On the complexity of computing optimal private park-and-ride plans

Abstract

We consider the problem where a group of people scattered in a weighted graph G(V,E) has to travel by car to a common destination (the number of vertices may be much bigger than the number of people) where the weight of an edge is the cost of traveling along the edge with a car. Every member of the group has a car at their disposal and the objective is to minimize the total cost for getting all the members to the common destination. The members have the possibility of meeting and parking at the vertices and continue the journey sharing a car. We examine the computational complexity of the problem. Among other things, we show that the problem is APX-complete for the realistic setting where the cars have capacity 4 even restricted to undirected graphs where all edges have cost 1. © 2013 Springer-Verlag.