The class of vehicle routing problems involves the optimization of freight or person transportation activities. These problems are generally treated via the representation of geographical data as a valued complete graph. Every arc of the graph represents the shortest path for a possible origin-destination connection. Several attributes can be defined for an arc (travel time, travel cost. . . ), but the path implied by this arc is computed according to a single criterion, generally travel time. Consequently, some alternative routes proposing a different compromise between the attributes of the arcs are dismissed at once from the solution space. In this work, we propose to represent geographic data with a multigraph, so that these alternative routes are considered, and to evaluate how it impacts on solution algorithms and solution values. A simple insertion algorithm is proposed and illustrated in the context of a demand responsive transportation system developed in a French region. Computational experiments on realistic data underline the potential cost savings brought by the multigraph model.