The economic consequences of a production and inventory control policy

We investigate the economic performance of a generalised Order-Up-To policy in response to an Auto Regressive stochastic demand process. We focus on the case where the physical production/distribution lead-time is one period and where we forecast demand with simple exponential smoothing. We consider two sets of convex piece-wise linear costs. The first set is the traditional inventory holding and backlog costs. The second set of costs are 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.