Finding the best in the presence of a stochastic constraint

Our problem is that of finding the best system - i.e., the system with the largest or smallest primary performance measure - among a finite number of simulated systems in the presence of a stochastic constraint on a secondary performance measure. In order to solve this problem, we first find a set that contains only feasible or near-feasible systems (phase I) and then choose the best among those systems in the set (phase II). We present a statistically valid procedure for phase I and then propose another procedure that performs phases I and II sequentially to find the best feasible system. Finally, we provide some experimental results for the second procedure.