On Optimality of a Class of Dynamic Myopic Policies for Continuous‐Time Replenishment with Periodic Updates

This paper is motivated by inventory problems arising in supply chains characterized by continuous replenishment programs based on information exchanged (reviewed) only intermittently between a manufacturing system (supplier) and a customer (retailer). When the replenishment is once‐per‐period, rather than at any point of time, a well‐known result is the optimality of the so‐called myopic base‐stock policy. We generalize the notion of the base‐stock policy and study the optimality of the corresponding class of dynamic myopic policies. We identify a myopic policy and prove that although the replenishment rule is dynamic, this policy is optimal when the demands are stationary and the number of review periods tends to infinity.