考慮雙邊風(fēng)險偏好的供應(yīng)鏈期權(quán)協(xié)調(diào)模型

蔡 鑫，孫靜春

考慮雙邊風(fēng)險偏好的供應(yīng)鏈期權(quán)協(xié)調(diào)模型

蔡 鑫1,2,3，孫靜春1,2,3

（1.西安交通大學(xué) 管理學(xué)院，陜西 西安，710049；2.西安交通大學(xué) 過程控制與效率工程教育部重點(diǎn)實(shí)驗(yàn)室，陜西 西安，710049；3.西安交通大學(xué) 機(jī)械制造系統(tǒng)工程國家重點(diǎn)實(shí)驗(yàn)室，陜西 西安，710049）

本研究針對供應(yīng)商和銷售商雙邊都具有風(fēng)險偏好的兩級供應(yīng)鏈系統(tǒng)，建立了由悲觀系數(shù)和風(fēng)險厭惡度兩個風(fēng)險偏好系數(shù)描述的基于M-CVaR（均值條件風(fēng)險價值）決策準(zhǔn)則的供應(yīng)鏈期權(quán)契約模型。首先根據(jù)銷售商的決策目標(biāo)函數(shù)推導(dǎo)了不同風(fēng)險偏好（風(fēng)險厭惡、風(fēng)險中性和風(fēng)險喜好）下的銷售商最優(yōu)總訂購量，分析了不同風(fēng)險偏好系數(shù)下銷售商最優(yōu)總訂購量的變化情況。然后，在考慮供應(yīng)商同樣具有風(fēng)險偏好的情況下，討論了銷售商和供應(yīng)商的風(fēng)險偏好對供應(yīng)鏈整體風(fēng)險偏好的影響，推出了供應(yīng)鏈整體在不同風(fēng)險偏好下的最優(yōu)訂購量。最后，給出了銷售商和供應(yīng)鏈整體不同風(fēng)險偏好組合下供應(yīng)鏈的協(xié)調(diào)條件，并通過算例分析了風(fēng)險偏好系數(shù)對銷售商訂購策略及供應(yīng)鏈整體風(fēng)險偏好的影響。研究表明：（1）M-CVaR準(zhǔn)則下，期權(quán)契約能夠協(xié)調(diào)雙邊都具有風(fēng)險偏好的供應(yīng)鏈，而且還能提高供應(yīng)鏈的最優(yōu)訂購量；（2）考慮雙邊風(fēng)險偏好時，供應(yīng)鏈整體的風(fēng)險偏好類型由供應(yīng)商和銷售商的風(fēng)險偏好共同決定，供應(yīng)鏈協(xié)調(diào)條件同時受到供應(yīng)商和銷售商的風(fēng)險偏好系數(shù)的影響。

