Locating stops along bus or railway lines – A bicriteria problem

In this paper we consider the location of stops along the edges of an already existing public transportation network. This can be the introduction of bus stops along given routes, or of railway stations along the tracks in a railway network. The goal is to achieve a maximal covering of given demand points with a minimal number of stops. This bicriteria problem is in general NP-hard. We present a finite dominating set yielding an IP-formulation as a bicriteria set covering problem. Using this formulation we discuss cases in which the bicriteria stop location problem can be solved in polynomial time. Extensions for tackling real-world instances are mentioned.