This research presents a continuous-time, deterministic model to address the problem of determining the order quantity and the dynamic pricing policy in scenarios where the quality of the product gradually decays over time. The decision variables include the order quantity as well as the pricing policy, which in turn consists of the initial price and the price reduction rate. Two conflicting objective functions are considered: maximizing profit and maximizing the average quality of the units sold. The paper examines the trade-offs between these two objectives across scenarios with different parameters, such as the price elasticity of the demand, the quality deterioration rate and the elasticity of the demand to quality. The results indicate that, in almost all scenarios, the optimal ordering policy is to order small quantities. Interestingly, in each scenario, there exists a maximum average quality compatible with positive profits. A higher average quality is only possible by incurring losses. Similarly, there is also a limit to the maximum rate of price discounting above which positive profits are not feasible.
Adenso-Dı́az et al. (Fri,) studied this question.