Abstract: Developing a sustainable manufacturing industry is important for improving resource utilization and realize environmental protection. The remanufacturing industry has become a pioneer of sustainable manufacturing worldwide. A multi-period closed-loop supply chain network is conducive to integrating different types of enterprises, realizing resource reuse, and conforming to the dynamic competitive market environment faced by enterprises, which has been widely recognized in the literature. In reality, information asymmetry between enterprises and markets often leads to randomness in product demand, and the advertising function transmits product information to the market so as to affect the purchase behavior of consumers. In addition, according to the logic of “manufacturing/remanufacturing→market”, enterprises that implement advertising behavior in a multi-period closed-loop supply chain network system are not limited to manufacturers, and remanufacturers also have advertising behavior. Previous studies have shown that the advertising effect includes not only immediacy but also the psychological factor of forgetting. Therefore, under the assumption of random demand and the advertising forgetting effect, it is important to study the multi-period closed-loop supply chain network equilibrium considering advertising investment by manufacturers and remanufacturers. This study supplements the literature on the closed-loop supply chain network equilibrium under the advertising forgetting effect. In this study, it is assumed that the multi-period closed-loop supply chain network system consists of suppliers, manufacturers, remanufacturersand demand markets, in which members at the same level compete with each other. Suppliers are responsible for converting primary materials into usable raw materials and selling them to manufacturers. Manufacturers are responsible for converting raw materials into new products and selling them to demand markets. Remanufacturers are responsible for recycling and remanufacturing. It is assumed that all members of the closed-loop supply chain network are risk-neutral, and the information among members is completely symmetrical. Each member of the system aims to maximize profits. First, under the assumption of random demand and advertising investment of manufacturers and remanufacturers, using the Nash non-cooperative game and variational inequality, the optimal behaviors of suppliers, manufacturersand remanufacturers are transformed into solvable variational inequalities. Second, using the Nash non-cooperative game, variational inequalityand spatial price equilibrium theory, the optimal behavior of demand markets considering advertising forgetting is transformed into variational inequality. Third, according to network equilibrium theory, a multi-period closed-loop supply chain network equilibrium model that considers advertising investment and the advertising forgetting effect is established, and the equilibrium conditions of the model are given. Finally, using the modified projection algorithm, the equilibrium results are verified and explained using numerical examples, and the influence of important parameters on the network equilibrium results under different situations is analyzed.
The main conclusions of this study are as follows. (1)Compared with remanufacturers' advertising investment, manufacturers' advertising investment has a more significant impact on the recycling rate and the profits of the system regardless of the advertising forgetting coefficient. The advertising forgetting effect is always unfavorable to the sales of new products and the recycling of waste products. (2)When the advertising investment level of manufacturers is higher, the profits of remanufacturers will always be higher; in contrast, the profits of suppliers, manufacturers, and the system will be higher when the advertising forgetting coefficient is less than a certain threshold. (3)The existence of advertising forgetting reduces the positive incentive effect of advertising investment on demand markets. The enhancement of the advertising forgetting coefficient reduces the recycling rate and the profits of members and the system. In particular, when advertising forgetting coefficient is dynamic, its value will have a more significant effect on the system in the early periods. Finally, according to the research conclusions, this study provides some management suggestions from the perspective of the government and members, which can provide theoretical and practical suggestions for the formulation of government mechanisms and members' decisions.
Previous studies have shown that advertising not only has the forgetting effect, but also has memory and delay effects. In the future, exploring other advertising effects, such as delay or memory effects, on the equilibrium of a multi-period closed-loop supply chain network is an interesting research problem. Also, this study examines a multi-period closed-loop supply chain network equilibrium under the channels of manufacturers and remanufacturers. Future researchcan consider the multi-period closed-loop supply chain equilibrium underthe sale channel of retailers. In addition, this study considers recycling and remanufacturing by remanufacturers. Future research can relax certain assumption. For example, it is assumed that manufacturers/third-party recyclers recycle waste products. Therefore, a multi-period closed-loop supply chain network equilibrium under the recycling mode of manufacturers/third-party recyclers is also an interesting research direction.This research is supported by the Philosophy and Social Science Research Planning Project of Heilongjiang Province (21GLC184). Particularly, the authors thank the editors and reviewers for their hard work.

Key words: multi-period closed-loop supply chain network, advertising investment, advertising forgetting, random demand, network equilibrium

摘要： 研究由供应商、制造商、再制造商及需求市场组成的多周期闭环供应链网络均衡问题。在随机需求假设下,利用变分不等式方法构建了考虑制造商和再制造商广告投入及广告遗忘效应的多周期闭环供应链网络均衡模型,给出了网络模型的均衡条件,利用算例分析对均衡结果进行了验证和解释,并得到管理学启示。研究表明,无论广告遗忘情境如何,制造商广告投入对回收率及整体利润的影响占据主导;当制造商广告投入水平较再制造商更高时,再制造商利润总是更高,而供应商、制造商及系统整体利润仅在广告遗忘系数小于某阈值时更高;广告遗忘性的存在降低了广告投入对目标市场的正向激励作用,随着广告遗忘系数的增加,回收率、成员企业及系统整体利润均降低,并且在广告遗忘系数呈非固定状态下,其前期的值对系统影响更显著。

关键词: 多周期闭环供应链网络, 广告投入, 广告遗忘, 随机需求, 网络均衡