This paper investigates a closed loop supply chain (CLSC) encompassing a manufacturer, a retailer, and consumers operating within the carbon trading scheme. Employing the focus theory of choice, we analyze the decision-making processes of the retailer, considering various personality traits. A Stackelberg game is formulated, wherein the manufacturer assumes responsibility for recycling activities. The research explores the impact of the retailer’s optimism and confidence levels on optimal decision-making within a positive evaluation system. Numerical examples are employed to elucidate equilibrium solutions, illustrating the correlation between the retailer’s personality traits and the manufacturer’s optimal decisions. Furthermore, a sensitivity analysis is conducted on the carbon trading price and the manufacturer’s carbon emission quota allocation within a single cycle under the carbon trading scheme. The investigation concludes with an examination of the influence of recycling prices on the manufacturer’s optimal revenue. The findings indicate that retailers with distinct personality traits adopt varied pricing strategies. Decreases in optimism and self-confidence levels prompt the retailer to opt for relatively lower retail profit pricing. Simultaneously, the manufacturer demonstrates a preference for collaborating with a retailer characterized by optimism and lower confidence levels, thereby enhancing overall manufacturing revenue. Notably, under the carbon trading scheme, fluctuations in carbon trading and recycling prices distinctly influence the manufacturer’s decisions.

As a useful strategy to improve the flexibility of the system to manage uncertainty in supply and demand and to improve the sustainability of the supply chain, vendor-managed inventory (VMI) programs have attracted widespread attention in the field of supply chain management. However, a growing body of empirical literature has shown that participants’ decisions deviate significantly from the standard theoretical predictions. Under a VMI program, the supplier bears not only the production cost, but also the risk of leftover inventory. Moreover, the inequality among participants and different personalities of decision-makers in VMI programs may lead to the divergence of decision-making. To understand the supplier’s replenishment decision in view of the behavioral pattern, we propose a new inventory model for the supplier with the focus theory of choice. The proposed model conceives that the retailer evaluates each replenishment quantity based on the most salient demand for him/her instead of calculating the expected utility. By employing this inventory model, we construct a two-tier supply chain model with revenue-sharing contract and theoretically derive the optimal sharing percentage of the revenue and replenishment quantity. Results analysis gains managerial insights into the strategic selection of the retailer who faces suppliers with different personalities. Comparisons between the classic revenue-sharing contract model and the proposed model are also carried out by illustrative examples. This research provides a new perspective to analyze individual supplier’s behavior in a VMI program with revenue-sharing contracts.