An Improved Robust Optimization Approach for Scheduling Under Uncertainty

In practice, the uncertainty in processing time data frequently affects the feasibility of optimal solution of the nominal production scheduling problem. Using the unit-specific event-based continuous time model for scheduling, we develop a novel multi-stage robust approach with corrective action to ensure robust feasibility of the worst case solution while reducing the conservatism arising from traditional robust optimization approaches. We quantify the probability of constraint satisfaction by using a priori and a posteriori probabilistic bounds for known and unknown uncertainty distributions, consequently, improving the objective value for a given risk scenario. Computational experiments on several examples were carried out to measure the effectiveness of the proposed method. For a given constraint satisfaction probability, the proposed method improves the objective value compared to the traditional robust optimization approaches