Comparison of heuristics for flowtime minimisation in permutation flowshops

In this paper, we address the problem of sequencing jobs in a permutation flow shop with the objective of minimising the sum of completion times or flowtime. This objective is considered to be relevant and meaningful for todayʹs dynamic production environment, and therefore it has attracted the attention of researchers during the last years. As a result, a number of different types of heuristics have recently been developed, each one claiming to be the best for the problem. However, some of these heuristics have been independently developed and only partial comparisons among them exist. Consequently, there are no conclusive results on their relative performance. Besides, some of these types of heuristics are of a different nature and could be combined in order to obtain composite heuristics. In this paper, we first classify and conduct an extensive comparison among the existing heuristics. Secondly, based on the results of the experiments, we suggest two new composite heuristics for the problem. The subsequent computational experience shows these two heuristics to be efficient for the problem under consideration.