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We propose four algorithms for the no-wait flow shop scheduling problem. The objective is minimizing total completion time such that makespan is not greater than a maximum value. We address the problem with sequence-dependent setup times, an important production constraint that has never been considered for this problem before. The proposed algorithms start from an initial solution and then iterate through a process that destroys and repairs the incumbent solution in order to improve it. The methods are build combining distinct destruction and construction mechanisms, where the search intensification-diversification is explored at different levels. After an initial assessment, the best proposed algorithm ( IG4 ) is chosen to be compared with three literature methods ( PAL ,  TOB ,  ISA-2 ) developed for similar problems. Computational experiments revealed that the overall average relative percentage deviation of  PAL ,  TOB ,  ISA-2 , and  IG4  are 10.97%, 4.44%, 2.07%, and 0.36%, respectively. The statistical analysis confirms that  IG4  significantly outperforms the existing methods.

Heuristics to optimize total completion time subject to makespan in no-wait flow shops with sequence-dependent setup times