Properties of the periodic review (R, T) inventory control policy for stationary, stochastic demand

This paper studies the single-item, periodic review, order-up-to policy in which both the review period and the order-up-to level are decision variables. The paper provides results similar to those of Roundy and Zhang for the periodic review inventory control policy. The cost function for the period review policy is shown to be jointly convex in its decision parameters for both the compound Poisson demand model and the Brownian motion demand process. Sensitivity analysis shows that the cost is insensitive to the review period T if the corresponding optimal order-up-to level is used. Moreover, powers-of-two intervals do not increase costs significantly. This yields a proof that a periodic-review-based policy for the joint replenishment problem is, in the worst case, within 50% of the unknown optimal. The results provide insights into how review periods and the base-stock levels can be jointly optimized and how to construct effective powers-of-two periodic review policies when demand is stochastic. These policies are easy to implement in practice and have provable performance guarantees.