Complexity of one-cycle robotic flow-shops

We study the computational complexity of finding the shortest route the robot should take when moving parts between machines in a flow-shop. Though this complexity has already been addressed in the literature, the existing attempts made crucial assumptions which were not part of the original problem. Therefore, they cannot be deemed satisfactory. We drop these assumptions in this paper and prove that the problem is NP-hard in the strong sense when the travel times between the machines of the cell are symmetric and satisfy the triangle inequality. We also impose no restrictions on the times of robot arrival at and departure from machines as it is the case in the related, but different, hoist scheduling problem. Our results hold for processing times equal on all machines in the cell. However, the equidistant case for equal processing times can be solved in O(1) time.