The most recent optimization algorithm for (s, S) order policies with continuous demand was developed byFedergruen and Zipkin (1985). This was also the first efficient algorithm, which uses policy iteration instead ofdiscretization. Zheng and Federgruen (1991) developed an even more efficient algorithm for computing discreteorder quantity (s, S) inventory policies. Since the continuous case prohibits enumeration, this algorithm does notapply to continuous order quantity systems. In this paper an efficient algorithm for continuous order quantity (s, S)policies is developed. A marginal cost approach is used for determining the optimal s. Furthermore, we constructtwo aid functions (generated by the optimality conditions for s and S) , and exploiting their special properties asimple and efficient algorithm is obtained. The algorithm converges monotonically, such that at every iteration apolicy improvement is obtained. Since every iteration finds a local minimum of the expected average cost, thenumber of iterations is at most N, where N < ? represents the number of local minimums. The algorithm alsoapplies to discrete order quantity systems, in which case it basically reduces to the algorithm of Zheng andFedergruen (with the difference that in general our algorithm will take larger than unit steps, since we are not usingenumeration).
