In this paper we propose a multigraph model and a heuristic for the Vehicle Routing Problem with Time Windows (VRPTW). In the classical VRPTW, travel information is commonly represented with a customer-based graph, where an arc is an abstraction of the best road-network path between two nodes. We consider the case when parallel arcs are added to this graph to introduce different compromises between travel time and cost. It has been shown in the literature that this multigraph modeling enables substantial gains in the solution quality, while highly complicating the problem. We develop an Adaptive Large Neighbourhood Search (ALNS) heuristic in which a special data structure and dynamic programming algorithms are used to efficiently address the multigraph setting. Computational experiments on several set of instances demonstrate the effectiveness of our solution method and the impact of alternative paths on the solution quality.