Robust optimization for process scheduling under uncertainty

This paper addresses the uncertainty problem in process scheduling using robust optimization. Compared to the traditional-scenario-based stochastic programming method, robust counterpart optimization method has a unique advantage, in that the scale of the corresponding optimization problem does not increase exponentially with the number of the uncertain parameters. Three robust counterpart optimization formulations-including Soyster's worst-case scenario formulation, Ben-Tal and Nemirovski's formulation, and a formulation proposed by Bertsimas and Sim-are studied and applied to uncertain scheduling problems in this paper. The results show that the formulation proposed by Bertsimas and Sim is the most appropriate model for uncertain scheduling problems, because it has the following advantages: (i) the model has the same size as the other formulations, (ii) it preserves its linearity, and (iii) it has the ability to control the degree of conservatism for every constraint and guarantees feasibility for the robust optimization problem.