A Lagrangian Relaxation based heuristic for the consolidation problem of airfreight forwarders

International air cargo is an operation-intensive industry, involving complex procedures and many players. As an important player, airfreight forwarders need to consolidate the collected goods skillfully in order to satisfy the requirements of the shippers and, at the same time minimize the expense charged by the airlines. However, the air cargo rate structure is very complicated, making the consolidation a difficult mixed-integer programming problem for the airfreight forwarder. In this paper, the consolidation problem is first transformed into a well-known set covering problem by treating a feasible consolidated shipment as a set. Lagrangian Relaxation is used as the backbone to develop a recursive heuristic algorithm. Based on the numerical experiment, the heuristic algorithm generates solutions very close to optimality. In particular, a sensitivity analysis is performed with respect to the degree of concavity. The results suggest that the solution algorithm can be used as a core module of the decision support system for air cargo consolidation. (C) 2006 Elsevier Ltd. All rights reserved.