Advanced Optimization for Process Systems Engineering

This chapter first describes general approaches for anticipating uncertainty in optimization models. The strategies include optimizing the expected value, minimax stategy, chance-constrained,two-stage and multistage programming, and robust optimization. The chapter focuses on the solution of two-stage stochastic MILP programming problems in which 0-1 variables are present in stage-1 decisions. The discretization of the uncertain parameters is described, which gives rise to scenario trees. We then present the extended MILP formulation that explicitly considers all possible scenarios. Since this problem can become too large, the Benders decomposition method (also known as the L-shaped method )is introduced, in which a master MILP problem is defined through duality in order to predict new integer values for stage-1 decisions, as well as a lower bound. The extension to multistage programming problems is also briefly discussed, as well as a brief reference to robust optmization in which the robust counterpart is derived.