ERROR ANALYSIS OF AN APPROXIMATE OPTIMAL POLICY FOR AN INVENTORY SYSTEM WITH STOCHASTIC AND CONTINUOUS DEMANDS

For a periodic-review inventory system with stochastic and continuous demands and without setup costs, it is known that there exists a base-stock policy to be optimal. For a finite-horizon system with non-stationary parameters, it is essential to find approximate optimal policies because of the computational intractability of finding the optimal policy. This paper provides an approach, by which an analytical bound of the error between the costs of the approximate optimal policy and the optimal policy is given. It is shown that the approximate optimal policy converges to the optimal policy as the size of the computational grid decreases. Numerical results are presented to illustrate the methodology.