A general approach for the location of transfer points on a network with a trip covering criterion and mixed distances

In this paper we consider a trip covering location model in a mixed planar-network space. An embedded network in the plane represents an alternative transportation system in which traveling is faster than traveling within the plane. We assume that the demand to be covered is given by a set of origin-destination pairs in the plane, with some traffic between them. An origin-destination pair is covered by two facility points on the network (or transfer points), if the travel time from the origin to destination by using the network through such points is not higher than a given acceptance level related to the travel time without using the network. The facility location problems studied in this work consist of locating one or two transfer points on the network such that, under several objective functions, the traffic through the network is maximized. Due to the continuous nature of these problems, a general approach is proposed for discretizing them. Since the non-convexity of the distance function on cyclic networks also implies the absence of convexity of the mixed distance function, such an approach is based on a decomposition process which leads to a collection of subproblems whose solution set can be found by adapting the general strategy to each problem considered.