供應(yīng)鏈協(xié)調(diào)；雙邊風(fēng)險偏好；均值-CVaR；期權(quán)契約

0 引言

經(jīng)濟(jì)的全球化及科技的迅速發(fā)展使得當(dāng)今的商業(yè)環(huán)境充滿了不確定性。為了增強(qiáng)在這種環(huán)境中的競爭力，公司必須提升靈活應(yīng)對市場環(huán)境變化的能力。尤其是經(jīng)營采購提前期較長而銷售周期較短的易逝品的企業(yè)，其承受的需求不確定風(fēng)險更大。為了對沖訂購量過高或過低帶來的風(fēng)險，銷售商通常會選擇少批量多批次地從上游制造商訂貨。而這種不規(guī)則的訂購策略大大增加了制造商的成本，給制造商帶來了巨大的壓力。由此，則會造成渠道合作伙伴之間的沖突，降低渠道效率。為了解決這個問題，一種有效的方法是設(shè)計激勵契約使得銷售商能靈活地應(yīng)對需求的變化，避免給制造商過大的壓力。期權(quán)契約是當(dāng)前比較常見的一種供應(yīng)鏈契約形式，它不僅能很好地對沖市場上的價格風(fēng)險而且在實(shí)踐中具有較強(qiáng)的可操作性，因此被廣泛應(yīng)用在供應(yīng)鏈協(xié)調(diào)中[1-3]。但是，如果將風(fēng)險偏好的特性引入到供應(yīng)鏈的決策機(jī)制中，那么之前在風(fēng)險中性條件下能夠?qū)崿F(xiàn)供應(yīng)鏈協(xié)調(diào)的契約也許會失效。而現(xiàn)實(shí)生活中，各種不確定因素往往會使得供應(yīng)鏈上的決策者表現(xiàn)出某種風(fēng)險偏好的特性。近年來，M-CVaR(Mean Conditional Value at Risk)由于能更加完整和客觀地描述決策者的風(fēng)險偏好而受到了管理者和學(xué)者們的青睞。例如，美國的Timberland公司采用M-CVaR來控制其資產(chǎn)投資組合的風(fēng)險，發(fā)現(xiàn)相比于傳統(tǒng)的VaR工具，M-CVaR能更好地控制投資風(fēng)險[4]。另外，許多學(xué)者也證明了M-CVaR能更完整地反映決策者的風(fēng)險偏好情況[5-7]。因此，本文在供應(yīng)商和銷售商雙邊都具有風(fēng)險偏好特性的基礎(chǔ)上，借助M-CVaR和期權(quán)契約研究成員不同風(fēng)險偏好組合下供應(yīng)鏈的最優(yōu)決策以及協(xié)調(diào)條件具有較大的實(shí)際意義和理論價值。

近年來，期權(quán)作為金融市場中最重要的風(fēng)險對沖工具逐漸被運(yùn)用到供應(yīng)鏈的風(fēng)險管理中來，它的優(yōu)勢是使企業(yè)能更靈活的應(yīng)對外界環(huán)境的變化。期權(quán)合約中涉及的與需求相關(guān)的信息讓供應(yīng)商能更加合理地安排生產(chǎn)計劃，而銷售商則可以通過期權(quán)提前確定未來采購的商品的價格，避免過分依賴現(xiàn)貨市場[8]。在很多行業(yè)中采購方都會利用期權(quán)合約進(jìn)行采購[9]，如著名的科技公司惠普(HP)有超過三分之一的零部件是利用期權(quán)契約采購的。Barnes-Schuster[1]是最早討論如何通過期權(quán)契約協(xié)調(diào)供應(yīng)鏈的學(xué)者，她的研究表明期權(quán)契約可以為銷售商提供良好的靈活性以應(yīng)對市場需求的不確定性，并能實(shí)現(xiàn)供應(yīng)鏈的協(xié)調(diào)。Zhao等[10]在一個包含制造商和零售商的兩級供應(yīng)鏈中，探討了如何設(shè)置雙向期權(quán)契約使供應(yīng)鏈實(shí)現(xiàn)協(xié)調(diào)。上述研究都是在風(fēng)險中性假設(shè)的基礎(chǔ)上進(jìn)行的，而在現(xiàn)實(shí)生活中，不確定性往往會使得決策者表現(xiàn)出一定的風(fēng)險偏好特性。于是，Chen等[11]在零售商風(fēng)險規(guī)避的條件下研究了如何用期權(quán)契約來協(xié)調(diào)一個二級供應(yīng)鏈，并發(fā)現(xiàn)風(fēng)險規(guī)避下零售商的最優(yōu)訂購量比風(fēng)險中性時低。岳朝龍[12]則在農(nóng)戶風(fēng)險規(guī)避的條件下，研究了農(nóng)產(chǎn)品供應(yīng)鏈的期權(quán)契約協(xié)調(diào)問題。除了下游企業(yè)的風(fēng)險偏好外，還有的學(xué)者關(guān)注了上游企業(yè)風(fēng)險偏好對供應(yīng)鏈協(xié)調(diào)的影響。田立平[13]在供應(yīng)商風(fēng)險規(guī)避的情形下引入期權(quán)契約機(jī)制對組裝供應(yīng)鏈進(jìn)行了協(xié)調(diào)。李剛[14]在需求不確定情況下研究了由風(fēng)險規(guī)避的供應(yīng)商和占主導(dǎo)地位的零售商組成的二級供應(yīng)鏈的協(xié)調(diào)問題。然而，無論是研究上游企業(yè)還有下游企業(yè)的風(fēng)險偏好特性，都忽略了供應(yīng)鏈成員同時具有風(fēng)險偏好的情況。李劍鋒[15]在集成商和供應(yīng)商都是風(fēng)險規(guī)避的情況下探討了期權(quán)契約對物流服務(wù)供應(yīng)鏈的協(xié)調(diào)作用。劉英[16]在現(xiàn)貨交易和期權(quán)采購的條件下研究了風(fēng)險厭惡型供應(yīng)商和零售商組成的最優(yōu)定價和訂貨決策問題。

