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 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-hound techniques. Computational results are presented for several data instances with different
structures that include the multiitem case