Minimizing the number of vehicles in periodic scheduling: The non-Euclidean case

In this paper we consider the problem of minimizing the number of vehicles needed to meet a fixed periodically repeating set of tasks where set-up times between tasks do not satisfy the triangle inequality. We reduce this problem to finding the minimal length cycle-cover in a graph. In a special case, where the set-up times satisfy the triangle inequality, we reduce the scheduling problem to the assignment problem.