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A Transportation Problem with Minimum Quantity Commitment

Author

Listed:
  • Andrew Lim

    (Department of Industrial Engineering and Engineering Management, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong)

  • Fan Wang

    (Department of Industrial Engineering and Engineering Management, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong)

  • Zhou Xu

    (Department of Industrial Engineering and Engineering Management, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong)

Abstract

We study a transportation problem with the minimum quantity commitment (MQC), which is faced by a famous international company. The company has a large number of cargos for carriers to ship to the United States. However, the U.S. Marine Federal Commission stipulates that when shipping cargos to the United States, shippers must engage their carriers with an MQC. With such a constraint of MQC, the transportation problem becomes intractable. To solve it practically, we provide a mixed-integer programming model defined by a number of strong facets. Based on this model, a branch-and-cut search scheme is applied to solve small-size instances and a linear programming rounding heuristic for large ones. We also devise a greedy approximation method, whose solution quality depends on the scale of the minimum quantity if the transportation cost forms a distance metric. Extensive experiments have been conducted to measure the performance of the formulations and the algorithms and have shown that the linear rounding heuristic behaves best.

Suggested Citation

  • Andrew Lim & Fan Wang & Zhou Xu, 2006. "A Transportation Problem with Minimum Quantity Commitment," Transportation Science, INFORMS, vol. 40(1), pages 117-129, February.
    • Handle: RePEc:inm:ortrsc:v:40:y:2006:i:1:p:117-129
    DOI: 10.1287/trsc.1050.0123
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    References listed on IDEAS

    as
    1. Gerald G. Brown & Robert F. Dell & Alexandra M. Newman, 2004. "Optimizing Military Capital Planning," Interfaces, INFORMS, vol. 34(6), pages 415-425, December.
    2. Jewel S. Bonser & S. David Wu, 2001. "Procurement Planning to Maintain Both Short-Term Adaptiveness and Long-Term Perspective," Management Science, INFORMS, vol. 47(6), pages 769-786, June.
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    Citations

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    Cited by:

    1. Chung‐Yee Lee & Shengnan Shu & Zhou Xu, 2021. "Optimal Global Liner Service Procurement by Utilizing Liner Service Schedules," Production and Operations Management, Production and Operations Management Society, vol. 30(3), pages 703-714, March.
    2. Andrew Lim & Brian Rodrigues & Zhou Xu, 2008. "Transportation Procurement with Seasonally Varying Shipper Demand and Volume Guarantees," Operations Research, INFORMS, vol. 56(3), pages 758-771, June.
    3. Wang, Tingsong & Meng, Qiang & Wang, Shuaian & Qu, Xiaobo, 2021. "A two-stage stochastic nonlinear integer-programming model for slot allocation of a liner container shipping service," Transportation Research Part B: Methodological, Elsevier, vol. 150(C), pages 143-160.
    4. Fang Yang & Yao-Huei Huang, 2021. "An optimization approach for winner determination problem considering transportation cost discounts," Journal of Global Optimization, Springer, vol. 80(3), pages 711-728, July.
    5. Weiwei Chen & Jie Song & Leyuan Shi & Liang Pi & Peter Sun, 2013. "Data mining-based dispatching system for solving the local pickup and delivery problem," Annals of Operations Research, Springer, vol. 203(1), pages 351-370, March.
    6. Talla Nobibon, Fabrice & Leus, Roel & Spieksma, Frits C.R., 2011. "Optimization models for targeted offers in direct marketing: Exact and heuristic algorithms," European Journal of Operational Research, Elsevier, vol. 210(3), pages 670-683, May.
    7. Clavijo López, Christian & Crama, Yves & Pironet, Thierry & Semet, Frédéric, 2024. "Multi-period distribution networks with purchase commitment contracts," European Journal of Operational Research, Elsevier, vol. 312(2), pages 556-572.
    8. Aghdas Badiee & Hamed Kalantari & Chefi Triki, 2023. "Leader-based diffusion optimization model in transportation service procurement under heterogeneous drivers’ collaboration networks," Annals of Operations Research, Springer, vol. 322(1), pages 345-383, March.

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