On Minimum Changeover Cost Arborescences

We are given a digraph G = (N,A), where each arc is colored with one among k given colors. We look for a spanning arborescence T of G rooted (wlog) at node 1 and having minimum changeover cost. We call this the Minimum Changeover Cost Arborescence problem. To the authors' knowledge, it is a new problem. The concept of changeover costs is similar to the one, already considered in the literature, of reload costs, but the latter depend also on the amount of commodity flowing in the arcs and through the nodes, whereas this is not the case for the changeover costs. Here, given any node j ≠1, if a is the color of the single arc entering node j in arborescence T, and b is the color of an arc (if any) leaving node j, then these two arcs contribute to the total changeover cost of T by the quantity dab, an entry of a k-dimensional square matrix D. We first prove that our problem is NPO-complete and very hard to approximate. Then we present Integer Programming formulations together with a combinatorial lower bound, a greedy heuristic and an exact solution approach. Finally, we report extensive computational results and exhibit a set of challenging instances.