Distributionally Robust Optimization for Permutation Flow Shop Scheduling with Sequence-Dependent Setup Times and Operational Cost Under Uncertainty in Industry 4.0 Manufacturing Systems

Production scheduling in sustainable manufacturing systems must cope with processing time uncertainty while maintaining operational efficiency and controlling operational costs. This paper proposes a Distributionally Robust Optimization (DRO) model for the permutation flow shop scheduling problem with sequence-dependent setup times (PFSP-SDST), where uncertain processing times are represented through multiple scenarios and evaluated under ambiguous probability distributions. An exact solution approach is developed for small-scale instances. For medium and large-scale problems, the Greedy Randomized Adaptive Search Procedure (GRASP), the proposed Hybrid GRASP (HGRASP), Ant Lion Optimizer (ALO) and Slime Mold Algorithm (SMA) are adapted and compared. Computational experiments show that most methods closely reproduce the exact benchmark solutions on small instances. For large-scale problems, the Friedman test reveals significant differences in both solution quality (p=9.91 ×10−6) and computational time (p=3.49 ×10−6). Post hoc comparisons indicate that ALO and SMA achieve the best solution quality performance and are statistically indistinguishable from each other, while SMA obtains the most favorable computational time rank. These findings indicate favorable performance of the population-based metaheuristics under the adopted experimental settings for the considered distributionally robust flow shop scheduling problems under processing time uncertainty. The proposed DRO framework offers a practical approach for generating reliable schedules while reducing operational costs in Industry 4.0 manufacturing systems.