基于公平关切和互惠社会偏好的供应链契约和协调研究
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摘要
运作管理(OM)一直是业界和学界关注的焦点,传统研究大多是建立在决策者完全理性或可被引导向理性行动的理想假设之上。然而,实践中存在许多复杂性、不确定性因素,人在这种情形下往往是“有限理性”的。有限理性具体表现在诸多行为倾向上,典型的如参考点依赖与损失规避、公平关切等。许多行为实验或实证研究证实了这些行为倾向的存在,进而发现现实决策常常偏离传统规范性理论的结论。鉴于在判断和决策的心理学理论、行为经济学以及实验经济学等方面的杰出工作,Daniel Kahneman和Vernon L.Smith在2002年被授予诺贝尔经济学奖,这一重要事件表明行为决策理论开始在经济学中占有重要位置,越来越受到学者们的关注,并不断挑战着传统的经济理论。许多经济学、市场营销等领域的学者己尝试在研究中考虑行为因素,并取得了显著进展,然而直至最近,行为因素与OM的融合研究仍处于初级阶段,此研究的深入开展有望形成一套完整的理论方法体系,即“行为运筹”,这无疑是OM领域发展的新契机。
为了引起学界对行为运筹的深层关注,美国运筹管理学会(INFORMS)创办的领域顶级期刊如MS, OR, MSOM于近两年频繁刊发行为运筹相关研究成果,08年第4期的MSOM甚至为此开辟专辑。目前行为运筹研究成果和所涉议题仍相对较少,且主要是由Wharton商学院、Harvard商学院和Berkeley Haas商学院等少数几家研究机构的知名学者撰写,但这些成果基本都集中发表在近两年的上述顶级期刊上。国内诸多研究机构和科研管理部门也开始高度关注此领域的研究。这充分说明：行为运筹研究尚处起步阶段,具有良好的研究前景和重要的理论价值。
纵观现有文献,目前针对供应链契约的行为研究刚刚兴起,己取得了一定进展。Schweitzer和Cachon(2000)最早对批发价契约下的报童问题展开行为研究,通过行为实验他们发现零售商会对高利润产品订购偏少,而对低利润产品订购偏多。他们分别建立了风险规避、风险爱好、损失规避报童模型,但仍未能很好解释实验发现。Wang(?)Webster(2009)进一步发展了损失规避报童模型发现：如果考虑缺货成本,零售商订货量在损失规避情况下会比传统报童模型中要多,且随批发价递增而随零售价递减。Ho(?)Zhang(2008)采用实验方法检验了标准报童背景下的二部定价与数量折扣契约,发现了有悖于传统研究结果的两个“异常”,进一步研究发现,参考点依赖可以较好地解释这些异常。此外,Ho和Zhang(2008)还进一步考虑了公平关切情形,建立了公平关切效用函数研究了两种契约的效果。Cui(2008)等将公平关切行为倾向引入报童背景下研究其对供应链契约协调的影响。传统研究认为批发价契约无法实现协调。而Cui等却研究发现：如果供应链成员关注公平,那么供应商就可以通过高于其边际成本的批发价契约促成协调。
不过现有研究只涉及到供应链契约中较少议题,尚未构成体系；即便在所涉议题上也尚欠深入,基本都是将简单刻画的决策者行为倾向嵌入标准报童背景中讨论,而很少考虑现实中供应链结构以及行为因素的复杂性。
本论文研究围绕OM领域中的热点问题-供应链契约与协调展开行为研究,探讨典型行为倾向在决策过程中的具体表现,重点分析公平关切和互惠社会偏好的影响方式,揭示其作用机理和规律,并加以形式刻画。进而构建与供应链实际特征相吻合的效用度量体系,对传统供应链契约与协调分析模型作行为修正,建立描述性的行为运筹模型。论文考虑典型行为倾向在供应链契约与协调中的现实影响,能在一定程度上克服传统供应链契约研究的不足,使模型更精细地描述现实。
行为运作管理(BOM)的一个重要特征在于,它是一个多种学科相结合的全新的研究领域,即包含了如参照点依赖、损失厌恶、后悔理论和社会偏好理论等行为因素,同时又在运作管理的大背景下研究问题。传统的经济学和运作管理问题对于决策主体都是基于“自利的经济人”假设,即他们只关心自己的利益得失,只是追求自身利润或是经济利益的最大化。这种假设下的理论在很多情形下可以很好的说明问题,但是在实验经济学的帮助下,越来越多的文献研究指出了现实的情形与“自利的经济人”假设存在系统性的偏差。在许多学科包括经济学、心理学、社会学、和医学研究中,行为实验都是研究人们行为因素的一种行之有效的研究方法。大量的实验结果表明,人们的选择往往没有最大化他们的经济回报,除了倾向于最大化自己的利润,他们还关心分配的公平性。在几个重要的行为实验,包括最后通牒博弈、独裁者博弈、礼物交换博弈、投资博弈以及信任博弈等都证明了人们存在公平社会偏好,而这个议题正是本论文研究的重点内容。
本论文主要研究在供应链管理中社会偏好对于决策者乃至整个供应链的影响,通过数学建模的方式研究了几种具有公平意味的典型社会偏好,主要包括不公平厌恶和互惠。对人类基本行为的数学建模研究,无论从个体层面还是人类社会的层面,都是始于经济学和社会学研究。例如,社会偏好模型关注于由于人们在社会交往中体现的行为偏差,典型的如人们往往不仅考虑自身的利益,还会关注其他个体的利益的公平偏好；参考点以及时间依赖的建模则关注于“个人的偏好分别在参考点和时间的作用下可以发生逆转”这一现象；对于文化的建模主要用于研究社会行为是如何发展的以及如何在人群中传播。
通过数学模型来研究行为的优势在于：首先,数学模型能够进行逻辑推演,便于形成严密的、系统的理论。现代运作管理问题往往涉及复杂的决策,决策之间有很多互相影响的变量或是参数,因此在没有模型的帮助下往往难以展开深入研究,也就难以形成系统的理论。其次,数学模型能够很好地指导行为实验研究,即一旦有了模型的描述,我们就可以基于模型,通过控制一些变量或是参数对相关问题进行实验设计和研究,这样不仅可以对模型进行检验,还可以带来新的研究问题,不断完善这一理论甚至整个领域的研究。许多传统的OM问题,例如报童问题、供应链契约与协调、牛鞭效应等都已经有了系统的、可用于分析的数学模型。正是这些数学模型使得许多传统的OM理论便于检验,同时通过模型参数的设置可以很容易地实现实验设计,也正是通过实验证明了传统的OM模型应用于实际还是不完善的。正如Loch和Wu(2007)指出的,“对传统的理性选择和博弈理论模型进行适当的扩展,将决策偏差、情感因素、社会偏好以及文化等纳入其中用数学建模的方式进行研究,可以在行为运作管理甚至更大的领域指导实证检验”
迄今为止关于公平偏好的建模可以分为两大类：基于结果导向的公平建模和基于意图导向的公平建模。前者倾向于通过比较两个或两个以上的行动结果来评价效用,而后者强调行动背后意图的重要性。行为经济学家往往把这两类公平偏好分别区分为“不公平厌恶偏好”和“互惠偏好”,并进行了建模研究,相应地建立了“不公平厌恶偏好”的效用函数和“互惠偏好”的效用函数。这两类模型的不同之处主要体现在以下两个方面：(1)在互惠模型中,同时考虑了结果和意图的影响,在不公平厌恶模型中,决策者只关注结果的比较。(2)在不公平厌恶模型中,只有当决策者看到了结果的不公平时才会惩罚对方。然而在互惠模型中,决策者回报或惩罚他们的对手更多地是基于对方的意图是否友好,而不仅仅只看结果。本论文的两部分核心内容就分别对应于这两种类型的公平建模,其中第三章属于基于结果导向的公平建模,第四章属于基于意图导向的公平建模。
