Discrete search methods for optimizing stochastic systems

✍ Scribed by Mohamed A. Ahmed; Talal M. Alkhamis; Douglas R. Miller

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 364 KB
• Volume: 34
• Category: Article
• ISSN: 0360-8352
• DOI: 10.1016/s0360-8352(98)00003-5

✦ Synopsis

AbstractÐIn simulation practice, although estimating the performance of a complex stochastic system is of great value to the decision maker, it is not always enough. For example, a warehouse manager may be interested in ®nding out the probability that all demands are met from on-hand inventory under a certain system con®guration of a ®xed safety stock and a ®xed order quantity. But he might be more interested in ®nding out what values of safety stock and order quantity will maximize this probability. In this paper we develop three strategies of a new iterative search procedure for ®nding the optimal parameters of a stochastic system, where the objective function cannot be evaluated exactly but must be estimated through Monte Carlo simulation. In each iteration, two neighboring con®gurations are compared and the one that appears to be the better one is passed on to the next iteration. The ®rst strategy of the proposed method uses a single observation of each con®guration in every iteration, while the second strategy uses a ®xed number of observations of each con®guration in every iteration. The third strategy uses sequential sampling with ®xed boundaries. We show that, for all of these three strategies, the search process satis®es local balance equations and its equilibrium distribution gives most weight to the optimal point (when suitably normalized by the size of the neighborhoods). We also show that the con®guration that has been visited most often in the ®rst m iterations converges almost surely to an optimum solution.