Inventory planning with forecast updates: approximate solutions and cost error bounds

We consider a finite-horizon, periodic-review inventory model with demand forecasting updates following the martingale model of forecast evolution. The optimal policy is a state-dependent base-stock policy, which, however, is computationally intractable to obtain. We develop tractable bounds on the optimal base-stock levels and use them to devise a general class of heuristic solutions. Through this analysis, we identify a necessary and sufficient condition for the myopic policy to be optimal. Finally, to assess the effectiveness of the heuristic policies, we develop upper bounds on their value loss relative to optimal cost. These solution bounds and cost error bounds also work for general dynamic inventory models with nonstationary and autocorrelated demands. Numerical results are presented to illustrate the results.