A Lagrangian Heuristic for the Vehicle Routing Problems with the Private Fleet and the Common Carrier

The delivery of goods from a warehouse to local customers is an important decision problem of a logistics operator. As the demand is fluctuating, the common carrier may be needed if the private fleet is insufficient. In this study, we focus on the vehicle routing problem with private fleet and common carrier (VRPPC). In order to balance computational load and solution quality, a heuristic algorithm is developed based on several classical mathematical programming techniques. The VRPPC is first formulated in the form of the set covering problem, and the Lagrangian relaxation is used as the backbone in designing the iterative algorithm. In addition, a concept similar to column generation is used to update the solution space, a partial set of routes. Based on the numerical experiment, the solution quality of the heuristic algorithm is stable, and the computation time is acceptable under the current highly dynamic environment.