精读期刊论文《考虑公平关切的供应链契约与协调》数值分析

摘要：This issue of tweets will introduce the numerical analysis of the intensive reading journal paper "Supply Chain Contracts and Coor

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“喆学（139）：精读期刊论文

《需求不确定性对绿色技术采用的消费者补贴的影响》

数值分析”

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"Zhexue (139): Intensive reading of journal articles

"supply Chain Coordination Considering Fairness Concerns "

Numerical analysis"

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本期推文将从思维导图、精读内容、知识补充三个方面介绍精读期刊论文《考虑公平关切的供应链契约与协调》的数值分析。

This issue of tweets will introduce the numerical analysis of the intensive reading journal paper "Supply Chain Contracts and Coordination Considering Fairness Concerns" from three aspects: Mind mapping, intensive reading content, and knowledge supplement.

一、思维导图（Mind Maps）

二、精读内容（Intensive reading content）

文章讨论了供应链协调均衡解的复杂性，并通过具体算例分析了公平关切行为对供应链契约和协调条件的影响。假设供应商不关注公平，供应商效用等于其利润，从而供应链效用等于零售商和供应商效用之和。文中给出了市场需求服从正态分布的参数，以及供应链其他参数，计算出系统最优订购量和供应链整体利润。批发价契约参数和回购契约参数被设定，收益共享契约参数满足特定条件，所有契约下的零售商公平关切效用函数都是严格凹函数，存在唯一最优目标值。通过计算三种契约形式下零售商的最优决策，得出相关表格。

This paper discusses the complexity of the coordinated equilibrium solution of the supply chain, and analyzes the impact of fairness-concerned behavior on supply chain contracts and coordination conditions through specific examples. Assuming that suppliers do not care about fairness, the supplier utility is equal to its profit, so the supply chain utility is equal to the sum of the retailer and supplier utilities. The paper gives the parameters of the market demand following the normal distribution, as well as other supply chain parameters, and calculates the optimal order quantity of the system and the overall profit of the supply chain. The wholesale price contract parameters and the repurchase contract parameters are set, and the revenue sharing contract parameters meet specific conditions. The fairness-concerned utility functions of retailers under all contracts are strictly concave functions, and there is a unique optimal target value. By calculating the optimal decision of retailers under three contract forms, the relevant table is obtained.

在分析批发价契约时，当零售商公平中性（λ=0）时，其最优订购量为1062，低于系统最优订购量1115，导致供应链无法实现协调。随着零售商公平关切程度（λ）从0增加到10，其最优订购量下降到1022，越来越偏离系统最优订购量。因此，零售商公平关切的批发价契约仍然无法实现供应链协调，但会使零售商的最优决策更加偏离系统最优决策，导致供应链效率降低。批发价契约下公平关切会对零售商的最优决策产生影响。

When analyzing the wholesale price contract, when the retailer is fair and neutral (λ=0), its optimal order quantity is 1062, which is lower than the system optimal order quantity of 1115, resulting in the inability to coordinate the supply chain. As the retailer's fairness concern (λ) increases from 0 to 10, its optimal order quantity drops to 1022, deviating more and more from the system optimal order quantity. Therefore, the wholesale price contract with retailers' fairness concerns still cannot achieve supply chain coordination, but will make the retailer's optimal decision deviate further from the system optimal decision, resulting in reduced supply chain efficiency. Fairness concerns under wholesale price contracts will have an impact on retailers' optimal decisions.

在分析表2中的回购契约时，当零售商公平中性（λ=0）时，其最优订购量为1115，零售商利润为92,530，供应链利润为116,707，供应链能够实现协调。即使在零售商公平关切的情况下，其最优决策不发生改变，仍然能够与系统最优决策保持一致，供应链实现协调。因此，回购契约下，公平关切不会影响零售商的最优决策，零售商的公平关切与否并不影响回购契约下供应链的协调状态。

When analyzing the buyback contract in Table 2, when the retailer is fair and neutral (λ=0), its optimal order quantity is 1115, the retailer's profit is 92,530, and the supply chain profit is 116,707, and the supply chain can achieve coordination. Even when the retailer is concerned about fairness, its optimal decision does not change, and it can still be consistent with the system's optimal decision, and the supply chain achieves coordination. Therefore, under the buyback contract, fairness concerns will not affect the retailer's optimal decision, and whether the retailer is concerned about fairness does not affect the coordination state of the supply chain under the buyback contract.

