Bounds and tabu search for a cyclic max–min scheduling problem

A cyclic scheduling problem with applications to transport efficiency is considered. Given a set of regular polygons, whose vertices represent regularly occurring events and are lying on a common circle line, the objective is to maximize the distance between the closest vertices of different polygons on the circle line. Lower and upper bounds for the optimal solution of this NP-hard scheduling problem are presented. They are used to improve the quality of a procedure which is applied to solve this problem heuristically. It consists of a greedy starting algorithm and a Tabu Search algorithm. The numerical results show the efficiency of the procedure proposed.