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

Kuan-cheng Huang*, Wenhou Chi

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

18 Scopus citations


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.

Original languageEnglish
Pages (from-to)235-245
Number of pages11
JournalTransportation Research Part C: Emerging Technologies
Issue number4
StatePublished - 1 Jan 2007


  • Air cargo
  • Concave minimization
  • Decision support
  • Freight consolidation
  • Lagrangian relaxation
  • Set covering problem

Fingerprint Dive into the research topics of 'A Lagrangian relaxation based heuristic for the consolidation problem of airfreight forwarders'. Together they form a unique fingerprint.

Cite this