Optimal Continuous Order Quantity (s,s) Policies

Emöke Bázsa () and Peter den Iseger
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Emöke Bázsa: Erasmus University Rotterdam
Peter den Iseger: Erasmus University Rotterdam

No 01-102/4, Tinbergen Institute Discussion Papers from Tinbergen Institute

Abstract: 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

Date: 2001-10-16
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