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On the uncapacitated K‐commodity network design problem with zero flow‐costs

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  • Ada Suk‐fung Ng
  • Trilochan Sastry
  • Janny M.Y. Leung
  • X.Q. Cai

Abstract

Extending Sastry's result on the uncapacitated two‐commodity network design problem, we completely characterize the optimal solution of the uncapacitated K‐commodity network design problem with zero flow costs for the case when K = 3. By solving a set of shortest‐path problems on related graphs, we show that the optimal solutions can be found in O(n3) time when K = 3, where n is the number of nodes in the network. The algorithm depends on identifying a list of “basic patterns”; the number of basic patterns grows exponentially with K. We also show that the uncapacitated K‐commodity network design problem can be solved in O(n3) time for general K if K is fixed; otherwise, the time for solving the problem is exponential. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004

Suggested Citation

  • Ada Suk‐fung Ng & Trilochan Sastry & Janny M.Y. Leung & X.Q. Cai, 2004. "On the uncapacitated K‐commodity network design problem with zero flow‐costs," Naval Research Logistics (NRL), John Wiley & Sons, vol. 51(8), pages 1149-1172, December.
    • Handle: RePEc:wly:navres:v:51:y:2004:i:8:p:1149-1172
    DOI: 10.1002/nav.20047
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    References listed on IDEAS

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    1. Itzhak Gilboa & Sunil Chopra & S. Trilochan Sastri, 1998. "Source Sink Flows with Capacity Installation in Batches," Post-Print hal-00753123, HAL.
    2. Kaj Holmberg & Di Yuan, 2000. "A Lagrangian Heuristic Based Branch-and-Bound Approach for the Capacitated Network Design Problem," Operations Research, INFORMS, vol. 48(3), pages 461-481, June.
    3. Kaj Holmberg & Johan Hellstrand, 1998. "Solving the Uncapacitated Network Design Problem by a Lagrangean Heuristic and Branch-and-Bound," Operations Research, INFORMS, vol. 46(2), pages 247-259, April.
    4. Teodor Gabriel Crainic & Michel Gendreau & Judith M. Farvolden, 2000. "A Simplex-Based Tabu Search Method for Capacitated Network Design," INFORMS Journal on Computing, INFORMS, vol. 12(3), pages 223-236, August.
    5. BIENSTOCK, Daniel & CHOPRA, Sunil & GÜNLÜK, Oktay & TSAI, Chih-Yang, 1998. "Minimum cost capacity installation for multicommodity network flows," LIDAM Reprints CORE 1391, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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