Optimal Linear Inventory Control and First Order Exponential Smoothing

A linear, fixed-interval stock replenishment policy that achieves an optimal cost balance between inventory and order-level variances is derived in this paper. The reorder rule relies on an exponentially weighted moving average to smooth random components of the demand sequence, which are assumed to be pairwise uncorrelated with mean zero and variance that either grows or decays geometrically, or remains constant in time.