This article deals with a dynamic decision-making model for a low-carbon supply chain which consists of a manufacturer and a platform retailer. Consideration of delay effects, a delayed differential equation for the effect of low-carbon investment efforts (LIE) in R&D and low-carbon promotional effort (LPE) on low-carbon goodwill (LG) is developed. Moreover, Hamilton's function is applied to solve the decision problem of optimal control. In the model, the differences between the agency selling and reselling patterns are analyzed by comparing LIE, LPE, LG, and net discounted profit. The commission system is a key measure for dynamic decision making on low-carbon products, while the commission rate is also an important reference point for decision making on cooperation patterns. In contrast to the findings of previous studies, this article derives specific thresholds for commissions. Furthermore, this study considers delay effects from a dynamic perspective. The findings show differences in both decentralized and centralized decision-making solutions for supply chains as the delay time changes. The proposed models are analyzed mathematically and numerical examples are illustrated to justify the feasibility of the model in reality. This study provides new insights into the choice of platform sales patterns for firms to develop agency selling and reselling partnership solutions in practice.
Keywords: Low-carbon supply chains; agency selling pattern; delay differential equation; delay effects; reselling pattern.