An ALNS to optimize makespan subject to total completion time for no-wait flow shops with sequence-dependent setup times

In this article, we address the no-wait flow shop scheduling problem with sequence dependent setup times. The objective is to minimize makespan subject to an upper bound on total completion time. Although these performance measures and constraints have been extensively studied, they have never been considered together in this problem before. To solve the problem, we propose an adaptive large neighborhood search algorithm called \(\textit{ALNS}_\textit{A}\) ${\mathit{ALNS}}_{\mathit{A}}$ . Essentially, \(\textit{ALNS}_\textit{A}\) ${\mathit{ALNS}}_{\mathit{A}}$ improves an initial solution by dynamically selecting and executing a pair of destroy and repair methods based on their performance history. In addition to classic greedy and random methods used, we present two new mechanisms in which the greediness-randomness behavior is balanced. To evaluate performance, the proposed approach is compared with three heuristic methods—GL, HH1 and TOB—developed for the most similar problems found in the literature. Computational experiments show that the proposed method outperforms state-of-the-art approaches in the literature for the no-wait flow shop scheduling problem with sequence dependent setup times and is therefore recommended to solve the problem.