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A Capacity Improvement Lower Bound for Fixed Charge Network Design Problems

Author

Listed:
  • Bruce W. Lamar

    (University of California, Irvine, California)

  • Yosef Sheffi

    (Massachusetts Institute of Technology, Cambridge, Massachusetts)

  • Warren B. Powell

    (Princeton University, Princeton, New Jersey)

Abstract

Network design problems concern flows over networks in which a fixed charge must be incurred before an arc becomes available for use. The uncapacitated, multicommodity network design problem is modeled with aggregate and disaggregate forcing constraints. (Forcing constraints ensure logical relationships between the fixed charge-related and the flow-related decision variables.) A new lower bound for this problem—referred to as the capacity improvement (CI) bound—is presented; and an efficient implementation scheme using shortest path and linearized knapsack programs is described. A key feature of the CI lower bound is that it is based on the LP relaxation of the aggregate version of the problem. A numerical example illustrates that the CI lower bound can converge to the optimal objective function value of the IP formulation.

Suggested Citation

  • Bruce W. Lamar & Yosef Sheffi & Warren B. Powell, 1990. "A Capacity Improvement Lower Bound for Fixed Charge Network Design Problems," Operations Research, INFORMS, vol. 38(4), pages 704-710, August.
    • Handle: RePEc:inm:oropre:v:38:y:1990:i:4:p:704-710
    DOI: 10.1287/opre.38.4.704
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    Citations

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    Cited by:

    1. Linos F. Frantzeskakis & Hanan Luss, 1999. "The network redesign problem for access telecommunications networks," Naval Research Logistics (NRL), John Wiley & Sons, vol. 46(5), pages 487-506, August.
    2. Julie A. Ward, 1999. "Minimum-Aggregate-Concave-Cost Multicommodity Flows in Strong-Series-Parallel Networks," Mathematics of Operations Research, INFORMS, vol. 24(1), pages 106-129, February.
    3. Cynthia Barnhart & Hong Jin & Pamela H. Vance, 2000. "Railroad Blocking: A Network Design Application," Operations Research, INFORMS, vol. 48(4), pages 603-614, August.
    4. 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.
    5. Xin Wang & Teodor Gabriel Crainic & Stein W. Wallace, 2019. "Stochastic Network Design for Planning Scheduled Transportation Services: The Value of Deterministic Solutions," INFORMS Journal on Computing, INFORMS, vol. 31(1), pages 153-170, February.
    6. Crainic, Teodor Gabriel, 2000. "Service network design in freight transportation," European Journal of Operational Research, Elsevier, vol. 122(2), pages 272-288, April.
    7. Arnt-Gunnar Lium & Teodor Gabriel Crainic & Stein W. Wallace, 2009. "A Study of Demand Stochasticity in Service Network Design," Transportation Science, INFORMS, vol. 43(2), pages 144-157, May.
    8. 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.
    9. Gavin J. Bell & Bruce W. Lamar & Chris A. Wallace, 1999. "Capacity improvement, penalties, and the fixed charge transportation problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 46(4), pages 341-355, June.
    10. Francesca Maggioni & Florian A. Potra & Marida Bertocchi, 2017. "A scenario-based framework for supply planning under uncertainty: stochastic programming versus robust optimization approaches," Computational Management Science, Springer, vol. 14(1), pages 5-44, January.

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