Makespan Minimization for the Two-Stage Hybrid Flow Shop Problem with Dedicated Machines: A Comprehensive Study of Exact and Heuristic Approaches

This paper presents a comprehensive approach for minimizing makespan in the challenging two-stage hybrid flowshop with dedicated machines, a problem known to be strongly NP-hard. This study proposed a constraint programming approach, a novel heuristic based on a priority rule, and Tabu search procedures to tackle this optimization problem. The constraint programming model, implemented using a commercial solver, serves as the exact resolution method, while the heuristic and Tabu search explore approximate solutions simultaneously. The motivation behind this research is the need to address the complexities of scheduling problems in the context of two-stage hybrid flowshop with dedicated machines. This problem presents significant challenges due to its NP-hard nature and the need for efficient optimization techniques. The contribution of this study lies in the development of an integrated approach that combines constraint programming, a novel heuristic, and Tabu search to provide a comprehensive and efficient solution. The proposed constraint programming model offers exact resolution capabilities, while the heuristic and Tabu search provide approximate solutions, offering a balance between accuracy and efficiency. To enhance the search process, the research introduces effective elimination rules, which reduce the search space and simplify the search effort. This approach improves the overall optimization performance and contributes to finding high-quality solutions. The results demonstrate the effectiveness of the proposed approach. The heuristic approach achieves complete success in solving all instances for specific classes, showcasing its practical applicability. Furthermore, the constraint programming model exhibits exceptional efficiency, successfully solving problems with up to n=500 jobs. This efficiency is noteworthy compared to instances solved by other exact solution approaches, indicating the scalability and effectiveness of the proposed method.