A new approach to maximize the overall return on investment with price and stock dependent demand under the nonlinear holding cost

This study investigates an inventory model for deteriorating products with a price and stock-dependent demand pattern where the holding cost is a non-linear function of both time and stock level. Moreover, a decreased price and a higher stock level lead to a higher rate of demand. Consequently, in this article, we present a new approach, aiming at maximization of the return on investment by maximizing the profit/cost ratio. If an inventory manager has the potential to invest in a variety of projects, but disposes of only limited resources, it is logical to strategically plan towards a better return on investment. As a result, the manager’s objective will be to develop an inventory policy with a possibly high return on investment. Therefore, a new strategy is considered in this article to optimize the profitability ratio in terms of replenishment time and selling price, which is determined as the proportion between the profit and the overall cost of the inventory scheme. This research demonstrates that optimizing the profitability ratio is equivalent to decreasing the average inventory cost of a product per unit. Also, the optimality is graphically checked and one numerical illustration is discussed to explain the result of the proposed model. Finally, sensitivity analysis of key parameters is performed to show the applicability of the proposed model. The profit/cost ratio is more sensitive to price elasticity markup or purchasing cost compared to the other parameters used. Also, for decision-makers, several helpful management insights are derived.