Abstract: The paper considers the problem of scheduling jobs in a three-machine flow-shop to minimize the makespan. Between the completion of an operation and the beginning of the next operation of the same job, there is a time lag, which we refer to it as the transportation time. All transportation times have to be done by a single robot, which can perform at most one transportation at a time. New complexity results are derived for special case.

Key words: Flow-shop scheduling problem, Transportation time, Robot, Complexity