Optimization in process planning under uncertainty

This paper develops a two-stage stochastic programming approach for process planning under uncertainty. We first extend a deterministic mixed-integer linear programming formulation to account for the presence of discrete random parameters. Subsequently, we devise a decomposition algorithm for the solution of the stochastic model. The case of continuous random variables is handled through the same algorithmic framework without requiring any a priori discretization of their probability space. Computational results are presented for process planning problems with up to 10 processes, 6 chemicals, 4 time periods, 24 random parameters, and 5²⁴ scenarios. The efficiency of the proposed algorithm enables for the first time not just solution but even on-line solution of these problems. Finally, a method is proposed for comparing stochastic and fuzzy programming approaches. Overall, even in the absence of probability distributions, the comparison favors stochastic programming.