A node rooted flow-based model for the local access network expansion problem

In the local access expansion problem we need to expand a given tree network by increasing the capacity of the edges or by installing concentrating devices in some nodes of the network, in order to satisfy the increase in node demands. It was shown in [4] that the problem can be viewed as an extension of the well-known Capacitated Minimum Spanning Tree Problem (CMSTP) and two flowbased models (a single and a multi-commodity model) with additional constraints were introduced. In this work we present a new flow-based model that includes additional information on the first node of each feasible path. We will show that this additional information permits us to write models with a tighter linear programming relaxation which, in turn, would permit us to solve, in an easier way, instances from the literature. We test and compare the new and old models for instances with 100, 200 and 500 nodes in order to show the advantages of the new proposed model.