Discrete search methods for optimizing stochastic systems

In simulation practice, although estimating the performance of a complex st ochastic system is of great value to the decision maker, it is not always e nough. For example, a warehouse manager may be interested in finding out th e probability that all demands are met from on-hand inventory under a certa in system configuration of a fixed safety stock and a fixed order quantity. But he might be more interested in finding out what values of safety stock and order quantity will maximize this probability. In this paper we develo p three strategies of a new iterative search procedure for finding the opti mal 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 configurations are compared and the one that appears to be the better one is passed on to the next iteration. The f irst strategy of the proposed method uses a single observation of each conf iguration in every iteration, while the second strategy uses a fixed number of observations of each configuration In every iteration. The third strate gy uses sequential sampling with fixed boundaries. We show that, for all of these three strategies, the search process satisfies local balance equatio ns and its equilibrium distribution gives most weight to the optimal point (when suitably normalized by the size of the neighborhoods). We also show t hat the configuration that has been visited most often in the first m itera tions converges almost surely to an optimum solution. (C) 1998 Elsevier Sci ence Ltd. All rights reserved.