概括来说,本论文的研究思路是：基于一些重要的行为实验中发现的,在传统理论中被忽视的典型社会偏好,如不公平厌恶和互惠,我们要把这些行为偏好引入到供应链背景来构建行为模型进行研究。通过深入细致的研究主要回答以下四个问题：(1)引入社会偏好之后的供应链系统的均衡会是什么样的?(2)传统供应链与加入社会偏好的行为供应链之间的差异体现在哪些地方?(3)引入的社会偏好是如何影响供应链成员的决策的?(4)引入社会偏好对于供应链渠道的协调会带来什么样的影响?因此,我的论文并不是通过实验发现新的社会偏好,而是将己知的、重要的社会偏好运用于特定的供应链背景或是对现有行为模型做进一步的发展。
围绕“将典型社会偏好引入供应链背景”这一主题,我们在论文的第一章阐明了本文的研究背景、研究方法、研究贡献以及论文结构之后,就进入了本文内容的主体部分,包括二、三、四章。第二章是文献回顾部分,我们详细回顾了与本文密切相关的一些重要理论,包括供应链管理理论、社会偏好理论、博弈论以及将社会偏好引入供应链方面的过往研究。其中供应链管理理论部分重点回顾了经典的报童模型及其相关扩展研究,另外还包括供应链契约设计与协调问题；社会偏好理论部分主要回顾了“公平关切”、“互惠”以及“地位寻求”这三种与本论文密切相关的行为偏好理论；博弈论则主要回顾了斯坦伯格博弈、纳什讨价还价博弈以及心里博弈这三种博弈理论及其扩展研究。在第三章,“纳什讨价还价解”被引入并作为决策双方各自所认为的公平参考标准,另外结合了具有“地位寻求”倾向的公平关切偏好对由一个供应商与一个零售商组成的简单批发价契约供应链在随机市场情形下进行了研究；第四章将最为主流的互惠理论引入供应链背景,重点研究”意图”因素对于决策双方以及整个供应链的影响,为了简化数学推导,这部分的供应链模型仍然采用由一个供应商和一个零售商组成的简单批发价契约供应链,但是与前一部分不同的是,这部分采用的是确定性市场情形。下面就简要介绍一下三、四两章的内容。
文章第三章内容的创新性与贡献在于首次将纳什讨价还价解作为公平参考点进行建模,从而以一个全新的视角来研究具有公平偏好的供应链优化和决策问题。公平参考点一直都是公平理论中的重要组成部分,然而以往的建模通常只是通过几个外生参数以“绝对公平”的方式对参考点进行简单地描述,对于某一特定决策主体而言,单位利益差异带来的效用影响是确定的,不受所处环境、对方的影响。而纳什讨价还价解却能更好描述个体的公平感知,它需要优化分析目标函数中的联合效用函数,即纳什积,显示了纳什解对双方的福利都很重视,不会鼓励一味追求自身利益而忽略对方的利益,所以它关注的是基于决策双方相对实力与贡献的“相对公平”,因而更加符合现实。
纳什讨价还价公平关切模型背景如下：考虑由一个供应商和一个零售商组成的二级供应链系统,零售商向供应商批发某种商品,并将其以某个高于批发价的零售价卖给消费者；零售商所面临的是一个随机市场环境,即市场需求量是一个随机变量；供应商和零售商进行类斯坦伯格博弈,批发价和订货量分别为供应商和零售商的决策变量。此问题与传统研究的最大不同在于假设供应链双方均具有公平关切社会偏好,并以纳什讨价还价解作为双方的公平参考点。值得注意的是,供应商和零售商之间的纳什讨价还价过程虽然未必真实存在,但决策主体都会综合考虑到各方实力与贡献形成公平的心理参考点。这个心理参考点也不会是具体分得多少利润,而是会通过纳什讨价还价形成一个公平的比例,据此对双方博弈之后形成的任何总利润进行分配,双方所得都将会是互相认为公平的结果。零售商和供应商的效用函数均由两部分组成：利润项和公平关切效用项。效用项等于公平关切参数乘以决策人自己所得利润与公平参考点之差。
基于以上决策双方的效用函数,我们根据标准斯坦伯格博弈的分析方式以效用最大化为决策准则求出了供应商和零售商的均衡决策。最后,我们对于得到的均衡解进行了深入地分析,包括模型中的关键参数对于均衡解的影响、行为均衡解与传统均衡解之间的比较以及引入具有”地位寻求”倾向的公平关切行为因素后的供应链协调情况,得到了一些重要的管理启示和结论。
在第四章中我们尝试研究考虑意图因子的互惠供应链。考虑互惠因素比只考虑公平因素更进了一步。具体表现在以下两个方面：第一,如果只是在供应链中考虑公平,那么意味着决策人关注的只是结果,而忽略了一个非常重要的因素-意图。我们在很多时候不仅仅关注结果,还要看对方采取某个行动的意图何在,如果对方是有意而为之,则毫无疑问,不管结果如何,决策人都有动机采取惩罚措施予以还击；相反,如果对方是好心办坏事,或者说对方做出某些决定是无奈之举,则可以被理解(也即决策人站在同样的立场上也很有可能选择这个策略),当结果可能对决策人来说不是太好的时候,他也很有可能不会采取措施制裁对方。第二,在考虑公平因素的情况下,只有决策人能够通过采取惩罚措施降低这种不公平的时候,他才会采取某个措施。而在互惠情况下,决策人是通过所感知的友好与否来决定是否惩罚对方的,如果感知对方友好,则会互惠对方,如果感知对方不友好,则会惩罚对方,而与是否能够降低不公平并没有直接关系。
这部分内容的创新性与贡献在于：大量的行为实验不仅证明了传统的”经济人”假设不符合现实,而且也指出单靠基于结果的公平关切仍不足以描述所有的决策规则。因此,我们有必要把一些重要的心理因素,例如意图或者动机,融入供应链背景进行研究,因为它们对决策有不可忽略的影响。我们首次从心理博弈的视角研究供应链问题,在公平偏好的基础上突出意图这一重要心理因素的影响。
互惠模型仍旧考虑由一个供应商和一个零售商组成的二级供应链系统。零售商从供应商处批发某种产品,然后制定高于批发价的零售价卖向市场。供应商和零售商之间进行类斯坦伯格博弈,供应商为领导者,零售商为追随者,前者和后者的决策变量分别为批发价和零售价。但是,由于模型计算上的复杂性,在此模型中,假设市场需求是价格的反函数。在Falk和] Fschbacher(2006)的模型框架基础上,文章建立和优化分析互惠关切供应链模型。
在此模型中,供应商和零售商分别想制定最优的批发价和零售价来最大化自己的效用。以零售商为例,它的效用函数主要由两部分组成,即利润项和互惠效用项。利润项即传统研究中唯一关注的项,互惠效用项即为加入互惠偏好之后多出的项,也是最为关键的部分。互惠效用项为四部分的乘积,它们是互惠关切参数,意图因子(或动机因子),结果项和互惠项。互惠关切参数为正数,体现了零售商对由互惠偏好所带来的效用的关注程度,即他认为互惠效用占其总效用的比例,它越大,则表示零售商相对来说越看重给对方奖励(对方对自己友好)或者惩罚对方(对方对自己不友好)而给自己带来的效用。意图因子大于0小于等于1,是用来衡量零售商感受到来自供应商友好与否明确度的量。有时候,在某一决策节点,决策人可以明确感受到对方对自己友好与否,即用1来表示,而有时候这种感觉较模糊,不是很清楚,这时候用某个大于0小于1的参数来表示。结果项可以帮助零售商判断当供应商选择某个策略之后,自己所得与期望所得的收益水平的差距,以此来判断供应商是否对自己友好：它大于0表示友好,相反则表示不友好。互惠项是用来衡量互惠行动的影响。零售商可以根据自己感知到的供应商是否友好来选择一个行动作为对供应商的奖励或者惩罚,它大于0表示对对方奖励,小于0表示对对方惩罚。供应商也根据类似的效用函数来优化自己的决策。
在决策双方的互惠效用函数基础上,我们首先按照Geanakoplos等(1989)的心理博弈分析范式,再根据标准斯坦伯格博弈的分析方式以效用最大化的决策准则求出了以下两种情形下的供应商和零售商的均衡决策,一是传统供应商VS互惠零售商；二是互惠供应商VS互惠零售商。然后,我们对于得到的均衡解进行了深入地分析,包括模型中的关键参数(如意图因子)对于均衡解的影响、行为均衡解与传统均衡解之间的比较以及引入互惠偏好后的供应链协调情况。同样得到了一系列重点的管理启示和结论。
结合三、四两章的内容,我们总结本论文重要的结论如下：
