Performance bound for myopic order-up-to inventory policies under stationary demand processes

We consider a single-item infinite-horizon inventory system operating in discrete time and study the performance of the popular myopic order-up-to policy when demand is driven by a general autoregressive moving average (ARMA) stationary process. We derive a suboptimality bound for a system that operates under full demand backlogging, linear holding and backordering costs, and a constant replenishment lead time. We illustrate our results for the case in which demand follows an ARMA(1,1) process, which includes two commonly used demand models, MA(1) and AR(1), as special cases.