Kanban, MRP and shaping the manufacturing environment
Management Science
A heuristic algorithm for mean flowtime objective in flowshop scheduling
Computers and Operations Research
An improved NEH heuristic to minimize makespan in permutation flow shops
Computers and Operations Research
An improved NEH-based heuristic for the permutation flowshop problem
Computers and Operations Research
A discrete differential evolution algorithm for the permutation flowshop scheduling problem
Computers and Industrial Engineering
Comparing three-step heuristics for the permutation flow shop problem
Computers and Operations Research
Computers and Operations Research
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The most efficient approximate procedures so far for the flowshop scheduling problem with makespan objective - i.e. the NEH heuristic and the iterated greedy algorithm - are based on constructing a sequence by iteratively inserting, one by one, the non-scheduled jobs into all positions of an existing subsequence, and then, among the so obtained subsequences, selecting the one yielding the lowest (partial) makespan. This procedure usually causes a high number of ties (different subsequences with the same best partial makespan) that must be broken via a tie-breaking mechanism. The particular tie-breaking mechanism employed is known to have a great influence in the performance of the NEH, therefore different procedures have been proposed in the literature. However, to the best of our knowledge, no tie-breaking mechanism has been proposed for the iterated greedy. In our paper, we present a new tie-breaking mechanism based on an estimation of the idle times of the different subsequences in order to pick the one with the lowest value of the estimation. The computational experiments carried out show that this mechanism outperforms the existing ones both for the NEH and the iterated greedy for different CPU times. Furthermore, embedding the proposed tie-breaking mechanism into the iterated greedy provides the most efficient heuristic for the problem so far.