The economic performance of a generalized Order-Up-To policy is investigated in response to an Auto Regressive stochastic demand process. Focus is on the case where the physical production/distribution lead time is one period and where demand is forecasted with simple exponential smoothing. Two sets of convex piece-wise linear costs are considered. The first set is the traditional inventory holding and backlog costs. The second set of costs is piece-wise linear and increasing convex costs associated with the production order rate within and above a capacity constraint. Numerical investigations reveal that the classical Order-Up-To policy is no longer optimal when a broader range of costs is considered in the objective function.