Ordered median hub location problems with capacity constraints

The Single Allocation Ordered Median Hub Location problem is a recent hub model introduced in Puerto et al. (2011) that provides a unifying analysis of a wide class of hub location models. In this paper, we deal with the capacitated version of this problem, presenting two formulations as well as some preprocessing phases for fixing variables. In addition, a strengthening of one of these formulations is also studied through the use of some families of valid inequalities. A battery of test problems with data taken from the AP library are solved where it is shown that the running times have been significantly reduced with the improvements presented in the paper.