Optimal robot scheduling to minimize the makespan in a three-machine flow-shop environment with job-independent processing times

•We study a non-cyclic three-machine robotic flow-shop scheduling problem.•Jobs are identical and the objective is to minimize the makespan.•A single robot is available for transferring jobs between machines.•A set of lower bounds for the minimum objective value is provided.•The problem is divided and an optimal schedule is provided for each subproblem.

We study a robotic three-machine flow-shop scheduling problem, in which n identical jobs are to be processed and the objective is to minimize the makespan. After the job’s completion on either the first or the second machine it is transferred by a robot to the next (consecutive) machine in the shop. A single robot is available for transferring the jobs. We show that the problem can be solved by decomposing it into a set of sub-problems, and by providing a robot schedule to each sub-problem that yields a makespan value which matches the lower bound value.