manufacturer will prefer external financing when capacity is lower. However, this paper only considers one period and symmetrical information. Asymmetrical information about the capital, multi-period operation will be a direction for future research.

Capital constraint; Yield random; Limited capacity; Operational strategy; Optimal choice of payment terms

2017-06-06

2017-11-02

Supported by the National Natural Science Foundation of China (71372106)

C93

A

1004-6062(2020)01-0210-013

10.13587/j.cnki.jieem.2020.01.023

2017-06-06

2017-11-02

國(guó)家自然科學(xué)基金資助項(xiàng)目（71372106）

沈建男（1981—），男，江蘇蘇州人；上海交通大學(xué)安泰經(jīng)濟(jì)與管理學(xué)院博士后；研究方向：供應(yīng)鏈金融。

中文編輯：杜 ??；英文編輯：Charlie C. Chen