基于上述分析可知，現(xiàn)有的關(guān)于供應(yīng)鏈期權(quán)契約的研究大多是在風(fēng)險中性假設(shè)下進(jìn)行的，也有部分文獻(xiàn)考慮了供應(yīng)鏈某一方具有風(fēng)險規(guī)避特性的情況。事實(shí)上，供應(yīng)鏈上各成員在面對現(xiàn)實(shí)中的各種不確定因素時通過都會表選出某種風(fēng)險偏好（風(fēng)險規(guī)避、風(fēng)險中性、風(fēng)險喜好）的特性[17]。此時，契約對供應(yīng)鏈的協(xié)調(diào)作用也會因?yàn)槌蓡T風(fēng)險偏好的特性而發(fā)生變化[18]。因此，研究如何測度供應(yīng)鏈成員不同的風(fēng)險偏好類型，并通過數(shù)學(xué)模型描述風(fēng)險偏好的變化是非常有必要的。

供應(yīng)鏈風(fēng)險測度方面，Choid等[19]研究了單個供應(yīng)鏈決策者采用均值-方差（M-V）目標(biāo)時的供應(yīng)鏈渠道協(xié)調(diào)問題。龐衛(wèi)宏[20]借助均值-方差方法研究基于產(chǎn)品生命周期的供應(yīng)鏈定價決策問題。因?yàn)榫捣讲罘ú粷M足一致性條件且對目標(biāo)函數(shù)要求較為嚴(yán)格，所以其實(shí)用性較差。很多學(xué)者也采用了VaR（風(fēng)險價值）工具對決策者風(fēng)險進(jìn)行了測度，但由于VaR存在一致性問題以及對尾部損失的測度不從發(fā)，容易導(dǎo)致優(yōu)化結(jié)果出現(xiàn)較大誤差。于是，Rockafellar和Uryasev提出了比VaR更一致的風(fēng)險度量方法—CVaR（條件風(fēng)險價值），并證明了其在實(shí)際運(yùn)用中的便捷性。由此，CVaR得到了學(xué)者們的廣泛關(guān)注。Li等[25]考慮了一個由風(fēng)險中性的供應(yīng)商和風(fēng)險厭惡的零售商組成的雙渠道供應(yīng)鏈，并基于CVaR測度工具和風(fēng)險分擔(dān)契約研究了雙渠道供應(yīng)鏈的協(xié)調(diào)問題。葉飛[26]借助CVaR模型研究了一類由風(fēng)險規(guī)避農(nóng)戶和風(fēng)險中性公司組成的農(nóng)產(chǎn)品供應(yīng)鏈的協(xié)調(diào)問題。CVaR測度工具的缺陷在于其過于關(guān)注尾部的風(fēng)險損失，使得決策比較保守[4,27]。Jammernegg和Kischka[5,28]基于CVaR提出了M-CVaR（均值條件風(fēng)險價值）測度工具，并構(gòu)建了一個具有兩個風(fēng)險參數(shù)的目標(biāo)函數(shù)，這個目標(biāo)函數(shù)可以描述管理者的風(fēng)險中性、風(fēng)險規(guī)避和風(fēng)險喜好三種特性。Xu和Li[29]運(yùn)用M-CVaR研究了一個風(fēng)險規(guī)避下的庫存模型。Gao等[30]探討了均值CVaR準(zhǔn)則中的聯(lián)合庫存決策問題。上述關(guān)于M-CVaR的應(yīng)用研究主要集中在供應(yīng)鏈的訂購或庫存決策方面，而針對M-CVaR測度下的供應(yīng)鏈協(xié)調(diào)問題則比較少。

