Black-Box Simulation-Optimization with Quantile Constraints: An Inventory Case Study

We apply a recent variant of “efficient global optimization” (EGO). EGO is closely related to Bayesian optimization (BO): both EGO and BOtreat the simulation model as a black box, and use a Kriging metamodel or Gaussian process. The recent variant of EGO combines (i) EGO for unconstrained optimization, and (ii) the Karush- Kuhn- Tucker optimality conditions for constrained optimization. EGO sequentially searches for the global optimum. We apply this variant and a benchmark EGO variant to an (s, S) inventory model. We aim to minimize the mean inventory costs—excluding disservice costs—while satisfying a prespecified threshold for the 90%-quantile of the disservice level. Our numerical results imply that the mean inventory costs increase by 2.5% if management is risk-averse instead of risk-neutral—using the mean value. Comparing the two EGO variants shows that these variants do not give significantly different results, for this application.