A New Tiebreaker in the NEH heuristic for the Permutation Flow Shop Scheduling Problem

Abstract

The most efficient constructive heuristic so far for the Permutation Flow shop Scheduling Problem (PFSSP) with makespan minimization criterion is the NEH heuristic. It iteratively inserts a non-scheduled job into the position of the partial schedule that reduces the makespan. It iterates until a complete schedule is produced. It usually produces a high number of ties when selecting the best position, and the recent literature is proposing tiebreakers to improve the results. In this paper we propose a new tiebreaker that is based on the estimation of the variation of idle times produced with the insertion of the new job, and that takes into account the reversibility property of the PFSSP. Computational results show that this tiebreaker outperforms the state-of-the-art methods.