Optimal replenishment for a periodic review inventory system with two supply modes

In this paper, we study periodic inventory systems with long review periods. We develop dynamic programming models for these systems in which regular orders as well as emergency orders can be placed periodically. We identify two cases depending on whether or not a fixed cost for placing an emergency order is present. We show that if the emergency supply mode can be used, there exists a critical inventory level such that if the inventory position at a review epoch falls below this critical level, an emergency order is placed. We also develop simple procedures for computing the optimal policy parameters. In all cases, the optimal order-up-to level is obtained by solving a myopic cost function. Thus, the proposed ordering policies are easy to implement.