一、公平参考点对供应链协调有重要影响。在行为运作管理的研究中,对于参考点的研究引起了不少学者的兴趣,特别是在经典的公平理论中,参考点都是不可或缺的重要因素,女Fehr和Schmidt (1999)的公平理论中将其他决策主体的收益作为被考察决策主体的公平参考点；Bolton和Ockenfels(2000)的公平理论中将其他决策主体的收益的平均值作为被考察决策主体的公平参考点。在本文的第三章中,将纳什讨价还价解引入作为被考察决策主体的公平参考点,并且将其与具有“地位寻求”倾向的公平关切模型进行结合,在这部分我们得到了一个重要结论,即公平关切偏好的引入不会对协调条件产生影响,但对协调难度(即协调所须满足的外部参数空间)会产生显著影响。在本文的第四章中,我们采用“对方收益的若干倍”,而不是“对方的收益”作为被考察决策主体的公平参考点,从而引入两个重要的参照参数γ和μ,分别对应两个倍数。在这部分我们得到了一个重要结论：当γμ≤1(“和谐供应链”)时,供应链无法实现协调；而当γμ>1(“尖刻供应链”)时,简单批发价契约是有可能实现供应链协调的,而传统研究认为这种情况难以发生。
二、决策者行为背后的动机,即意图对供应链协调有着重要影响。在现实与实验中,研究人员发现许多现象即使用经典公平理论也无法很好的得到解释,原因在于决策人除了具有“结果导向”的公平关切外,还具有“动机导向”即意图的公平关切,于是在经典公平理论的基础上发展了含有意图因素的互惠理论,因此意图正是区别经典公平理论与互惠理论的关键因素。意图对供应链协调的影响在本文第四章就有很好的体现,在这部分中,“和谐供应链”的情形下,不存在意图的影响,此时我们只得到一种均衡解,而且该均衡解不能协调供应链；而在“尖刻供应链”的情形下,存在意图的影响,此时我们得到的四种均衡解,并且其中一种均衡解在一定条件下可以实现渠道协调。这意味着在供应链成员考虑意图之后,批发价契约可以协调简单二级供应链。
三、行为因素合作性的程度对供应链协调有重要影响。所谓“行为因素的合作性”是本文新加入的一种对于行为社会性的分类方式,简单的说,如果一种行为因素更多的考虑到他人,并在一定程度上照顾到他人的利益,那么我们就将这种行为归类为具有较高程度合作性的行为；反之,如果一种行为因素更多的还是考虑自己,并不愿意照顾到他人的利益,那么我们就将这种行为归类为具有较低程度合作性的行为。行为因素合作性的程度对供应链协调的影响可以结合本文的三、四两章关于公平供应链的协调讨论来说明。本文的第三章研究对于公平关切的刻画涉及到另一种行为因素,即“地位寻求”偏好,属于较低程度合作性的社会偏好,这体现在：相比于Fehr和Schmidt (1999)的公平模型,本文的公平关切效用部分只含有一项正向效用项,且具有单调递增性。这部分我们的结论是“无论决策目标是基于利润最大化还是效用最大化,在一定的参数环境下,传统的能够实现(不能实现)渠道协调的供应链契约在线性仿射变换下仍旧能够实现(不能实现)渠道协调”,由于我们研究的是批发价契约,在传统情形下不能协调,因此,地位寻求偏好的引入仍旧无法实现渠道协调。本文的第四章研究的行为因素是互惠,友好评价与互惠项的引入体现了其属于较高程度合作性的社会偏好,这部分我们的结论是在“尖刻供应链”的情形中并且具备一定参数条件下,传统批发价契约供应链可以实现渠道协调。
四、同一类型的行为参数对于供应链双方决策的影响存在明显的不同,并且传统供应链的斯坦伯格博弈中零售商由于后行动所带来的弱势地位有可能在引入社会偏好的行为供应链环境下得到改善。本论文第三章的结果显示,具有“地位寻求”倾向的公平关切程度对于供应链双方的决策影响显著不同：零售商的均衡订货量关于其自身的关切参数递减,而关于对方即供应商的关切参数递增；然而供应商的均衡批发价却相反,随着其自身的关切参数递增,而关于对方即零售商的关切参数递减。在第四章中,分析结果显示公平基准点与意图因子这两个行为因素对于供应链双方决策的影响也是完全不同的：零售商的公平基准点越高会使得双方的均衡价格都下降,然而供应商的公平基准点越高则会降低零售商的均衡定价,只对供应商自身的均衡批发价起到了抬高作用。另外,供应商的意图越明显,零售商的均衡定价就越高；然而当零售商的意图越明显时,却降低了供应商的均衡定价。
五、供应链双方同一类型的行为因素对于整个供应链效率的影响显著不同。本论文第三章的结果显示供应链双方的公平关切程度以及讨价还价能力对于整个供应链效率的影响显著不同。具体地,供应商的公平关切程度对于整个供应链效率的影响要比零售商的更为显著。另外,供应商讨价还价能力的提升会使得整个供应链效率下降,然而零售商讨价还价能力的提升则会改善整个供应链效率。第四章的分析结果显示,供应链双方的意图对于整个供应链效率的影响也是完全不同的,供应商决策意图越明显,整个供应链效率越低,然而零售商的决策意图越明显,却会提高整个供应链的效率。
This thesis studies how to incorporate social preferences, such as fairness concerns and reci-procity, into the context of operations management, especially the supply chain. Besides, the impacts of theses social preferences on the the supply chain's decisions and channel's efficiency are also investigated. Specifically, it focuses on four important questions:firstly, what are the equilibria after incorporating social preferences of fairness concerns and reciprocity? secondly, what are the differences between the conventional channel and the behavioral channel (e.g., fairness-concerned channel and reciprocal channel)? thirdly, how do these behavioral factors influence the decisions of the supplier and the retailer in the supply chain? finally, what ef-fects do these social preferences on the coordination of the channel? In order to answer these questions, two models of behavioral operations are formulated.
