The location-dispatching problem: Polyhedral results and content delivery network design

Let G=(V,A) be a directed graph and F be a set of items. The Location-Dispatching Problem consists of determining subsets L_i ⊆ F located at nodes i ∈ V, minimizing the sum of two costs: a piecewise linear installation cost associated with L_i and an access cost for each node of V to reach a copy of each item of F. We formulate this problem as a linear program with binary variables x and integer variables z. We propose a facial study of the associated polytope and we introduce the so-called integrity hop cost inequalities that force z to be an integer as soon as x is binary. Using this, we devise a branch-and-cut algorithm and report some experimental results. This algorithm has been used to solve Content Delivery Network instances in order to optimize a Video On Demand (VoD) system.