Optimal dynamic pricing and replenishment cycle for non-instantaneous deterioration items with inventory-level-dependent demand

This paper considers a problem of determining the optimal dynamic pricing strategy and replenishment cycle for non-instantaneous deteriorating items, where the consumer demand depends on the sales price and the quantity of the items displayed in the store. For the given replenishment cycle, we derive the optimal dynamic pricing strategy by applying Pontryagin׳s maximum principle, and then design an effective algorithm to obtain the optimal dynamic pricing strategy and replenishment cycle simultaneously. Numerical examples are provided to illustrate the effectiveness of the proposed methods and solution procedure. Furthermore, sensitivity analysis of the key system parameters is carried out and some interesting managerial insights are presented.