An optimal replenishment policy for deteriorating items with stock‐dependent demand and relaxed terminal conditions under limited storage space

This paper deals with the problem of determining the optimal replenishment policy for deteriorating items with stock‐dependent demand in which the terminal condition of zero‐ending inventory is relaxed. In the model, shortages are allowed and partial backlogging/lost sales. That is, the zero/non‐zero ending inventory models are considered simultaneously. The items in stock are displayed to the customers in shelves with limited storage capacity. In theoretical analysis, the necessary and sufficient conditions of the existence and uniqueness of the optimal solutions under various cases are shown. We then also provide a simple algorithm to find the optimal solutions for various situations. Further, a couple of numerical examples are presented to demonstrate the developed model and solution procedure, and several management insights are obtained from the numerical examples. Finally, sensitivity analysis of the optimal solution with respect to major parameters is also carried out.