Two-agent two-machine flowshop scheduling with learning effects to minimize the total completion time

•We study a two-agent two-machine flowshop scheduling problem.•The branch-and-bound algorithm can solve problems of up to 20 jobs.•Four genetic algorithms are proposed and evaluated.

We study a two-agent scheduling problem in a two-machine permutation flowshop with learning effects. The objective is to minimize the total completion time of the jobs from one agent, given that the maximum tardiness of the jobs from the other agent cannot exceed a bound. We provide a branch-and-bound algorithm for the problem. In addition, we present several genetic algorithms to obtain near-optimal solutions. Computational results indicate that the algorithms perform well in either solving the problem or efficiently generating near-optimal solutions.