A new approach to maximize the profit/cost ratio in a stock-dependent demand inventory model

Abstract

This work analyzes an inventory system with stock-dependent demand and non-linear holding cost. It presents a new approach to maximize the return on investment, that is, the profit/cost ratio. When an inventory manager can invest in different projects and the resources are limited, it seems sensible to select those projects that provide a higher return on investment. Thus, the goal of the manager will be to find the inventory policy that gives a major return on investment. Note that the solution for the maximum profit per unit time does not necessarily match the solution of the maximum profit/cost ratio. Consequently, a new procedure to obtain the inventory policy that maximizes the return on investment should be proposed. In this paper, it is proved that maximizing the profit/cost ratio is equivalent to minimizing the inventory cost per unit of an item, instead of minimizing the inventory cost per unit time. The optimal policy can be obtained in a closed form and the replacement should be done when the stock is depleted. Thus, the inventory manager does not need to process a new order while there are items available in stock. This optimal solution is different from the other policies proposed for the problems of minimum cost or maximum profit per unit time. Finally, numerical examples are solved to illustrate the theoretical results and the solution methodology proposed in the work.