晴读（33）：精读期刊论文

摘要：逆向供应链结构与回收商关系界定。首先，明确研究对象为“单个制造商+两个回收商”构成的双渠道逆向供应链，核心在于区分回收商签约前的两种关系模式：竞争关系下，两回收商独立服务制造商，一方回收努力水平提升会削弱另一方业务表现；合作关系下，二者通过优势互补、资源共享开

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“晴读（33）：精读期刊论文《基于委托代理理论的逆向供应链激励机制设计与回收模式选择》的问题描述与模型说明”

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"Qing Du (33): Close Reading of

The Problem Description and Model Explanation in the Journal Paper: Incentive Mechanism Design and Recycling Mode Selection in Reverse Supply Chains Based on the Principal-Agent Theory

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今天小编将从思维导图、精读内容、知识补充三个板块为大家带来《基于委托代理理论的逆向供应链激励机制设计与回收模式选择》的问题描述与模型说明。

一、思维导图（Mind Map）

二、内容精读（Conduct in-depth reading of the material）

1.逆向供应链结构与回收商关系界定。首先，明确研究对象为“单个制造商+两个回收商”构成的双渠道逆向供应链，核心在于区分回收商签约前的两种关系模式：竞争关系下，两回收商独立服务制造商，一方回收努力水平提升会削弱另一方业务表现；合作关系下，二者通过优势互补、资源共享开展业务，一方努力提升能正向改善另一方业务表现。同时，指出制造商面临的核心问题——在回收商能力禀赋为私有信息、努力行为不可观测的双重约束下，需设计激励契约以实现信息甄别与最优努力激励，并依据契约配置的预期效用确定最优回收模式，保障供应链配置效率。

1. Definition of Reverse supply chain Structure and Recycler Relationships. First, the research object is clearly defined as a dual-channel reverse supply chain composed of "one manufacturer + two recyclers", with the core being distinguishing between two relationship models of recyclers before contract signing: under a competitive relationship, the two recyclers serve the manufacturer independently, and an increase in one recycler’s recycling effort level will weaken the other’s business performance; under a cooperative relationship, the two conduct business through complementary advantages and resource sharing, and an increase in one’s effort can positively improve the other’s business performance. At the same time, it points out the core problem faced by the manufacturer—under the dual constraints that recyclers’ capacity endowments are private information and their effort behaviors are unobservable, it is necessary to design incentive contracts to achieve information screening and optimal effort incentives, and determine the optimal recycling model based on the expected utility of contract allocation, to ensure the supply chain allocation efficiency.

2.模型符号与基础假设设定。通过符号说明与五大假设搭建模型框架：符号体系清晰界定了回收商能力禀赋（θi）、竞争/ 合作强度系数（k/t）、激励契约参数（固定支付α、绩效分享比例β）等关键变量，并用特定上角标区分信息对称（S）/ 不对称（D）、竞争（N）/ 合作（C）等场景；假设内容涵盖主体风险态度（制造商风险中性、回收商风险规避且服从不变绝对风险厌恶效用函数）、回收绩效函数（竞争关系下含负向相互影响，合作关系下含正向相互影响，且均满足自身努力对绩效的主导作用）、回收商能力禀赋分布（私有信息且失效效率函数单调递增）、努力成本函数（二次型边际递增形式）及激励契约形式（线性契约{S (Qi)=α(θi)+β(θi) Qi}），为后续模型推导奠定基础。

2. Model Symbol Definition and Basic Assumption Setting. A model framework is built through symbol explanation and five major assumptions: the symbol system clearly defines key variables such as recyclers’ capacity endowments (θi), competition/cooperation intensity coefficients (k/t), and incentive contract parameters (fixed payment α, performance sharing ratio β), and uses specific superscripts to distinguish scenarios including information symmetry (S)/asymmetry (D) and competition (N)/cooperation (C); the assumptions cover subjects’ risk attitudes (the manufacturer is risk-neutral, while recyclers are risk-averse and follow a constant absolute risk aversion utility function), recycling performance functions (with negative interaction effects under competitive relationships and positive interaction effects under cooperative relationships, both satisfying the leading role of recyclers’ own efforts on performance), the distribution of recyclers’ capacity endowments (private information with a monotonically increasing failure rate function), effort cost functions (in the form of quadratic marginal increase), and the form of incentive contracts (linear contract {S (Qi)=α(θi)+β(θi) Qi}), laying a foundation for subsequent model derivation.

