A polynomial algorithm for 2-cyclic robotic scheduling: A non-Euclidean case

In this paper we consider the problem of no-wait cyclic scheduling of identical parts in an mm-machine production line in which a robot is responsible for moving each part from a machine to another. The aim is to find the minimum cycle time for the so-called 2-cyclic schedules, in which exactly two parts enter and two parts leave the production line during each cycle. The earlier known polynomial-time algorithms for this problem are applicable only under the additional assumption that the robot travel times satisfy the triangle inequalities. We lift this assumption on robot travel times and present a polynomial-time algorithm with the same time complexity as in the metric case, O(m5logm)O(m5logm).