綜上所述，為了完善當(dāng)前的研究，本文以供應(yīng)商和銷售商都具有風(fēng)險偏好的二級供應(yīng)鏈為對象，在期權(quán)契約及M-CVaR測度下，研究了銷售商在不同風(fēng)險偏好下的最優(yōu)訂購策略問題以及雙邊風(fēng)險偏好下的供應(yīng)鏈協(xié)調(diào)問題。文章主要解決以下四個問題：

（1） M-CVaR測度下，不同風(fēng)險偏好下銷售商的最優(yōu)訂購策略分別是什么，風(fēng)險偏好的變化對最優(yōu)訂購策略有什么影響？

（2）期權(quán)契約對銷售商的最優(yōu)訂購策略有什么影響？

（3）銷售商和供應(yīng)商的風(fēng)險偏好類型對供應(yīng)鏈整體的風(fēng)險偏好類型有什么影響？

（4）銷售商和供應(yīng)鏈整體不同風(fēng)險偏好組合下供應(yīng)鏈的協(xié)調(diào)條件是什么？

1 問題描述及假設(shè)

此外，本文還做如下假設(shè)：

（2）一旦銷售期開始后，銷售商無法通過其他的途徑來補(bǔ)充庫存；

（3）銷售商向供應(yīng)商購買商品期權(quán)沒有數(shù)量上的限制；

（4）供應(yīng)商不允許缺貨，必須保證供應(yīng)銷售商所訂購的商品量；

2 銷售商的決策模型

2.1 CVaR及M-CVaR模型

CVaR最早由Rockafellar和Uryase[19,20]提出并證明了其可用于度量風(fēng)險規(guī)避的程度。通常假設(shè)CVaR的一般化定義公式為：

CVaR的不足在于只度量了收益較低的部分，忽略了高收益的部分，這導(dǎo)致了決策目標(biāo)過于保守。鑒于此，本文引入了M-CVaR測度工具，M-CVaR是低于某一分位數(shù)收益的期望值和高于某一分位數(shù)收益的期望值的凸組合，因此M-CVaR的度量公式可以寫為：

參考(1)式，式(3)的定義也可表示成：

令

于是有：

2.2 基于M-CVaR測度的銷售商期權(quán)契約模型

將式(11)代入到式(7)中可以得到M-CVaR測度下銷售商的決策函數(shù)：

定理1：在期權(quán)契約及M-CVaR測度下，銷售商的最優(yōu)現(xiàn)貨訂購量和最優(yōu)期權(quán)訂購量存在并且唯一。

證明略。

根據(jù)式(13)可以推出銷售商在不同風(fēng)險偏好下的最優(yōu)總訂購量的表達(dá)式，如定理2所示。

定理2：

證明略。

推論1

3 供應(yīng)鏈整體風(fēng)險偏好及決策模型

表1 時，銷售商和供應(yīng)商的風(fēng)險偏好類型對供應(yīng)鏈整體風(fēng)險偏好類型的影響

表2 時，銷售商的風(fēng)險偏好類型對供應(yīng)鏈整體風(fēng)險偏好類型的影響

表3 時，供應(yīng)商的風(fēng)險偏好類型對供應(yīng)鏈整體風(fēng)險偏好類型的影響

結(jié)合式(16)供應(yīng)鏈整體的收益函數(shù)，采用與分析銷售商最優(yōu)訂購策略相同的方法可得供應(yīng)鏈整體在不同風(fēng)險偏好類型下的最優(yōu)訂購量，具體如定理3所示。

