Robust scheduling for manufacturing with energy consumption limits

Our work considers a scheduling problem in which manufacturing companies with large energy demand are obligated to comply with total energy consumption limits in specified time intervals, e.g. 15 minutes. Moreover, the problem is complicated by the fact that in reality the production schedules are not executed exactly as planned due to unexpected disturbances such as machine breakdowns or material unavailability. Therefore, the goal is to find a robust schedule which guarantees that the energy consumption limits are not violated if the start times of operations are arbitrary delayed within a given limit. To circumvent the problem of an exponential number of constraints in the mixed integer linear programming formulation, we propose an exact algorithm based on a decomposition approach. The decomposition approach exploits the fact that the robustness of a given schedule can be checked in a pseudo-polynomial time. We evaluated the proposed algorithm on instances with varying bound of the start times delays.