Optimization using common random numbers, control variates and multiple comparisons with the best

Abstract

This paper considers the problem of determining the best of a finite number of system designs by simulation experimentation when the criterion of interest is maximum or minimum expected performance. This is a special case of the general problem of optimization via simulation. The proposed method is based on multiple comparisons with the best (MCB), due to Hsu which constructs simultaneous interval estimates for the difference between the expected performance of each system design and the best of the other designs. We propose a refinement of Hsu's procedure through the use of two variance reduction techniques, common random numbers and control variates, that are particularly useful in simulation experiments. We show that the proposed procedure is better than the standard MCB in the sense that it is more sensitive to differences in expected performance.