Maximizing profits in an inventory model with both demand rate and holding cost per unit time dependent on the stock level

► We study an EOQ inventory model with demand rate and holding cost rate per unit time, both potentially dependent on the stock level. ► The objective is to maximize the average profit per unit time. ► We demonstrate the existence and uniqueness of the optimal cycle time. ► We provide an algorithm to obtain the optimal policy. We study an EOQ inventory model with demand rate and holding cost rate per unit time, both potentially dependent on the stock level. The ordering cost, the holding cost and the gross profit from the sale of the item are considered. The objective is to maximize the average profit per unit time. We present the analytical formulation of the problem and demonstrate the existence and uniqueness of the optimal cycle time, giving a numerical algorithm to obtain it. Moreover, we provide two fundamental theoretical results: a rule to check when a given cycle time is the optimal policy, and a necessary and sufficient condition for the profitability of the system. Several EOQ models analyzed by other authors are particular cases of the one here studied. We present some numerical examples to illustrate the proposed algorithm and analyze the sensitivity of the optimal solution with respect to changes in various parameters of the system.