In production/inventory control systems, the goal of the controller is to generate sophisticated decisions by controlling the order rate and inventory level. This paper aims at modeling a dynamic-stochastic production/inventory control system under two sources of variability (uncertainty) including uncertainties on demand rate and frustrating rate. The study deals with obtaining a robust optimal design of a Proportional-Integral-Derivative (PID) controller in in the stochastic control system. For this purpose, a new robust simulation-optimization method in the class of computational intelligence is proposed. To cope with the unknown distribution of uncertainty, the crossing weighted uncertainty scenarios are combined with the proposed method. Within this study, a new sequential robust efficient global optimization is proposed to make a trade-off between optimal and robustness terms in final optimization results. Finally, a numerical case with simulation experiments is conducted to demonstrate the advantages of the proposed policy in terms of optimal result, robustness, and computational cost.

In the real world of engineering problems, in order to reduce optimization costs in physical processes, running simulation experiments in the format of computer codes have been conducted. It is desired to improve the validity of simulation-optimization results by attending the source of variability in the model’s output(s). Uncertainty can increase complexity and computational costs in Designing and Analyzing of Computer Experiments (DACE). In this state of the art review paper, a systematic qualitative and quantitative review is implemented among Metamodel Based Robust Simulation Optimization (MBRSO) for black-box and expensive simulation models under uncertainty. This context is focused on the management of uncertainty, particularly based on the Taguchi worldview on robust design and robust optimization methods in the class of dual response methodology when simulation optimization can be handled by surrogates. At the end, while both trends and gaps in the research field are highlighted, some suggestions for future research are directed.