Optimization of makespan for no-wait flowshop scheduling problems using efficient matheuristics

• The presented matheuristics outperform all existing algorithms.
• Two matheuristics solve the no-wait flowshop scheduling problem (NWFSP) optimally.
• The proposed matheuristics can solve very hard and large NWFSPs optimally.

The no-wait flowshop scheduling problem (NWFSP) with makespan minimization is a well-known strongly NP-hard problem with applications in various industries. This study formulates this problem as an asymmetric traveling salesman problem, and proposes two matheuristics to solve it. The performance of each of the proposed matheuristics is compared with those of the best existing algorithms on 21 benchmark instances of Reeves and 120 benchmark instances of Taillard. Computational results show that the presented matheuristics outperform all existing algorithms. In particular, all tested instances of the problem, including a subset of 500-job and 20-machine test instances, are solved to optimality in an acceptable computational time. Moreover, the proposed matheuristics can solve very hard and large NWFSPs to optimality, including the benchmark instances of Vallada et al. and a set of 2000-job and 20-machine problems. Accordingly, this study provides a feasible means of solving the NP-hard NWFSP completely and effectively.