To stop or not to stop: a time-constrained trip covering location problem on a tree network

Location of new stations/stops in public transportation networks has attracted much interest from both the point of views of theory and applications. In this paper we consider a set of pairs of points in the plane demanding traveling between the elements of each pair, and a tree network embedded in the plane representing the transportation system. An alternative mode of transportation competes with the combined plane-network mode so that the modal choice is made by distance (time) comparisons. The aim of the problem dealt with in this paper is to locate a new station/stop so that the traffic through the network would be maximized. Since stops at new stations increases the time of passengers that already used the combined mode, and may persuade them to change the mode, a constraint on the increase of the overall time is imposed. A quadratic in the number of pairs time algorithm is proposed.