Mathematical model and solution approach for collaborative logistics in less than truckload (LTL) transportation

Collaborative logistics is achieved when two or more carriers or shippers form partnerships to optimize their transportation operations by sharing vehicle capacities and delivery tasks in order to cut empty back hauls and to increase vehicle utilization rate. This paper studies collaborative logistics in less than truckload transportation and develops a general mathematical model and a Lagrangian relaxation approach to solve this problem. From the model´s optimal solution, a set of feasible vehicle tours corresponding to the transportation operations in collaborative logistics can be constructed. The model is suitable for both shipper collaboration and carrier collaboration. Furthermore, ten randomly generated examples are tested to demonstrate the validity of our proposed model and solution approach.