Robust Optimization for Scheduling under Bounded Uncertainty in Processing Times

A novel robust optimization methodology is proposed for scheduling under bounded uncertainty in processing times. This approach generates “robust” solutions which are in a sense immune against uncertainty when it is applied to Mixed-Integer Linear Programming (MILP) problems with uncertain coefficients and right-hand-side parameters of the inequality constraints. By introducing a small number of auxiliary variables, a deterministic robust counterpart problem is formulated to determine the optimal solution given the (relative) magnitude of uncertain data and feasibility tolerance. Based on a novel continuous-time short-term scheduling model, uncertainty in processing times of operational tasks is considered. Preliminary computational results are presented to demonstrate the effectiveness of the proposed approach.