Robust economic optimization of process design under uncertainty

In this study, ranges of model parameters are analyzed for robustness measures. In particular, the properties of partial mean and worst-case cost in robust optimization are investigated. The robust optimization models are considered as multiobjective problems having two objectives, the expected performance (i.e., expected cost) and a robustness measure. The robust partial mean model is defined with objectives of expected value and partial mean. The robust worst-case model is defined with the objective of expected value and worst-case. They are proved to guarantee Pareto optimality, which should be satisfied for multiobjective optimization problems. A graphical representation of the meaningful parameter ranges is clearly defined with mathematical proofs. The robustness of the solution is discussed, based on the analysis of the ranges of the parameters. Three meaningful ranges of the parameters are investigated to choose a proper target value for the robust partial mean model. The worst-case value obtained from the worst-case analysis is recommended as the most effective target value, in order to obtain the optimal solution in a tradeoff between robustness and optimality. The proposed analysis in this study is validated with examples in chemial process design problems.