A linear programming approach to the optimum network orientation problem

In this paper a procedure is described to orient arcs of a graph so as to mimimize the sum of the distances between certain given source-sink pairs. This work is a substantial part of the more general problem of orienting a road network in such a way as to optimize a specified objective subject to the requirement that one can go from any point of the network to any other one. The proposed method, related to the ideas of sequential optimization [1, 2, 3], uses column-generation as well as row-generation.