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The freight allocation problem with all-units quantity-based discount: A heuristic algorithm


  • Qin, Hu
  • Luo, Meifeng
  • Gao, Xiang
  • Lim, Andrew


This paper studies a problem encountered by a buying office for one of the largest retail distributors in the world. An important task for the buying office is to plan the distribution of goods from Asia to various destinations across Europe. The goods are transported along shipping lanes by shipping companies, which offer different discount rates depending on the freight quantity. To increase the reliability of transportation, the shipper imposes a quantity limit on each shipping company on each shipping lane. To guarantee a minimum business volume, each shipping company requests a minimum total freight quantity over all lanes if it is contracted. The task involves allocating projected demand of each shipping lane to shipping companies subject to the above conditions such that the total cost is minimized.

Suggested Citation

  • Qin, Hu & Luo, Meifeng & Gao, Xiang & Lim, Andrew, 2012. "The freight allocation problem with all-units quantity-based discount: A heuristic algorithm," Omega, Elsevier, vol. 40(4), pages 415-423.
  • Handle: RePEc:eee:jomega:v:40:y:2012:i:4:p:415-423
    DOI: 10.1016/

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    References listed on IDEAS

    1. Schotanus, Fredo & Telgen, Jan & de Boer, Luitzen, 2009. "Unraveling quantity discounts," Omega, Elsevier, vol. 37(3), pages 510-521, June.
    2. Xia, Weijun & Wu, Zhiming, 2007. "Supplier selection with multiple criteria in volume discount environments," Omega, Elsevier, vol. 35(5), pages 494-504, October.
    3. Benton, W. C. & Park, Seungwook, 1996. "A classification of literature on determining the lot size under quantity discounts," European Journal of Operational Research, Elsevier, vol. 92(2), pages 219-238, July.
    4. Goossens, D.R. & Maas, A.J.T. & Spieksma, F.C.R. & van de Klundert, J.J., 2007. "Exact algorithms for procurement problems under a total quantity discount structure," European Journal of Operational Research, Elsevier, vol. 178(2), pages 603-626, April.
    5. Sawik, Tadeusz, 2010. "Single vs. multiple objective supplier selection in a make to order environment," Omega, Elsevier, vol. 38(3-4), pages 203-212, June.
    6. Chauhan, Satyaveer Singh & Proth, Jean-Marie, 2003. "The concave cost supply problem," European Journal of Operational Research, Elsevier, vol. 148(2), pages 374-383, July.
    7. Rubin, Paul A. & Benton, W. C., 2003. "Evaluating jointly constrained order quantity complexities for incremental discounts," European Journal of Operational Research, Elsevier, vol. 149(3), pages 557-570, September.
    8. Burke, Gerard J. & Carrillo, Janice & Vakharia, Asoo J., 2008. "Heuristics for sourcing from multiple suppliers with alternative quantity discounts," European Journal of Operational Research, Elsevier, vol. 186(1), pages 317-329, April.
    9. Jiefeng Xu & Leonard Lu & Fred Glover, 2000. "The deterministic multi-item dynamic lot size problem with joint business volume discount," Annals of Operations Research, Springer, vol. 96(1), pages 317-337, November.
    10. Chung, Chia-Shin & Hum, Sin-Hoon & Kirca, Omer, 1996. "The coordinated replenishment dynamic lot-sizing problem with quantity discounts," European Journal of Operational Research, Elsevier, vol. 94(1), pages 122-133, October.
    11. Chen, Frank Y. & Krass, Dmitry, 2001. "Analysis of supply contracts with minimum total order quantity commitments and non-stationary demands," European Journal of Operational Research, Elsevier, vol. 131(2), pages 309-323, June.
    12. Crama, Y. & Pascual J., R. & Torres, A., 2004. "Optimal procurement decisions in the presence of total quantity discounts and alternative product recipes," European Journal of Operational Research, Elsevier, vol. 159(2), pages 364-378, December.
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    Cited by:

    1. Kowalski, Krzysztof & Lev, Benjamin & Shen, Wenjing & Tu, Yan, 2014. "A fast and simple branching algorithm for solving small scale fixed-charge transportation problem," Operations Research Perspectives, Elsevier, vol. 1(1), pages 1-5.
    2. Zhou, Yuan & Xie, Jinxing, 2014. "Potentially self-defeating: Group buying in a two-tier supply chain," Omega, Elsevier, vol. 49(C), pages 42-52.
    3. repec:spr:annopr:v:258:y:2017:i:2:d:10.1007_s10479-015-1941-2 is not listed on IDEAS
    4. McDonald, Conor M., 2016. "Integrating packaging and supply chain decisions: Selection of economic handling unit quantities," International Journal of Production Economics, Elsevier, vol. 180(C), pages 208-221.


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