Heuristics Based on Lagrangian Relaxation for the Vehicle Routing Problem with Time Windows

In this paper, two different heuristics for the vehicle routing problem with time windows (VRPTW) are presented: the Sequential Insertion Heuristic and the Cluster and Sequential Insertion Heuristic. Both are based on the Lagrangian relaxation of the constraints which require each customer to be serviced exactly once. They were evaluated based on the classical six test problem sets described in the literature. The paper also describes a practical application of the Cluster and Sequential Insertion Heuristic to a real-life application involving a wholesale goods distribution in the metropolitan area of São Paulo, Brazil, which yielded good results with significant savings in vehicle-km and total cost.