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Minimum-Cost Multicommodity Network Flows

Author

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  • J. A. Tomlin

    (University of Adelaide, Adelaide, South Australia)

Abstract

The minimum-cost multicommodity network flow problem is formulated in both node-arc and arc-chain form, leading to very large linear programs. The special structure of these programs is utilized in algorithms for their solution.

Suggested Citation

  • J. A. Tomlin, 1966. "Minimum-Cost Multicommodity Network Flows," Operations Research, INFORMS, vol. 14(1), pages 45-51, February.
    • Handle: RePEc:inm:oropre:v:14:y:1966:i:1:p:45-51
    DOI: 10.1287/opre.14.1.45
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    Cited by:

    1. Dewil, R. & Vansteenwegen, P. & Cattrysse, D. & Van Oudheusden, D., 2015. "A minimum cost network flow model for the maximum covering and patrol routing problem," European Journal of Operational Research, Elsevier, vol. 247(1), pages 27-36.
    2. Lin, Cheng-Chang, 2001. "The freight routing problem of time-definite freight delivery common carriers," Transportation Research Part B: Methodological, Elsevier, vol. 35(6), pages 525-547, July.
    3. Jose L. Walteros & Andrés L. Medaglia & Germán Riaño, 2015. "Hybrid Algorithm for Route Design on Bus Rapid Transit Systems," Transportation Science, INFORMS, vol. 49(1), pages 66-84, February.
    4. Shiva Prakash Gupta & Urmila Pyakurel & Tanka Nath Dhamala, 2023. "Multi-commodity flow problem on lossy network with partial lane reversals," Annals of Operations Research, Springer, vol. 323(1), pages 45-63, April.
    5. Lin, Yi-Kuei, 2007. "Reliability of a computer network in case capacity weight varying with arcs, nodes and types of commodity," Reliability Engineering and System Safety, Elsevier, vol. 92(5), pages 646-652.
    6. Kaj Holmberg & Di Yuan, 2003. "A Multicommodity Network-Flow Problem with Side Constraints on Paths Solved by Column Generation," INFORMS Journal on Computing, INFORMS, vol. 15(1), pages 42-57, February.
    7. Larsson, Torbjörn & Patriksson, Michael, 1995. "An augmented lagrangean dual algorithm for link capacity side constrained traffic assignment problems," Transportation Research Part B: Methodological, Elsevier, vol. 29(6), pages 433-455, December.
    8. Moradi, Siamak & Raith, Andrea & Ehrgott, Matthias, 2015. "A bi-objective column generation algorithm for the multi-commodity minimum cost flow problem," European Journal of Operational Research, Elsevier, vol. 244(2), pages 369-378.
    9. Khodakaram Salimifard & Sara Bigharaz, 2022. "The multicommodity network flow problem: state of the art classification, applications, and solution methods," Operational Research, Springer, vol. 22(1), pages 1-47, March.
    10. Wang, Shuaian, 2014. "A novel hybrid-link-based container routing model," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 61(C), pages 165-175.

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