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Robust Optimization of Experimentally Derived Objective Functions

In the design or improvement of systems and processes, the objective function is often a performance response surface estimated from experiments. A standard approach is to identify the levels of the design variables that optimize the estimated model. However, if the estimated model varies from the true model due to random error in the experiment, the resulting solution may be quite far from optimal. We consider all points in the confidence intervals associated with the estimated model and construct a minimax deviation model to find a robust solution that is resistant to the error in the estimated empirical model. We prove a reduction theorem to reduce the optimization model to a tractable, finite, mathematical program. The proposed approach is applied to solve for a robust order policy in an inventory problem and is compared with the canonical approach using a Monte Carlo simulation.