An inventory model with both stock-dependent demand rate and stock-dependent holding cost rate

摘要

In this paper, we develop an inventory model under a stock-dependent demand rate and stock-dependent holding cost rate with relaxed terminal conditions. Shortages are allowed and partially backlogged in the model. The purpose of this study is to determine the optimal order quantity and the ending inventory level such that the total profit per unit time is maximized for the retailer. We first establish a proper model for a mathematical formulation. Then we develop several theoretical results and provide the decision-maker with an algorithm to determine the optimal solution. Finally, numerical examples are provided to illustrate the solution procedure, and a sensitivity analysis of the optimal solution with respect to major parameters is carried out.