Chance Constrained Selection of the Best

Selecting the solution with the largest or smallest mean of a primary performance measure from a finite set of solutions while requiring secondary performance measures to satisfy certain constraints is called constrained selection of the best (CSB) in the simulation ranking and selection literature. In this paper, we consider CSB problems with secondary performance measures that must satisfy probabilistic constraints, and we call such problems chance constrained selection of the best (CCSB). We design procedures that first check the feasibility of all solutions and then select the best among all the sample feasible solutions. We prove the statistical validity of these procedures for variations of the CCSB problem under the indifference-zone formulation. Numerical results show that the proposed procedures can efficiently handle CCSB problems with up to 100 solutions, each with five chance constraints.