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The permutation flowshop scheduling problem is a vital production management concern of industries such as electronic product manufacturing and integrated circuit fabrication. In many studies, jobs are prioritized independently according to their features or properties. This article develops a new perspective by introducing the self-attention mechanism into scheduling for the first time. The job similarities are characterized by the dot-product of processing time matrices and taken as job priorities. Based on this idea, a new priority rule denoted by PRSAT is proposed, and a heuristic named NEHLJP2 is presented with makespan minimization. The computational results with the Taillard and VRF benchmarks and 640 random instances demonstrate that the new priority rule and heuristic dominate the existing ones at a nominal cost of computation time. [ABSTRACT FROM AUTHOR]

The blocking flow-shop scheduling problem, which is an NP-hard problem, has wide applications in industry. Many studies have focused primarily on single-objective optimization, such as minimizing the makespan or total flow time, which is insufficient for practical problems. In this study, a blocking flow-shop scheduling problem with bicriteria of the makespan and machine utilization is considered. A simple constructive heuristic, NEHCG, is proposed by developing new priority and tie-breaking rules based on the Nawaz–Enscore–Ham heuristic. In the new priority rule, the quartile deviation of job processing times is included for the first time, and the new tie-breaking rule is designed to break ties effectively in the insertion phase. Then, an improved constructive heuristic, PW_NEHCG, is presented by effectively combining NEHCG with an improved profile-fitting approach. Computational experiments show that the proposed constructive heuristics exhibit excellent performance compared to other well-known heuristics. [ABSTRACT FROM AUTHOR]