Identifying the Best System in the Presense of Stochastic Constraints with Varying Thresholds

We consider the problem of finding a system with the best primary performance measure among a finite number of simulated systems in the presence of stochastic constraints on secondary performance measures. When no feasible system exists, the decision maker may be willing to consider looser thresholds. Given that there is no change in the underlying simulated systems, we adopt the concept of green simulation and perform feasibility check across all potential thresholds simultaneously. We propose an indifference-zone procedure that takes multiple threshold values for each constraint based on the user's inputs and returns the best system that is feasible to the most desirable thresholds. We prove that our procedure yields the best system in the most desirable feasible region possible with at least a prespecified probability. Our experimental results show that the proposed procedure performs well with respect to the number of required observations as compared with an existing procedure.