Simultaneous location of a service facility and a rapid transit line

This paper presents a location problem on the plane where a single service facility and a rapid transit line have to be simultaneously located. The rapid transit line represents an alternative transportation line which can be used by clients whenever it provides a cost-saving or time-saving service, and it is given by a segment with fixed and known length. This type of problems has not previously been considered in the Location Theory literature, as we are only aware of the existence of models that consider the location of service facilities in the presence of an already located alternative transportation system or models dealing with the location of rapid transit lines to minimize the travelling time among a set of points. To solve this problem we will develop an algorithm based on some characterizations of the objective function behavior.