A simple heuristic policy for stochastic inventory systems with both minimum and maximum order quantity requirements

In this paper, we consider a periodic-review stochastic inventory system with both minimum and maximum order quantity (MinOQ and MaxOQ, respectively) requirements. In each period, if an order is placed, the order quantity is bounded, at least at the MinOQ and at most the MaxOQ. The optimal policy of such a system is unknown, and even if it exists, it must be quite complicated. We propose a heuristic policy, called the modified (s, S) policy, under which whenever the inventory position drops to the reorder point s or below, an order is placed to raise the inventory position as close as possible to the order-up-to level S. Applying a discrete-time Markov chain approach, we are able to compute the system-wide long-run average cost. We provide bounds for the optimal values of s and S and design an efficient algorithm to optimize our proposed policy. In addition, the proposed heuristic policy has excellent performance in our numerical studies. We also measure the impact of some inventory parameters. SUPPLEMENTARY INFORMATION: The online version supplementary material available at 10.1007/s10479-021-04441-1.