A disjunctive graph-based metaheuristic for flexible job-shop scheduling problems considering fixture shortages in customized manufacturing systems

Customized manufacturing systems represent a promising production paradigm capable of producing a variety of products to meet diverse customer needs. However, limited resources and complex processes complicate the optimization of production scheduling and resource allocation. In particular, fixture shortages frequently arise in a highly customized manufacturing enterprise, as multiple new jobs may require the same fixture simultaneously. Consequently, certain fixtures must be machined as part of production tasks in workshops. To derive high-quality scheduling solutions, this paper proposes an improved genetic algorithm with a disjunctive graph-based local search for flexible job-shop scheduling problems considering on-site machining fixtures. First, several problem-specific genetic operators are introduced to enhance exploration capabilities. Second, a disjunctive graph for total weighted tardiness is established to identify critical paths. Third, a critical path-based local search method is proposed, incorporating three knowledge-based neighborhood structures to improve exploitation capabilities. Finally, the proposed algorithm is evaluated in 20 instances and compared against five state-of-the-art algorithms. The experimental results demonstrate that the proposed algorithm significantly outperforms its competitors regarding convergence and statistical metrics. A daily order from the enterprise is examined as a case study to evaluate the practical benefits of the proposed algorithm. From this case study, the total weighted tardiness and makespan are reduced by 62.71% and 42.13%, respectively, compared to the original scheduling solution.