Weber problems with alternative transportation systems

In this paper we address a planar p-facility location problem where, together with a metric induced by a gauge, there exists a series of rapid transit lines, which can be used as alternative transportation system to reduce the total transportation cost. The location problem is reduced to solving a finite number of (multi)-Weber problems, from which localization results are obtained. In particular, it is shown that, if the gauge in use is polyhedral, then the problem is reduced to finding a p-median.