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 embed- ded network in the plane represents an alternative transportation system in which traveling is fasterthan 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 bytwo facility points on the network (or transfer points), if the travel time from the origin to destinationby using the network through such points is not higher than a given acceptance level related to the traveltime without using the network. The facility location problems studied in this work consist of locatingone or two transfer points on the network such that, under several objective functions, the traffic throughthe network is maximized. Due to the continuous nature of these problems, a general approach is pro- posed for discretizing them. Since the non-convexity of the distance function on cyclic networks alsoimplies the absence of convexity of the mixed distance function, such an approach is based on a decom- position process which leads to a collection of subproblems whose solution set can be found by adaptingthe general strategy to each problem considered.