The class of vehicle routing problems involves the optimization of freight or passenger transportation activities. These problems are generally treated via the representation of the road network as a weighted complete graph. Each arc of the graph represents the shortest route for a possible origin-destination connection. Several attributes can be defined for one arc (travel time, travel cost . . . ), but the shortest route modelled by this arc is computed according to one single criterion, generally travel time. Consequently, some alternative routes proposing a different compromise between the attributes of the arcs are discarded from the solution space. In this work, we propose to represent the road network 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 on-demand transportation system developed in a French area. Computational experiments on academic and realistic data underline the potential cost savings brought by the multigraph model.