Efficient exact formulations for the flexible job shop scheduling with flexible maintenance

In modern manufacturing systems, integrating preventive maintenance into production scheduling is essential to ensure operational efficiency and equipment reliability. This paper addresses the flexible job shop scheduling problem under machine unavailability constraints caused by non‐fixed maintenance tasks. We propose four enhanced mixed‐integer programming models subject to maintenance tasks in flexible job shops. We present four formulation enhancements that significantly improve the performance of the mathematical models. In addition, an efficient constraint programming model is introduced. We introduce a comprehensive dataset of 2010 instances derived and extended from classical flexible job‐shop scheduling benchmarks. The proposed benchmark covers a wide range of configurations, making it suitable for evaluating solution robustness and scalability. An extensive computational study demonstrates the strengths and trade‐offs among the proposed models. The computational experiments show the superiority of the constraint programming formulation compared to mixed‐integer programming models. This work proposes both efficient modeling approaches and a valuable benchmark for future research.