An Evaluation of Mathematical Programming and Lower-Bound Methods for Hybrid Flow Shop Problems With a Makespan Criterion

This paper considers the hybrid flow shop scheduling problem, where jobs are processed in m stages with same route of stage. Each stage has identical parallel machines for processing jobs. Some mathematical programming formulations and lower bound calculations have been proposed literature such cases. Nevertheless, there is a lack complete comparisons these bounds literature. In this paper, we propose new mixed integer model two based on bin-packing concept considered problem. To evaluate model, sets small small-to-medium problems used to compare our existing models. Moreover, propositions discussed bounds. The experimental results show that efficiently found optimal solutions because it needs smaller number binary variables constraints, can also serve as strong indicator distances between obtained by heuristic algorithms solution.