An efficient hybrid algorithm for the two-machine no-wait flow shop problem with separable setup times and single server

We consider the two-machine no-wait flow shop problem with separable setup times and single server side constraints, and makespan as the performance measure. This problem is strongly NP-hard. A mathematical model of the problem is developed and a number of propositions are proven for the special cases. Furthermore, a hybrid algorithm of variable neighbourhood search (VNS) and Tabu search (TS) is proposed for the generic case. For evaluation, a number of test problems with small instances are generated and solved to optimality. Computational results show that the proposed algorithm is able to reproduce the optimal solutions of all of the small-instance test problems. For larger instances, proposed solutions are compared with the results of the famous two-opt algorithm as well as a lower bound that we develop in this paper. This comparison demonstrates the efficiency of the algorithm to find good-quality solutions.