Newsvendor model for a dyadic supply chain with Nash bargaining fairness concerns is built first. In this model, a supplier plays Stackelberg game with a retailer under a frame of the newsbendor problem. Both of them are assumed to have the preferences of status seeking, which means they have the desires for a higher relative payoff compared with the other party's. Simultaneously, Nash bargaining solution is used as fairness reference to formally depict per-ceptively fair compromise, which is a new perspective to study fairness concerns in a supply chain. Our analysis shows that in a dyadic supply chain, the channel efficiency will decrease because of the preference for status seeking. The retailer's share will be larger when the supplier concerns fairness less, and the supplier's sensitivity to fairness plays a relatively more important role in alleviating double marginalization and improving the channel's efficiency. Additionally, another interesting managerial insight is concluded that fairness concerns will not change the status of channel coordination in certain conditions. More specifically, those contracts able (unable) to coordinate fairness-neutral supply chain, based on affine transformations with scale factors within certain ranges, still succeed (fail) to coordinate the fairness-concerned. Though the introduction of fairness concern into the supply chain will not change the conditions of coordination, it has great impact on the difficulty of coordinating the channel.
Then a dyadic channel in which the retailer or (and) the supplier has (have) a preference for reciprocity is investigated. The two players play Stackelberg game. When both of them have preferences for reciprocity, as the leader, the supplier makes optimal wholesale price to maximize her ("her" represents the supplier and "he" represents the retailer) utility which con-sists of profit term and reciprocal utility term. As the follower, the retailer determines his retail price as the best response to the supplier's optimal decision in order to maximize his utility. In this model, the factors, such as psychological game and intention, are introduced to the context of supply chain for the first time since the theory of reciprocity emphasizes the importance of intentions behind actions. Additionally, two scenarios were discussed:(1) the retailer has a preference for reciprocity while the supplier doesn't have;(2) both the retailer and the supplier have preferences for reciprocity. Each scenario may have several sub-scenarios since we are not sure which is greater, γμ or1. Thus, two kinds of supply chains, acrimonious supply chain if γμ>1and harmonious supply chain if γμ≤1, are discussed and analyzed in reciprocity model. Furthermore, equilibria are derived under the two scenarios and the existence and the uniqueness of the equilibria of different scenarios can be guaranteed. Finally, numerical ex-amples are conducted to study the impacts of major parameters on reciprocal equilibria. The results show that the reciprocal channel can be coordinated by using a constant wholesale price in the acrimonious supply chain, which implies that the problem of double marginalization is not necessary to be present all the time. However, it is impossible to coordinate the channel with a wholesale-price contract in the harmonious supply chain. The paper also shows that compared with traditional retail price, the retailer charges a lower retail price to reward the sup-plier's lower wholesale price and a higher retail price to punish the supplier's higher wholesale price in the harmonious supply chain.
