Stop location design in public transportation networks: covering and accessibility objectives

We consider the location of new stops along the edges of an existing public transportation network. Examples of StopLoc include the location of bus stops along some given bus routes or of railway stations along the tracks in a railway system. In order to evaluate the decision assume that potential customers in given demand facilities are known. Two objectives are proposed. In the first one, we minimize the number of stations such that any of the demand facilities can reach a closest station within a given distance of r. In the second objective, we fix the number of new stations and minimize the sum of the distances between demand facilities and stations. The resulting two problems CovStopLoc and AccessStopLoc are solved by a reduction to a classical set covering and a restricted location problem, respectively. We implement the general ideas in two different environments, the plane, where demand facilities are represented by coordinates, and in networks, where they are nodes of a graph.