On minimum reload cost paths, tours, and flows

The concept of reload cost, that is of a cost incurred when two consecutive arcs along a path are of different types, naturally arises in a variety of applications related to transportation, telecommunication, and energy networks. Previous work on reload costs is devoted to the problem of finding a spanning tree of minimum reload cost diameter (with no arc costs) or of minimum reload cost. In this article, we investigate the complexity and approximability of the problems of finding optimum paths, tours, and flows under a general cost model including reload costs as well as regular arc costs. Some of these problems, such as shortest paths and minimum cost flows, turn out to be polynomially solvable while others, such as minimum shortest path tree and minimum unsplittable multicommodity flows, are NP-hard to approximate within any polynomial-time computable function.