Scheduling a flow shop with dual sources of uncertainty: a distributionally robust approach

This article addresses a two-stage flow-shop scheduling problem (FSSP) considering uncertain job processing and release time. To minimize the worst-case expected makespan, a distributionally robust optimization (DRO) approach is designed. By introducing effective bounds and valid inequalities, the problem is transformed into a mixed integer linear program (MlLP), which is solvable via off-the-shelf commercial solvers. To verify the performance of the model, the DRO model is compared with the stochastic linear program (SLP) and its deterministic counterpart under various parameter settings, where the DRO model exhibits greater robustness and computational efficiency in handling almost all the scenarios. Besides, the DRO model demonstrates a prominent advantage when the uncertain interval of the mean is larger, the release time is less scattered and more jobs are scheduled. It is discovered that the proposed DRO model is capable of providing robust schedules in a highly volatile environment, thereby enhancing the resilience and robustness of manufacturing operations.