A high-performing constructive heuristic for minimizing makespan in permutation flowshops

Minimizing makespan in permutation flowshops is one of the most frequently investigated problems in scheduling theory. The NEH heuristic is commonly regarded as the best current constructive heuristic for solving this NP-hard problem. In this paper, we propose a novel constructive heuristic with an effective tie-breaking strategy to improve the scheduling quality of this problem. Experimental results reveal that the proposed approach outperforms NEH for all problem sizes on the standard benchmark problem set of Taillard. This study thus appears to successfully demonstrate a high-performing constructive heuristic that can serve as a new foundation for future research on this extremely challenging scheduling problem.