为了引起学界对行为运筹的深层关注,美国运筹管理学会(INFORMS)创办的领域顶级期刊如MS, OR, MSOM于近两年频繁刊发行为运筹相关研究成果,08年第4期的MSOM甚至为此开辟专辑。目前行为运筹研究成果和所涉议题仍相对较少,且主要是由Wharton商学院、Harvard商学院和Berkeley Haas商学院等少数几家研究机构的知名学者撰写,但这些成果基本都集中发表在近两年的上述顶级期刊上。国内诸多研究机构和科研管理部门也开始高度关注此领域的研究。这充分说明：行为运筹研究尚处起步阶段,具有良好的研究前景和重要的理论价值。
纵观现有文献,目前针对供应链契约的行为研究刚刚兴起,己取得了一定进展。Schweitzer和Cachon(2000)最早对批发价契约下的报童问题展开行为研究,通过行为实验他们发现零售商会对高利润产品订购偏少,而对低利润产品订购偏多。他们分别建立了风险规避、风险爱好、损失规避报童模型,但仍未能很好解释实验发现。Wang(?)Webster(2009)进一步发展了损失规避报童模型发现：如果考虑缺货成本,零售商订货量在损失规避情况下会比传统报童模型中要多,且随批发价递增而随零售价递减。Ho(?)Zhang(2008)采用实验方法检验了标准报童背景下的二部定价与数量折扣契约,发现了有悖于传统研究结果的两个“异常”,进一步研究发现,参考点依赖可以较好地解释这些异常。此外,Ho和Zhang(2008)还进一步考虑了公平关切情形,建立了公平关切效用函数研究了两种契约的效果。Cui(2008)等将公平关切行为倾向引入报童背景下研究其对供应链契约协调的影响。传统研究认为批发价契约无法实现协调。而Cui等却研究发现：如果供应链成员关注公平,那么供应商就可以通过高于其边际成本的批发价契约促成协调。
不过现有研究只涉及到供应链契约中较少议题,尚未构成体系；即便在所涉议题上也尚欠深入,基本都是将简单刻画的决策者行为倾向嵌入标准报童背景中讨论,而很少考虑现实中供应链结构以及行为因素的复杂性。
本论文研究围绕OM领域中的热点问题-供应链契约与协调展开行为研究,探讨典型行为倾向在决策过程中的具体表现,重点分析公平关切和互惠社会偏好的影响方式,揭示其作用机理和规律,并加以形式刻画。进而构建与供应链实际特征相吻合的效用度量体系,对传统供应链契约与协调分析模型作行为修正,建立描述性的行为运筹模型。论文考虑典型行为倾向在供应链契约与协调中的现实影响,能在一定程度上克服传统供应链契约研究的不足,使模型更精细地描述现实。
行为运作管理(BOM)的一个重要特征在于,它是一个多种学科相结合的全新的研究领域,即包含了如参照点依赖、损失厌恶、后悔理论和社会偏好理论等行为因素,同时又在运作管理的大背景下研究问题。传统的经济学和运作管理问题对于决策主体都是基于“自利的经济人”假设,即他们只关心自己的利益得失,只是追求自身利润或是经济利益的最大化。这种假设下的理论在很多情形下可以很好的说明问题,但是在实验经济学的帮助下,越来越多的文献研究指出了现实的情形与“自利的经济人”假设存在系统性的偏差。在许多学科包括经济学、心理学、社会学、和医学研究中,行为实验都是研究人们行为因素的一种行之有效的研究方法。大量的实验结果表明,人们的选择往往没有最大化他们的经济回报,除了倾向于最大化自己的利润,他们还关心分配的公平性。在几个重要的行为实验,包括最后通牒博弈、独裁者博弈、礼物交换博弈、投资博弈以及信任博弈等都证明了人们存在公平社会偏好,而这个议题正是本论文研究的重点内容。
本论文主要研究在供应链管理中社会偏好对于决策者乃至整个供应链的影响,通过数学建模的方式研究了几种具有公平意味的典型社会偏好,主要包括不公平厌恶和互惠。对人类基本行为的数学建模研究,无论从个体层面还是人类社会的层面,都是始于经济学和社会学研究。例如,社会偏好模型关注于由于人们在社会交往中体现的行为偏差,典型的如人们往往不仅考虑自身的利益,还会关注其他个体的利益的公平偏好；参考点以及时间依赖的建模则关注于“个人的偏好分别在参考点和时间的作用下可以发生逆转”这一现象；对于文化的建模主要用于研究社会行为是如何发展的以及如何在人群中传播。
通过数学模型来研究行为的优势在于：首先,数学模型能够进行逻辑推演,便于形成严密的、系统的理论。现代运作管理问题往往涉及复杂的决策,决策之间有很多互相影响的变量或是参数,因此在没有模型的帮助下往往难以展开深入研究,也就难以形成系统的理论。其次,数学模型能够很好地指导行为实验研究,即一旦有了模型的描述,我们就可以基于模型,通过控制一些变量或是参数对相关问题进行实验设计和研究,这样不仅可以对模型进行检验,还可以带来新的研究问题,不断完善这一理论甚至整个领域的研究。许多传统的OM问题,例如报童问题、供应链契约与协调、牛鞭效应等都已经有了系统的、可用于分析的数学模型。正是这些数学模型使得许多传统的OM理论便于检验,同时通过模型参数的设置可以很容易地实现实验设计,也正是通过实验证明了传统的OM模型应用于实际还是不完善的。正如Loch和Wu(2007)指出的,“对传统的理性选择和博弈理论模型进行适当的扩展,将决策偏差、情感因素、社会偏好以及文化等纳入其中用数学建模的方式进行研究,可以在行为运作管理甚至更大的领域指导实证检验”
迄今为止关于公平偏好的建模可以分为两大类：基于结果导向的公平建模和基于意图导向的公平建模。前者倾向于通过比较两个或两个以上的行动结果来评价效用,而后者强调行动背后意图的重要性。行为经济学家往往把这两类公平偏好分别区分为“不公平厌恶偏好”和“互惠偏好”,并进行了建模研究,相应地建立了“不公平厌恶偏好”的效用函数和“互惠偏好”的效用函数。这两类模型的不同之处主要体现在以下两个方面：(1)在互惠模型中,同时考虑了结果和意图的影响,在不公平厌恶模型中,决策者只关注结果的比较。(2)在不公平厌恶模型中,只有当决策者看到了结果的不公平时才会惩罚对方。然而在互惠模型中,决策者回报或惩罚他们的对手更多地是基于对方的意图是否友好,而不仅仅只看结果。本论文的两部分核心内容就分别对应于这两种类型的公平建模,其中第三章属于基于结果导向的公平建模,第四章属于基于意图导向的公平建模。
概括来说,本论文的研究思路是：基于一些重要的行为实验中发现的,在传统理论中被忽视的典型社会偏好,如不公平厌恶和互惠,我们要把这些行为偏好引入到供应链背景来构建行为模型进行研究。通过深入细致的研究主要回答以下四个问题：(1)引入社会偏好之后的供应链系统的均衡会是什么样的?(2)传统供应链与加入社会偏好的行为供应链之间的差异体现在哪些地方?(3)引入的社会偏好是如何影响供应链成员的决策的?(4)引入社会偏好对于供应链渠道的协调会带来什么样的影响?因此,我的论文并不是通过实验发现新的社会偏好,而是将己知的、重要的社会偏好运用于特定的供应链背景或是对现有行为模型做进一步的发展。
