Optimal and near-optimal inventory control policies for a make-to-order inventory–production system

This paper examines several inventory replenishment policies for a make-to-order inventory–production system that consists of a production workshop and a warehouse. Demands arrive to the production workshop according to a Poisson process, and are processed in an first-come-first-served manner. The production workshop requires that the warehouse provides, as needed, raw materials for use in the production process. The warehouse inventory is replenished according to an inventory replenishment policy. The optimal replenishment policy, which minimizes the average total cost per product, is derived using a Markov decision process approach. The structure of the optimal replenishment policy is explored. Simple ‘order-up-to’, ‘myopic’, and heuristic replenishment policies are introduced. The myopic and heuristic replenishment policies are easy to compute, and yet perform almost as well as the optimal replenishment policy.