As an important engine for high-quality economic development, the digital economy is gradually integrating with the rural logistics industry. This trend is contributing to making rural logistics a fundamental, strategic, and pioneering industry. However, some valuable topics remain unstudied, such as whether they are coupled and whether there is variability in the coupling system across the provinces. Therefore, this article takes system theory and coupling theory as the analytical framework, aiming to better elaborate the subject’s logical relationship and operational structure of the coupled system, which is composed of a digital economy subsystem and a rural logistics subsystem. Furthermore, 21 provinces are seen as the research object in China, and the coupling coordination model is constructed, aiming to verify the coupling and coordination relationship between the two subsystems. The results suggest that two subsystems are coupled and coordinated in the same direction, and they feed back and influence each other. During the same period, four echelons are divided and there is variability in the coupling and coordination between the digital economy and rural logistics, according to the coupling degree (CD) and coupling coordination degree (CCD). Findings presented can serve as a useful reference for the evolutionary laws of the coupled system. The findings presented here can serve as a useful reference for the evolutionary laws of coupled systems. Moreover, it further provides ideas for the development between rural logistics and the digital economy.

Quality is not only the basis for business survival and development but also a key issue that cannot be ignored in supply chain management decisions. In practice, the impact of quality on goodwill does not show an immediate effect, and there is a dynamic delayed effect. Therefore, we developed a dynamic model that considers the delayed effect of quality on goodwill. Firstly, we constructed a delayed differential equation for the effect of quality on goodwill based on the Nerlove–Arrow model for a two-channel supply chain in a competitive environment and studied the dynamic quality decision problem of manufacturers and retailers under the delay effect. Secondly, we constructed the manufacturer and retailer Hamilton functions based on the principles of being of great value, solving and comparing the optimal product quality level, having an optimal service quality level, product goodwill, and overall profit of the supply chain under both decentralized and centralized decision modes, and investigated the effect of delay time on the profit and quality decisions of supply chain members. The conclusions show that: (i) delay time is an important reference for supply chain members when choosing the decision mode, and the overall profit size of the supply chain has different relationships with the different values of delay time taken into account with the two decision scenarios. (ii) Adopting a centralized decision mode can motivate manufacturers and retailers to improve the quality level, which in turn promotes the sales of products and the accumulation of brand goodwill.

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.