围绕“将典型社会偏好引入供应链背景”这一主题,我们在论文的第一章阐明了本文的研究背景、研究方法、研究贡献以及论文结构之后,就进入了本文内容的主体部分,包括二、三、四章。第二章是文献回顾部分,我们详细回顾了与本文密切相关的一些重要理论,包括供应链管理理论、社会偏好理论、博弈论以及将社会偏好引入供应链方面的过往研究。其中供应链管理理论部分重点回顾了经典的报童模型及其相关扩展研究,另外还包括供应链契约设计与协调问题；社会偏好理论部分主要回顾了“公平关切”、“互惠”以及“地位寻求”这三种与本论文密切相关的行为偏好理论；博弈论则主要回顾了斯坦伯格博弈、纳什讨价还价博弈以及心里博弈这三种博弈理论及其扩展研究。在第三章,“纳什讨价还价解”被引入并作为决策双方各自所认为的公平参考标准,另外结合了具有“地位寻求”倾向的公平关切偏好对由一个供应商与一个零售商组成的简单批发价契约供应链在随机市场情形下进行了研究；第四章将最为主流的互惠理论引入供应链背景,重点研究”意图”因素对于决策双方以及整个供应链的影响,为了简化数学推导,这部分的供应链模型仍然采用由一个供应商和一个零售商组成的简单批发价契约供应链,但是与前一部分不同的是,这部分采用的是确定性市场情形。下面就简要介绍一下三、四两章的内容。
文章第三章内容的创新性与贡献在于首次将纳什讨价还价解作为公平参考点进行建模,从而以一个全新的视角来研究具有公平偏好的供应链优化和决策问题。公平参考点一直都是公平理论中的重要组成部分,然而以往的建模通常只是通过几个外生参数以“绝对公平”的方式对参考点进行简单地描述,对于某一特定决策主体而言,单位利益差异带来的效用影响是确定的,不受所处环境、对方的影响。而纳什讨价还价解却能更好描述个体的公平感知,它需要优化分析目标函数中的联合效用函数,即纳什积,显示了纳什解对双方的福利都很重视,不会鼓励一味追求自身利益而忽略对方的利益,所以它关注的是基于决策双方相对实力与贡献的“相对公平”,因而更加符合现实。
纳什讨价还价公平关切模型背景如下：考虑由一个供应商和一个零售商组成的二级供应链系统,零售商向供应商批发某种商品,并将其以某个高于批发价的零售价卖给消费者；零售商所面临的是一个随机市场环境,即市场需求量是一个随机变量；供应商和零售商进行类斯坦伯格博弈,批发价和订货量分别为供应商和零售商的决策变量。此问题与传统研究的最大不同在于假设供应链双方均具有公平关切社会偏好,并以纳什讨价还价解作为双方的公平参考点。值得注意的是,供应商和零售商之间的纳什讨价还价过程虽然未必真实存在,但决策主体都会综合考虑到各方实力与贡献形成公平的心理参考点。这个心理参考点也不会是具体分得多少利润,而是会通过纳什讨价还价形成一个公平的比例,据此对双方博弈之后形成的任何总利润进行分配,双方所得都将会是互相认为公平的结果。零售商和供应商的效用函数均由两部分组成：利润项和公平关切效用项。效用项等于公平关切参数乘以决策人自己所得利润与公平参考点之差。
基于以上决策双方的效用函数,我们根据标准斯坦伯格博弈的分析方式以效用最大化为决策准则求出了供应商和零售商的均衡决策。最后,我们对于得到的均衡解进行了深入地分析,包括模型中的关键参数对于均衡解的影响、行为均衡解与传统均衡解之间的比较以及引入具有”地位寻求”倾向的公平关切行为因素后的供应链协调情况,得到了一些重要的管理启示和结论。
在第四章中我们尝试研究考虑意图因子的互惠供应链。考虑互惠因素比只考虑公平因素更进了一步。具体表现在以下两个方面：第一,如果只是在供应链中考虑公平,那么意味着决策人关注的只是结果,而忽略了一个非常重要的因素-意图。我们在很多时候不仅仅关注结果,还要看对方采取某个行动的意图何在,如果对方是有意而为之,则毫无疑问,不管结果如何,决策人都有动机采取惩罚措施予以还击；相反,如果对方是好心办坏事,或者说对方做出某些决定是无奈之举,则可以被理解(也即决策人站在同样的立场上也很有可能选择这个策略),当结果可能对决策人来说不是太好的时候,他也很有可能不会采取措施制裁对方。第二,在考虑公平因素的情况下,只有决策人能够通过采取惩罚措施降低这种不公平的时候,他才会采取某个措施。而在互惠情况下,决策人是通过所感知的友好与否来决定是否惩罚对方的,如果感知对方友好,则会互惠对方,如果感知对方不友好,则会惩罚对方,而与是否能够降低不公平并没有直接关系。
这部分内容的创新性与贡献在于：大量的行为实验不仅证明了传统的”经济人”假设不符合现实,而且也指出单靠基于结果的公平关切仍不足以描述所有的决策规则。因此,我们有必要把一些重要的心理因素,例如意图或者动机,融入供应链背景进行研究,因为它们对决策有不可忽略的影响。我们首次从心理博弈的视角研究供应链问题,在公平偏好的基础上突出意图这一重要心理因素的影响。
互惠模型仍旧考虑由一个供应商和一个零售商组成的二级供应链系统。零售商从供应商处批发某种产品,然后制定高于批发价的零售价卖向市场。供应商和零售商之间进行类斯坦伯格博弈,供应商为领导者,零售商为追随者,前者和后者的决策变量分别为批发价和零售价。但是,由于模型计算上的复杂性,在此模型中,假设市场需求是价格的反函数。在Falk和] Fschbacher(2006)的模型框架基础上,文章建立和优化分析互惠关切供应链模型。
在此模型中,供应商和零售商分别想制定最优的批发价和零售价来最大化自己的效用。以零售商为例,它的效用函数主要由两部分组成,即利润项和互惠效用项。利润项即传统研究中唯一关注的项,互惠效用项即为加入互惠偏好之后多出的项,也是最为关键的部分。互惠效用项为四部分的乘积,它们是互惠关切参数,意图因子(或动机因子),结果项和互惠项。互惠关切参数为正数,体现了零售商对由互惠偏好所带来的效用的关注程度,即他认为互惠效用占其总效用的比例,它越大,则表示零售商相对来说越看重给对方奖励(对方对自己友好)或者惩罚对方(对方对自己不友好)而给自己带来的效用。意图因子大于0小于等于1,是用来衡量零售商感受到来自供应商友好与否明确度的量。有时候,在某一决策节点,决策人可以明确感受到对方对自己友好与否,即用1来表示,而有时候这种感觉较模糊,不是很清楚,这时候用某个大于0小于1的参数来表示。结果项可以帮助零售商判断当供应商选择某个策略之后,自己所得与期望所得的收益水平的差距,以此来判断供应商是否对自己友好：它大于0表示友好,相反则表示不友好。互惠项是用来衡量互惠行动的影响。零售商可以根据自己感知到的供应商是否友好来选择一个行动作为对供应商的奖励或者惩罚,它大于0表示对对方奖励,小于0表示对对方惩罚。供应商也根据类似的效用函数来优化自己的决策。
在决策双方的互惠效用函数基础上,我们首先按照Geanakoplos等(1989)的心理博弈分析范式,再根据标准斯坦伯格博弈的分析方式以效用最大化的决策准则求出了以下两种情形下的供应商和零售商的均衡决策,一是传统供应商VS互惠零售商；二是互惠供应商VS互惠零售商。然后,我们对于得到的均衡解进行了深入地分析,包括模型中的关键参数(如意图因子)对于均衡解的影响、行为均衡解与传统均衡解之间的比较以及引入互惠偏好后的供应链协调情况。同样得到了一系列重点的管理启示和结论。
结合三、四两章的内容,我们总结本论文重要的结论如下：
一、公平参考点对供应链协调有重要影响。在行为运作管理的研究中,对于参考点的研究引起了不少学者的兴趣,特别是在经典的公平理论中,参考点都是不可或缺的重要因素,女Fehr和Schmidt (1999)的公平理论中将其他决策主体的收益作为被考察决策主体的公平参考点；Bolton和Ockenfels(2000)的公平理论中将其他决策主体的收益的平均值作为被考察决策主体的公平参考点。在本文的第三章中,将纳什讨价还价解引入作为被考察决策主体的公平参考点,并且将其与具有“地位寻求”倾向的公平关切模型进行结合,在这部分我们得到了一个重要结论,即公平关切偏好的引入不会对协调条件产生影响,但对协调难度(即协调所须满足的外部参数空间)会产生显著影响。在本文的第四章中,我们采用“对方收益的若干倍”,而不是“对方的收益”作为被考察决策主体的公平参考点,从而引入两个重要的参照参数γ和μ,分别对应两个倍数。在这部分我们得到了一个重要结论：当γμ≤1(“和谐供应链”)时,供应链无法实现协调；而当γμ>1(“尖刻供应链”)时,简单批发价契约是有可能实现供应链协调的,而传统研究认为这种情况难以发生。
