Optimality of Myopic Inventory Policies for Certain Dependent Demand Processes

This paper shows that the optimal policy for single-product periodic ordering systems with proportional holding and stockout costs and zero lead time is myopic for both stationary and nonstationary demand processes as described by Box and Jenkins. The proof of optimality is based on a theorem by Veinott showing that the myopic policy is optimal in each period if the beginning inventory for that period is less than the critical number which is the optimal policy for that period considered in isolation.