定理3：

證明：參考定理2的證明過程。

4 供應(yīng)鏈協(xié)調(diào)分析

定理4：銷售商和供應(yīng)鏈整體不同風(fēng)險偏好組合下供應(yīng)鏈的協(xié)調(diào)條件為：

表4 時，銷售商和供應(yīng)鏈不同風(fēng)險偏好組合下供應(yīng)鏈的協(xié)調(diào)條件

（2）當(dāng)時，供應(yīng)鏈的協(xié)調(diào)條件如表5所示。

表5 時，銷售商和供應(yīng)鏈不同風(fēng)險偏好組合下供應(yīng)鏈的協(xié)調(diào)條件

表6 表4和5中各符號所代表的式子

表6（續(xù)） 表4和表5中各符號所代表的式子

證明：結(jié)合定理2和定理3可證。

5 算例分析

圖1 變化對銷售商最優(yōu)訂購策略的影響（=0.7）

圖2 變化對銷售商最優(yōu)訂購策略的影響（=0.8）

圖3 和變化對供應(yīng)鏈整體風(fēng)險偏好系數(shù)的影響

圖4 變化對供應(yīng)鏈整體風(fēng)險偏好系數(shù)的影響

6 結(jié)語

現(xiàn)有的供應(yīng)鏈協(xié)調(diào)的研究在考慮決策者的風(fēng)險偏好時，往往采用方差、VaR或CVaR來測度決策者的風(fēng)險偏好，但這些測度工具要么不滿足一致性風(fēng)險度量準(zhǔn)則的公理要求，要么并不能完整地刻畫決策者的不同風(fēng)險偏好。基于此，本文通過引入一種改進(jìn)的CVaR風(fēng)險度量準(zhǔn)則—M-CVaR風(fēng)險測度來刻畫決策者的風(fēng)險偏好，以銷售商和供應(yīng)商都具有風(fēng)險偏好的二級易逝品供應(yīng)鏈為對象，在期權(quán)契約框架下建立了基于M-CVaR準(zhǔn)則的銷售商和供應(yīng)鏈整體的決策模型，分析了銷售商和供應(yīng)商的風(fēng)險偏好類型對供應(yīng)鏈整體風(fēng)險偏好類型的影響，并給出了銷售商和供應(yīng)鏈整體不同風(fēng)險偏好組合下供應(yīng)鏈的協(xié)調(diào)條件。

文章的主要結(jié)論有：（1）M-CVaR風(fēng)險測度下，當(dāng)銷售商表現(xiàn)出風(fēng)險規(guī)避時，其最優(yōu)總訂購量的表達(dá)式存在三種情況，當(dāng)銷售商表現(xiàn)出風(fēng)險喜歡時，其最優(yōu)總訂購量的表達(dá)式存在兩種情況，當(dāng)銷售商為風(fēng)險中性時，其最優(yōu)總訂購量的表達(dá)式只有一種情況；（2）考慮M-CVaR測度時，銷售商在無契約協(xié)調(diào)下的最優(yōu)總訂購量小于期權(quán)契約協(xié)調(diào)下的最優(yōu)總訂購量，但大于期權(quán)契約下銷售商的最優(yōu)現(xiàn)貨訂購量；（3）考慮雙邊風(fēng)險偏好時，供應(yīng)鏈整體的風(fēng)險偏好類型取決于銷售商和供應(yīng)商的影響力，若銷售商（供應(yīng)商）的影響系數(shù)為零，則供應(yīng)鏈整體的風(fēng)險偏好情況與供應(yīng)商（銷售商）一致，若兩者的影響系數(shù)都不為零，則供應(yīng)鏈整體的風(fēng)險偏好情況介于兩者之間；（4）雙邊風(fēng)險偏好下，銷售商和供應(yīng)鏈整體不同風(fēng)險偏好組合下供應(yīng)鏈的協(xié)調(diào)條件也不同，且協(xié)調(diào)條件同時受到銷售商和供應(yīng)商風(fēng)險偏好系數(shù)的影響。

本文討論了期權(quán)契約對雙邊風(fēng)險偏好供應(yīng)鏈的協(xié)調(diào)，那么其他常見的契約形式（收益共享契約、回購契約等）能否協(xié)調(diào)該類型的供應(yīng)鏈？這也是值得進(jìn)一步探討的問題。

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The supply chain option contract coordination model with bilateral risk preferences

CAI Xin1,2,3，SUN Jingchun1,2,3

（1. School of management, Xi’an Jiaotong University, Xi’an, 710049, China;2. Key Laboratory of Process Control & Efficiency Engineering (Xi’an Jiaotong University), Ministry of Education, Xi’an, 710049, China;3. State Key Laboratory for Manufacturing Systems Engineering (Xi’an Jiaotong University), Xi’an, 710049, China）

