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Hyperbolic integer programming

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  • M. Grunspan
  • M. E. Thomas

Abstract

The hyperbolic integer program is treated as a special case of a hyperbolic program with a finite number of feasible points. The continuous hyperbolic program also belongs to this class since its solution can be obtained by considering only the extreme points of the feasible set. A general algorithm for solving the hyperbolic integer program which reduces to solving a sequence of linear integer problems is proposed. When the integer restriction is removed, this algorithm is similar to the Isbell‐Marlow procedure. The geometrical aspects of the hyperbolic problem are also discussed and several cutting plane algorithms are given.

Suggested Citation

  • M. Grunspan & M. E. Thomas, 1973. "Hyperbolic integer programming," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 20(2), pages 341-356, June.
    • Handle: RePEc:wly:navlog:v:20:y:1973:i:2:p:341-356
    DOI: 10.1002/nav.3800200214
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    Cited by:

    1. Park, Chong Hyun & Lim, Heejong, 2021. "A parametric approach to integer linear fractional programming: Newton’s and Hybrid-Newton methods for an optimal road maintenance problem," European Journal of Operational Research, Elsevier, vol. 289(3), pages 1030-1039.
    2. Chong Hyun Park & Gemma Berenguer, 2020. "Supply Constrained Location‐Distribution in Not‐for‐Profit Settings," Production and Operations Management, Production and Operations Management Society, vol. 29(11), pages 2461-2483, November.
    3. Jose Joaquin del Pozo-Antúnez & Francisco Fernández-Navarro & Horacio Molina-Sánchez & Antonio Ariza-Montes & Mariano Carbonero-Ruz, 2021. "The Machine-Part Cell Formation Problem with Non-Binary Values: A MILP Model and a Case of Study in the Accounting Profession," Mathematics, MDPI, vol. 9(15), pages 1-16, July.

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