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