Mathematical Modeling and A Novel Heuristic Method for Flexible Job-Shop Batch Scheduling Problem with Incompatible Jobs

This paper investigates a novel flexible job-shop scheduling problem, where the machines have batch-processing capacity, but incompatible jobs cannot be processed in batch (FJSPBI) simultaneously. problem has wide applications discrete manufacturing, especially chemical and steel casting industries. For first time, this study, 3-indexed mixed-integer linear programming (MILP) model is proposed, which can efficiently optimally solved by commercial solvers for small-scale problems. In addition, an improved large neighborhood search (LNS) algorithmic framework with optimal insertion tabu-based components (LNSIT) achieve high-quality solutions large-scale FJSPBI reasonable time. A perturbation strategy are then additionally embedded to improve exploitation exploration ability of algorithm. The proposed algorithm tested on numerous existing benchmark instances without incompatibility characteristics, newly generated FJSPBI. experimental results indicate effectiveness MILP algorithm, including strategies, significantly reduce computational burden LNS comparison further verify that LNSIT directly solve specific incompatibility, better than methods, instances. Additionally, impacts range rate, instance scale, machine processing performance analyzed presented.