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Solving Generalized Networks

Author

Listed:
  • Gerald G. Brown

    (Naval Postgraduate School, Monterey, California 93943)

  • Richard D. McBride

    (School of Business Administration, University of Southern California, Los Angeles, California 90089-4121)

Abstract

A complete, unified description is given of the design, implementation and use of a family of very fast and efficient large-scale minimum-cost (primal simplex) network programs. The class of capacitated generalized transshipment problems solved includes the capacitated and uncapacitated generalized transportation problems and the continuous generalized assignment problem, as well as the pure network flow models which are specializations of these problems. These formulations are used for a large number of diverse applications to determine how (or at what rate) flows through the arcs of a network can minimize total shipment costs. A generalized network problem can also be viewed as a linear program with at most two nonzero entries in each column of the constraint matrix; this property is exploited in the mathematical presentation with special emphasis on data structures for basis representation, basis manipulation, and pricing mechanisms. A literature review accompanies computational testing of promising ideas, and extensive experimentation is reported which has produced GENNET, an extremely efficient family of generalized network systems.

Suggested Citation

  • Gerald G. Brown & Richard D. McBride, 1984. "Solving Generalized Networks," Management Science, INFORMS, vol. 30(12), pages 1497-1523, December.
    • Handle: RePEc:inm:ormnsc:v:30:y:1984:i:12:p:1497-1523
    DOI: 10.1287/mnsc.30.12.1497
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    Citations

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    Cited by:

    1. John W. Mamer & Richard D. McBride, 2000. "A Decomposition-Based Pricing Procedure for Large-Scale Linear Programs: An Application to the Linear Multicommodity Flow Problem," Management Science, INFORMS, vol. 46(5), pages 693-709, May.
    2. Elsie Sterbin Gottlieb, 2002. "Solving generalized transportation problems via pure transportation problems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 49(7), pages 666-685, October.
    3. Richard D. McBride & John W. Mamer, 2004. "Implementing an LU Factorization for the Embedded Network Simplex Algorithm," INFORMS Journal on Computing, INFORMS, vol. 16(2), pages 109-119, May.
    4. Rajagopalan, S. & Yu, Hung-Liang, 2001. "Capacity planning with congestion effects," European Journal of Operational Research, Elsevier, vol. 134(2), pages 365-377, October.

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