尽管零售商的最优决策不发生变化，但由于零售商利润大于供应商利润，零售商的效用会随着公平关切系数的增加而正向增加，整个供应链的效用也随之增加，从而提高了系统总福利水平。公平关切虽然对零售商和供应链的利润没有影响，但会对零售商和供应链的效用产生很大影响。例如，当公平关切系数从0.1增加到1时，零售商的效用从99,304增加到160,730，供应链的效用从123,532增加到184,958。因此，公平关切系数越大，产生的影响就越大。

Although the retailer's optimal decision does not change, because the retailer's profit is greater than the supplier's profit, the retailer's utility will increase positively with the increase of the fairness concern coefficient, and the utility of the entire supply chain will also increase, thereby improving the total welfare level of the system. Although fairness concerns have no effect on the profits of retailers and supply chains, they will have a great impact on the utility of retailers and supply chains. For example, when the fairness concern coefficient increases from 0.1 to 1, the retailer's utility increases from 99,304 to 160,730, and the supply chain's utility increases from 123,532 to 184,958. Therefore, the larger the fairness concern coefficient, the greater the impact.

共享契约与回购契约的分析类似，结论也相似：零售商的公平关切与否并不影响收益共享契约下供应链的协调状态。公平关切并不影响回购契约与收益共享契约的等价关系。零售商的公平关切不影响其最优决策，对供应链的利润不产生影响，但会对零售商和供应链的效用产生影响，影响程度由公平关切系数大小决定。

The analysis of the sharing contract is similar to that of the repurchase contract, and the conclusions are similar: the fairness concern of the retailer does not affect the coordination state of the supply chain under the revenue sharing contract. Fairness concern does not affect the equivalence relationship between the repurchase contract and the revenue sharing contract. The fairness concern of the retailer does not affect its optimal decision and has no impact on the profit of the supply chain, but it will affect the utility of the retailer and the supply chain, and the degree of impact is determined by the size of the fairness concern coefficient.

三、知识补充（Knowledge supplement）

供应链效用通常指的是供应链系统中各个环节（如供应商、制造商、分销商和零售商等）在协同工作时所创造的总价值或收益。它是衡量供应链整体性能的一个重要指标，反映了供应链在满足客户需求、降低成本、提高效率和增强竞争力方面的表现。

Supply chain utility usually refers to the total value or benefits created by each link in the supply chain system (such as suppliers, manufacturers, distributors and retailers, etc.) when working together. It is an important indicator to measure the overall performance of the supply chain, reflecting the performance of the supply chain in meeting customer needs, reducing costs, improving efficiency and enhancing competitiveness.

供应链效用可以从以下几个方面进行衡量：

Supply chain utility can be measured from the following aspects:

1.客户满意度：供应链能否及时、准确地满足客户需求。

1. Customer satisfaction: whether the supply chain can meet customer needs in a timely and accurate manner.

2.成本效率：供应链运营的总成本，包括采购、生产、库存、运输和分销等成本。

2. Cost efficiency: the total cost of supply chain operations, including procurement, production, inventory, transportation and distribution costs.

3.响应速度：供应链对市场变化的响应速度，如新产品推出、需求波动等。

3. Response speed: the speed of response of the supply chain to market changes, such as new product launches, demand fluctuations, etc.

4.库存管理：库存水平的优化，减少过剩库存和缺货情况。

4. Inventory management: optimization of inventory levels, reducing excess inventory and out-of-stock situations.

5.质量控制：供应链中产品和服务的质量。

5. Quality control: the quality of products and services in the supply chain.

6.合作与协调：供应链各环节之间的合作和协调程度。

6. Cooperation and coordination: the degree of cooperation and coordination between various links in the supply chain.

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