3.主体收益与期望效用函数构建。基于前文假设，分别推导制造商与回收商的收益及期望效用函数：制造商收益函数考虑绩效分享比例对回收绩效的扣减与固定支付成本，因风险中性其期望效用等于期望收益，需积分遍历回收商能力禀赋分布区间；回收商收益函数包含激励契约收入与努力成本，因风险规避，其期望效用采用确定性等价收益计算，需扣除风险成本（与风险厌恶系数、绩效分享比例及市场不确定性方差相关），最终形成的函数式为后续分析契约最优配置与回收模式选择提供量化工具。

3. Construction of Subjects' Revenue and Expected Utility Functions. Based on the previous assumptions, the revenue and expected utility functions of manufacturers and recyclers are derived respectively: the manufacturer’s revenue function takes into account the deduction of recycling performance by the performance sharing ratio and fixed payment costs; due to risk neutrality, its expected utility is equal to the expected revenue, which requires integration over the distribution interval of recyclers’ capacity endowments. The recycler’s revenue function includes incentive contract income and effort costs; due to risk aversion, its expected utility is calculated using the certainty equivalent income, which needs to deduct the risk cost (related to the risk aversion coefficient, performance sharing ratio, and variance of market uncertainty). The finally formed functional formulas provide a quantitative tool for the subsequent analysis of the optimal allocation of contracts and the selection of recycling models.

三、知识补充（Supplementary Knowledge）

1.风险厌恶效用函数（u(Πi) = -e^(-ρΠi)）：这是经济学中描述风险规避者决策偏好的经典函数。其中Πi表示收益，ρ是风险厌恶系数（ρ越大说明越害怕风险）。函数呈concave 形态（曲线向下弯曲），意味着同样的收益增加带来的效用提升，会小于同等损失带来的效用下降，直观体现了“损失厌恶”心理。

1. Risk-Averse Utility Function (u(Πi) = -e^(-ρΠi)). This is a classic function in economics that describes the decision-making preferences of risk-averse individuals. Among them, Πi represents income, and ρ is the risk aversion coefficient (the larger ρ is, the greater the fear of risk). The function takes a concave form (the curve bends downward), which means that the utility increase brought by a given increase in income is smaller than the utility decrease caused by an equivalent loss, intuitively reflecting the "loss aversion" psychology.

2.回收绩效函数（Qi = θi + bei + gi(ei, ej) + ε）：这个公式把回收商的工作成果拆解成了可量化的要素。θi是回收商的“先天能力”（比如现有设备水平），bei是“后天努力”的贡献（b是努力的产出效率），gi(ei, ej)体现与另一家回收商的互动（竞争时是负影响，合作时是正影响），最后加ε代表市场随机波动（比如突然出台的环保政策）。

2. Recycling Performance Function (Qi = θi + bei + gi(ei, ej) + ε). This formula decomposes a recycler’s work output into quantifiable elements. Among them, θi represents the recycler’s "innate capability" (such as the level of existing equipment), bei denotes the contribution of "acquired effort" (where b is the output efficiency of effort), gi(ei, ej) reflects the interaction with the other recycler (exerting a negative impact in the case of competition and a positive impact in the case of cooperation), and the final term ε represents random market fluctuations (such as the sudden introduction of environmental protection policies).

3.线性激励契约（S(Qi) = α(θi) + β(θi)Qi）：这是委托代理关系中常见的“底薪+提成”模式。α是固定报酬（类似基本工资，不看业绩），β是绩效分成比例（类似提成率，业绩越好拿得越多）。制造商通过调整这两个参数，既能保证回收商的基本收入（满足保留效用），又能激励其多努力（β越大，努力的回报越高）。

3. Linear Incentive Contract (S(Qi) = α(θi) + β(θi)Qi). This is a common "basic salary + commission" model in principal-agent relationships. Here, α represents fixed remuneration (similar to a base salary, which is not dependent on performance), and β stands for the performance sharing ratio (similar to a commission rate, meaning the better the performance, the higher the income). By adjusting these two parameters, the manufacturer can not only ensure the recycler’s basic income (to meet the reservation utility) but also motivate the recycler to make greater efforts (the larger β is, the higher the return for the recycler’s efforts).

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