Abstract: In the context of increasing global attention to sustainable development and the continuous growth of the remanufacturing industry, remanufacturing businesses face numerous challenges. Among them, the quality uncertainty of waste products and patent licensing issues are particularly prominent. When faced with these uncertainties, remanufacturers usually exhibit risk-averse attitudes. This paper focuses on the remanufacturing supply chain under patent licensing and explores the impact of risk aversion on supply chain decision-making and coordination. We mainly address the following issues: What impact does risk aversion have on the production and price of new and remanufactured products, as well as the recovery rate and unit patent licensing fees? What are the impacts of risk aversion from the perspectives of consumers, the environment, and social welfare? How to coordinate the remanufacturing supply chain considering risk aversion under patent licensing?
This paper constructs a single-period decision making model for a two-level remanufacturing supply chain consisting of a manufacturer and a remanufacturer. In this model, the manufacturer is responsible for the production and sales of new products and charges a remanufacturing patent license fee from the remanufacturer. The remanufacturer is responsible for recycling, remanufacturing, and then selling the products in the market. The model takes into account the fact that the quality of recycled products follows a random distribution within a specific interval, which makes the unit cost of remanufacturing uncertain. Meanwhile, a risk-aversion coefficient is introduced, and the mean-variance method is used to measure the risk-averse utility of the remanufacturer. It is assumed that there is a Stackelberg game between the manufacturer and the remanufacturer, and the information between them is completely symmetric.
This paper analyzes two scenarios: risk-neutral and risk-averse. In the risk-neutral scenario, the optimal solutions for the quantity of new products, the quantity of remanufactured products, the unit patent license fee, and the recycling rate are derived. In the risk-averse scenario, the corresponding equilibrium solutions are also obtained. By comparison, it is found that as the risk-aversion coefficient increases, the quantity of new products increases, while the quantity of remanufactured products and the recycling rate decrease. In terms of prices, the price of new products remains unchanged, the price of remanufactured products rises, and the unit patent license fee decreases. This is because the risk-averse remanufacturer would reduce recycling and remanufacturing activities to maintain its utility, thus affecting the quantity and price decisions of the total supply chain.
The impact of risk aversion is further examined from the perspectives of consumers, the environment, and social welfare. The results show that risk aversion reduces consumer surplus. This is because of a decrease in the quantity and an increase in the price of remanufactured products. Although the quantity of new products increases, it still cannot compensate for the losses of consumers. In terms of environmental impact, due to an increase in the quantity of new products and a decrease in the quantity of remanufactured products, as well as an increase in the quantity of waste products, the environmental impact increases. However, under a certain condition (when the environmental impact of waste products is not considered and the unit carbon emissions of new products are lower than a certain threshold), risk-averse behavior may reduce the environmental impact. Social welfare also decreases due to a reduction in the utilities of manufacturers and remanufacturers, a decrease in consumer surplus, and an increase in environmental impact.
Additionally, a two-part tariff contract is designed to coordinate the remanufacturing supply chain. We find that when the unit license fee and the fixed transfer fee meet certain conditions, this contract can achieve supply chain coordination, enabling the recycling rate and the total utility of the remanufacturing supply chain to reach the level of centralized scenario, while increasing consumer surplus and social welfare and reducing environmental impact.

Key words: patent licensing, risk aversion, remanufacturing supply chain, quality uncertainty

摘要： 基于回收品质量的不确定性,研究专利许可下考虑风险规避的再制造供应链决策与协调。构建了由制造商和再制造商组成的再制造供应链模型,其中制造商向再制造商征收再制造专利许可费,然后双方分别销售新品和再制造品。分别研究了风险中性和风险规避情形,并对两种情形下的均衡解进行了比较分析。然后,从消费者、环境和社会福利的角度探讨了风险规避的影响。研究发现,与风险中性情形相比,风险规避行为会提高新品产量和再制造品的价格,且会降低再制造品的产量、回收率和单位许可费用,但不会改变新品的价格;从消费者、环境和社会福利层面来看,再制造商的风险规避行为均会产生负面影响;两部定价契约能够有效地协调再制造供应链,且能够使回收率和再制造供应链的总效用达到集中式决策水平。

关键词: 专利许可, 风险规避, 再制造供应链, 质量不确定