Maximization of the return on inventory management expense in a system with price- and stock-dependent demand rate

Abstract

This paper considers an inventory model where the demand rate depends on the selling price and the stock level. A lower price or higher stock level lead to a higher demand rate. Three decision variables are considered: the selling price, the order-level and the reorder point. The goal is the maximization of the return on inventory management expense (ROIME), which is defined as the ratio between the profit and the total cost of the inventory system. The optimal values of the selling price, the order level, the reorder point, the lot size, the maximum ROIME and the cycle time are proposed, and the condition that ensures the profitability of the inventory system is established. The partial derivatives of these optimal values with respect to the initial parameters are calculated to analyse the sensitivity of the optimal policy concerning the parameters of the model. The profitability thresholds for each parameter, keeping all the others fixed, are also evaluated. A comparison between the solution with maximum ROIME and the solution with maximum profit per unit time is illustrated by using a numerical example. The solutions can be very different. Maximizing the return on inventory management expense leads to a zero-ending policy at the end of an inventory cycle, so the order-level is equal to the lot size. On the other hand, maximizing the profit per unit time requires a lower selling price, a higher lot size and a non-zero reorder point.