Abstract
We consider the shipment consolidation and freight forwarding problem under two discount schemes: the system-wide and the double-discount. In the system-wide scheme, the cost associated with one flight does not only depend on the quantity of freight assigned to that flight, but also on the total freight assigned to other flights operated by the same carrier. In the double-discount scheme, there are cost savings based on the quantity shipped on a given flight on top of the system-wide discount. We propose models based on multi-commodity network flow formulations that take into account practical aspects such as cargo unsplitability, shipment volume and over-declaration. We propose solution methodologies based on Lagrangrean relaxation and local branching. Numerical testing reveals the efficiency of the approaches presented and sheds light on some managerial implications. We find that freight forwarders do not only reduce costs from the system-wide and the double-discount schemes, but are also likely to engage with fewer airlines, thus reducing administrative fees.
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References
Chang T-S (2008) Best routes selection in international intermodal networks. Comput Oper Res 35(9):2877–2891
Cohn A, Davey M, Schkade L, Siegel A, Wong C (2008) Network design and flow problems with cross-arc costs. Eur J Oper Res 189(3):890–901
Croxton KL, Gendron B, Magnanti TL (2003) Models and methods for merge-in-transit operations. Transp Sci 37(1):1–22
Croxton KL, Gendron B, Magnanti TL (2007) Variable disaggregation in network flow problems with piecewise linear costs. Oper Res 55(1):146–157
Fischetti M, Lodi A (2003) Local branching. Math Program 98(1–3):23–47
Fisher ML (1981) The Lagrangian relaxation method for solving integer programming problems. Manag Sci 27(1):1–18
Higginson JK, Bookbinder JH (1994) Policy recommendations for a shipment-consolidation program. J Bus Logist 15(1):87–112
Huang K, Chi W (2007) A Lagrangian relaxation based heuristic for the consolidation problem of airfreight forwarders. Transp Res Part C 15(4):235–245
Li Z, Bookbinder JH, Elhedhli S (2012) Optimal shipment decisions for an airfreight forwarder: formulation and solution methods. Transp Res Part C 21(1):17–30
Muriel A, Munshi F (2004) Capacitated multicommodity network flow problems with piecewise linear concave costs. IIE Trans 36 (7):683–696. ISSN 0740-817X
Rodriguez-Martin I, Salazar-Gonzalez JJ (2010) A local branching heuristic for the capacitated fixed-charge network design problem. Comput Oper Res 37(3):575–581
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We thank two anonymous referees for their valuable feedback and comments that helped improve the content of the paper.
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Elhedhli, S., Li, Z. & Bookbinder, J.H. Airfreight forwarding under system-wide and double discounts. EURO J Transp Logist 6, 165–183 (2017). https://doi.org/10.1007/s13676-015-0093-5
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DOI: https://doi.org/10.1007/s13676-015-0093-5