二、决策者行为背后的动机,即意图对供应链协调有着重要影响。在现实与实验中,研究人员发现许多现象即使用经典公平理论也无法很好的得到解释,原因在于决策人除了具有“结果导向”的公平关切外,还具有“动机导向”即意图的公平关切,于是在经典公平理论的基础上发展了含有意图因素的互惠理论,因此意图正是区别经典公平理论与互惠理论的关键因素。意图对供应链协调的影响在本文第四章就有很好的体现,在这部分中,“和谐供应链”的情形下,不存在意图的影响,此时我们只得到一种均衡解,而且该均衡解不能协调供应链；而在“尖刻供应链”的情形下,存在意图的影响,此时我们得到的四种均衡解,并且其中一种均衡解在一定条件下可以实现渠道协调。这意味着在供应链成员考虑意图之后,批发价契约可以协调简单二级供应链。
三、行为因素合作性的程度对供应链协调有重要影响。所谓“行为因素的合作性”是本文新加入的一种对于行为社会性的分类方式,简单的说,如果一种行为因素更多的考虑到他人,并在一定程度上照顾到他人的利益,那么我们就将这种行为归类为具有较高程度合作性的行为；反之,如果一种行为因素更多的还是考虑自己,并不愿意照顾到他人的利益,那么我们就将这种行为归类为具有较低程度合作性的行为。行为因素合作性的程度对供应链协调的影响可以结合本文的三、四两章关于公平供应链的协调讨论来说明。本文的第三章研究对于公平关切的刻画涉及到另一种行为因素,即“地位寻求”偏好,属于较低程度合作性的社会偏好,这体现在：相比于Fehr和Schmidt (1999)的公平模型,本文的公平关切效用部分只含有一项正向效用项,且具有单调递增性。这部分我们的结论是“无论决策目标是基于利润最大化还是效用最大化,在一定的参数环境下,传统的能够实现(不能实现)渠道协调的供应链契约在线性仿射变换下仍旧能够实现(不能实现)渠道协调”,由于我们研究的是批发价契约,在传统情形下不能协调,因此,地位寻求偏好的引入仍旧无法实现渠道协调。本文的第四章研究的行为因素是互惠,友好评价与互惠项的引入体现了其属于较高程度合作性的社会偏好,这部分我们的结论是在“尖刻供应链”的情形中并且具备一定参数条件下,传统批发价契约供应链可以实现渠道协调。
四、同一类型的行为参数对于供应链双方决策的影响存在明显的不同,并且传统供应链的斯坦伯格博弈中零售商由于后行动所带来的弱势地位有可能在引入社会偏好的行为供应链环境下得到改善。本论文第三章的结果显示,具有“地位寻求”倾向的公平关切程度对于供应链双方的决策影响显著不同：零售商的均衡订货量关于其自身的关切参数递减,而关于对方即供应商的关切参数递增；然而供应商的均衡批发价却相反,随着其自身的关切参数递增,而关于对方即零售商的关切参数递减。在第四章中,分析结果显示公平基准点与意图因子这两个行为因素对于供应链双方决策的影响也是完全不同的：零售商的公平基准点越高会使得双方的均衡价格都下降,然而供应商的公平基准点越高则会降低零售商的均衡定价,只对供应商自身的均衡批发价起到了抬高作用。另外,供应商的意图越明显,零售商的均衡定价就越高；然而当零售商的意图越明显时,却降低了供应商的均衡定价。
五、供应链双方同一类型的行为因素对于整个供应链效率的影响显著不同。本论文第三章的结果显示供应链双方的公平关切程度以及讨价还价能力对于整个供应链效率的影响显著不同。具体地,供应商的公平关切程度对于整个供应链效率的影响要比零售商的更为显著。另外,供应商讨价还价能力的提升会使得整个供应链效率下降,然而零售商讨价还价能力的提升则会改善整个供应链效率。第四章的分析结果显示,供应链双方的意图对于整个供应链效率的影响也是完全不同的,供应商决策意图越明显,整个供应链效率越低,然而零售商的决策意图越明显,却会提高整个供应链的效率。
This thesis studies how to incorporate social preferences, such as fairness concerns and reci-procity, into the context of operations management, especially the supply chain. Besides, the impacts of theses social preferences on the the supply chain's decisions and channel's efficiency are also investigated. Specifically, it focuses on four important questions:firstly, what are the equilibria after incorporating social preferences of fairness concerns and reciprocity? secondly, what are the differences between the conventional channel and the behavioral channel (e.g., fairness-concerned channel and reciprocal channel)? thirdly, how do these behavioral factors influence the decisions of the supplier and the retailer in the supply chain? finally, what ef-fects do these social preferences on the coordination of the channel? In order to answer these questions, two models of behavioral operations are formulated.
Newsvendor model for a dyadic supply chain with Nash bargaining fairness concerns is built first. In this model, a supplier plays Stackelberg game with a retailer under a frame of the newsbendor problem. Both of them are assumed to have the preferences of status seeking, which means they have the desires for a higher relative payoff compared with the other party's. Simultaneously, Nash bargaining solution is used as fairness reference to formally depict per-ceptively fair compromise, which is a new perspective to study