A branch-and-price algorithm for the multi-source Weber problem

We present a branch-and-price algorithm for the exact solution of the multi-source Weber problem, a classical NP-hard optimisation problem in location science with binary variables and non-linear objective. The algorithm is based on a set covering reformulation whose linear relaxation is solved via column generation at every node of a search tree. The pricing subproblem is equivalent to a single-source Weber problem with limited distances. The algorithm solved to optimality several previously unsolved instances with some thousands of points and some hundreds of sources. Computational experiments show that the algorithm is particularly effective at solving instances in which the ratio between the number of sources and the number of points is high.