A branch-and-bound algorithm for the transportation problem with location of p transshipment points

A transshipment-related problem is considered. This problem involves a system with a choice of p transshipment points from a set of them, each with a (possibly) different associated location cost. We show that this problem is also an extension of the p-median location problem, and we emphasize two interesting applications: one of them can be seen as a p-median problem such that that the product is not only sent from the located facilities to the customers, but also returned from the customers to the facilities; the other one is a capacitated two-stage p-median location problem. The developed algorithm uses Lagrangean decomposition and branch-and-bound techniques. Computational results are presented for several data instances with different structures that include the multiitem case.