Quality, Carbon, and Competition: A Profit-Maximizing EOQ Model for Duopolists

This paper investigates a profit-maximizing Economic Order Quantity (EOQ) model for duopolistic firms under carbon emission constraints and quality investment. Firms can enhance their product quality through investment, which in turn affects market demand and production costs. Simultaneously, their inventory operations generate carbon emissions, necessitating participation in carbon trading under a given emission allowance. We first construct two distinct models: one with an exogenous carbon cap and another with an endogenous carbon cap, and derive the optimal decisions for firms under both frameworks. By introducing a quality investment cost to elevate product quality, we study a duopoly's profit-maximizing EOQ model and explore the operational decisions of the leader and follower firms under a Stackelberg game. Based on this, we conduct sensitivity analyses of the optimal decisions. Our findings reveal that, in the exogenous cap model, the optimal order quantity is an increasing function of the sales rate and a decreasing function of the carbon emission coefficient. For the endogenous cap model, an optimal solution for the duopolists exists only when the carbon price is below a critical threshold. Furthermore, the leader firm’s optimal retail price and optimal quality level are both higher than those of the follower. Finally, using a symmetric scenario as an example, we examine the impact of the quality sensitivity coefficient and the carbon price on a firm's maximum profit. This research provides valuable decision-making guidance for competing firms aiming to integrate quality investment with low-carbon operations.