Tractable Cases of Facility Location on a Network with a Linear Reliability Order of Links

In this paper we study the problem of locating k facilities to maximize the expected demand serviced in a network with unreliable links. Given a linear ordering of links, which models the dependencies among link failures, we assume that when a strong link fails, all weaker links with lower reliability also fail. This model is due to Gunnec and Salman [1], and for the single ordering case, an exact algorithm for maximizing expected serviced demand was provided in our earlier work [2] via a greedy method and dynamic programming.