Efficient heuristic algorithms for the blocking flow shop scheduling problem with total flow time minimization

• Two efficient constructive heuristics for the Fm|block|ΣCi are proposed.
• We show that the insertion phase of heuristic NEH can worsen the solution.
• The structure of each constructive method is used in a GRASP combined with VNS.
• The computational evaluation shows the good performance of these algorithms.

This paper proposes two constructive heuristics, i.e. HPF1 and HPF2, for the blocking flow shop problem in order to minimize the total flow time. They differ mainly in the criterion used to select the first job in the sequence since, as it is shown, its contribution to the total flow time is not negligible. Both procedures were combined with the insertion phase of NEH to improve the sequence. However, as the insertion procedure does not always improve the solution, in the resulting heuristics, named NHPF1 and NHPF2, the sequence was evaluated before and after the insertion to keep the best of both solutions. The structure of these heuristics was used in Greedy Randomized Adaptive Search Procedures (GRASP) with variable neighborhood search in the improvement phase to generate greedy randomized solutions. The performance of the constructive heuristics and of the proposed GRASPs was evaluated against other heuristics from the literature. Our computational analysis showed that the presented heuristics are very competitive and able to improve 68 out of 120 best known solutions of Taillard’s instances for the blocking flow shop scheduling problem with the total flow time criterion.