Scheduling a dual-resource flexible job-shop with sequence-dependent setup times: an industrial case study in garment manufacturing

This paper addresses a dual-resource constrained flexible job-shop scheduling problem (DRC-FJSSP) motivated by operational challenges in a French textile sewing workshop. Given the significant labour costs associated with Made-in-France garment production and the high variability of incoming orders, the scheduling objective is to maximise operator productivity over a short planning horizon. The problem is modelled using two frameworks: Mixed-Integer Programming (MIP) and Constraint Programming (CP). A constructive heuristic is presented, the Lowest Continuity Score (LCS) heuristic, is introduced to efficiently maximise operator throughput at industrial scale. A benchmark of industrial instances is derived from real production data. Computational experiments show that exact methods cannot solve instances beyond 200 operations within one hour, while the LCS heuristic consistently achieves solutions within 23% of the analytical upper bound across the large majority of instance classes and quartiles, with gaps below 20% for medium and large instances (Q2–Q4). A second heuristic, the Earliest Starting Time Interval (ESTI), is proposed to improve the balance between productivity and due-date satisfaction. The results indicate that, relative to LCS, ESTI significantly decreases total tardiness while maintaining productivity at a comparable level. This makes it a useful option for practitioners facing urgent orders.