A new robust optimization approach for scheduling under uncertainty: : I. Bounded uncertainty

The problem of scheduling under bounded uncertainty is addressed. We propose a novel robust optimization methodology, which when applied to mixed-integer linear programming (MILP) problems produces “robust” solutions which are in a sense immune against bounded uncertainty. Both the coefficients in the objective function, the left-hand-side parameters and the right-hand-side parameters of the inequalities are considered. Robust optimization techniques are developed for two types of uncertain data: bounded uncertainty and bounded and symmetric uncertainty. By introducing a small number of auxiliary variables and constraints, a deterministic robust counterpart problem is formulated to determine the optimal solution given the (relative) magnitude of uncertain data, feasibility tolerance, and “reliability level” when a probabilistic measurement is applied. The robust optimization approach is then applied to the scheduling under uncertainty problem. Based on a novel and effective continuous-time short-term scheduling model proposed by Floudas and coworkers [Ind. Eng. Chem. Res. 37 (1998a) 4341; Ind. Eng. Chem. Res. 37 (1998b) 4360; Ind. Eng. Chem. Res. 38 (1999) 3446; Comp. Chem. Engng. 25 (2001) 665; Ind. Eng. Chem. Res. 41 (2002) 3884; Ind. Eng. Chem. Res. (2003)], three of the most common sources of bounded uncertainty in scheduling problems are addressed, namely processing times of tasks, market demands for products, and prices of products and raw materials. Computational results on several small examples and an industrial case study are presented to demonstrate the effectiveness of the proposed approach. © 2003 Elsevier Ltd. All rights reserved.