Optimal sampling laws for constrained simulation optimization on finite sets: the bivariate normal case

Consider the context of selecting an optimal system from amongst a finite set of competing systems, based on a "stochastic" objective function and subject to a single "stochastic" constraint. In this setting, and assuming the objective and constraint performance measures have a bivariate normal distribution, we present a characterization of the optimal sampling allocation across systems. Unlike previous work on this topic, the characterized optimal allocations are asymptotically exact and expressed explicitly as a function of the correlation between the performance measures.