An Asymptotic Test of Optimality Conditions in Multiresponse Simulation Optimization

This paper derives a novel, asymptotic statistical test of the Karush–Kuhn–Tucker first-order necessary optimality conditions in random simulation models with multiple responses. This test combines a simple form of the delta method and a generalized version of Wald's statistic. The test is applied to both a toy problem and an (s, S) inventory-optimization problem with a service-level constraint; its numerical results are encouraging.