fairness concerns in a supply chain. Our analysis shows that in a dyadic supply chain, the channel efficiency will decrease because of the preference for status seeking. The retailer's share will be larger when the supplier concerns fairness less, and the supplier's sensitivity to fairness plays a relatively more important role in alleviating double marginalization and improving the channel's efficiency. Additionally, another interesting managerial insight is concluded that fairness concerns will not change the status of channel coordination in certain conditions. More specifically, those contracts able (unable) to coordinate fairness-neutral supply chain, based on affine transformations with scale factors within certain ranges, still succeed (fail) to coordinate the fairness-concerned. Though the introduction of fairness concern into the supply chain will not change the conditions of coordination, it has great impact on the difficulty of coordinating the channel.
Then a dyadic channel in which the retailer or (and) the supplier has (have) a preference for reciprocity is investigated. The two players play Stackelberg game. When both of them have preferences for reciprocity, as the leader, the supplier makes optimal wholesale price to maximize her ("her" represents the supplier and "he" represents the retailer) utility which con-sists of profit term and reciprocal utility term. As the follower, the retailer determines his retail price as the best response to the supplier's optimal decision in order to maximize his utility. In this model, the factors, such as psychological game and intention, are introduced to the context of supply chain for the first time since the theory of reciprocity emphasizes the importance of intentions behind actions. Additionally, two scenarios were discussed:(1) the retailer has a preference for reciprocity while the supplier doesn't have;(2) both the retailer and the supplier have preferences for reciprocity. Each scenario may have several sub-scenarios since we are not sure which is greater, γμ or1. Thus, two kinds of supply chains, acrimonious supply chain if γμ>1and harmonious supply chain if γμ≤1, are discussed and analyzed in reciprocity model. Furthermore, equilibria are derived under the two scenarios and the existence and the uniqueness of the equilibria of different scenarios can be guaranteed. Finally, numerical ex-amples are conducted to study the impacts of major parameters on reciprocal equilibria. The results show that the reciprocal channel can be coordinated by using a constant wholesale price in the acrimonious supply chain, which implies that the problem of double marginalization is not necessary to be present all the time. However, it is impossible to coordinate the channel with a wholesale-price contract in the harmonious supply chain. The paper also shows that compared with traditional retail price, the retailer charges a lower retail price to reward the sup-plier's lower wholesale price and a higher retail price to punish the supplier's higher wholesale price in the harmonious supply chain.
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