The globalization of economy and the rapid development of science and technology have made the current business environment full of uncertainty. In order to enhance competitiveness in this environment, companies must enhance their ability to flexibly respond to the changes of market environment. This is particularly true for enterprises dealing with perishable goods with comparatively long production lead- times and short selling seasons and subject to high demand uncertainty. In order to hedge against the risk associated with over- and under-ordering, retailers usually have to order less but more frequently from their upstream firms such as manufacturers so that they can well accommodate demand volatility. Such an order policy, however, exerts great pressure on the manufacturers because it requires them to have flexible capacity to cater for the irregular orders, which results in an increase in the manufacturers’ costs. As a result, it will lead to conflict between channel partners and reduce channel efficiency. To solve this problem, an effective approach is to design incentive contracts that enable retailers to respond flexibly to changes in demand and avoid undue pressure on manufacturers. In all forms of contract, the option contract has attracted the attention of scholars thanks to its good flexibility and risk-sharing, and has been proved to be effective in resolving the channel conflicts described above (Barnes-Schuster et al., 2002; Zhao et al., 2010). However, when considering the risk preferences of decision makers, the decision criteria of the supply chain members changed, and the contract that originally coordinated the risk-neutral supply chain tended to lose efficacy. Therefore, under the option contract, it is of certain academic and practical significance to discuss the influence of different risk preferences (risk aversion, risk neutral and risk appetite) of decision makers on the optimal strategies of supply chain members and supply chain coordination.

This paper studies the coordination problem of a two-stage supply chain whose retailer and supplier are both risk preferences under option contract. Firstly, aiming at the disadvantages of CVaR, the M-CVaR model which is described by two risk preference parameters-pessimism coefficient and degree of risk averse was put forward. Then, the retailer’s objective function based on the M-CVaR (mean conditional value at risk) was established under option contract, the retailer’s optimal total order quantity under different risk preferences was derived, and the effect of the two risk preference parameters on retailer’s optimal total order quantity was analyzed. Next, the effect of the retailer’s and supplier’s risk preferences on the centralized supply chain’s risk preference was discussed in the case of considering the supplier’s risk preference, and the centralized supply chain’s optimal order quantity under different risk preferences was also obtained. After that, the coordination conditions of supply chain under different risk preference combinations of the retailer and centralized supply chain were provided. Finally, the impact of risk preference parameters on retailer’s optimal ordering strategy and the centralized supply chain’s risk preference are discussed through calculating examples.

The main conclusions of this paper are: (1) Under the M-CVaR criterion, the option contract can coordinate the supply chain with bilateral risk preference, and also can improve the optimal order quantity of the supply chain. (2) When considering the M-CVaR measure, the optimal total order quantity of the seller under the contract free coordination is smaller than the optimal total order quantity under the option contract coordination, but larger than the optimal spot order quantity of the seller under the option contract; (3) when the retailer (the centralized supply chain) shows risk neutral, risk appetite or risk aversion, the optimal total order quantity of the retailer (the centralized supply chain) have one, two or three situations respectively; (4) When considering bilateral risk preference, the type of risk preference of the whole supply chain depends on the influence of the seller and the supplier. If the influence coefficient of the seller (Supplier) is zero, the risk preference of the whole supply chain is the same as that of the supplier (Supplier). If both influence coefficients are not zero, the risk preference of the whole supply chain is between the two; (5) when considering the bilateral risk preferences, the risk preference type of the centralized supply chain is determined by the supplier’s and retailer’s risk preferences, the coordination conditions of supply chain are different under different risk preference combinations of retailer and centralized supply chain, and the coordination conditions of the supply chain is affected by the risk preference parameters of the supplier and the retailer.

Supply chain coordination; Bilateral risk preference; Mean-CVaR; Option contract

F274

A

1004-6062(2020)06-0128-010

10.13587/j.cnki.jieem.2020.06.013

2018-04-10

2020-05-29

Supported by the National Science Foundation of China (71372164)

2018-04-10

2020-05-29

國家自然科學(xué)基金資助項(xiàng)目（71372164）

蔡鑫（1990—），男，江西南昌人；西安交通大學(xué)管理學(xué)院博士研究生；研究方向：供應(yīng)鏈風(fēng)險管理。

中文編輯：杜 健；英文編輯：Boping Yan