Two-Level Robust Optimization for Uncertain Job Shop Scheduling Problem

This paper proposes a two-level robust optimization model in the context of job shop scheduling problem. The job shop scheduling problem optimizes the makespan under uncertain processing times, which are described by a set of scenarios. In the first-level optimization, a traditional stochastic optimization model is conducted to obtain the optimal expected performance as a standard performance, on which a concept of bad-scenario set is defined. In the second-level optimization, a robustness measure is given based on bad-scenario set. The objective function for the second robust optimization model is to combine expected performance and robustness measure. Finally, an extensive experiment was conducted to investigate the advantages of the proposed robust optimization model. The computational results show that the two-level model can achieve a better compromise between average performance and robustness than the existing robust optimization models.