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Technical Note—An Improved Branch-and-Bound Method for Integer Programming

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  • J. A. Tomlin

    (Scientific Control Systems Ltd., London, England)

Abstract

This note proposes two extensions of the successful Beale and Small branch-and-bound mixed-integer algorithm. The integer requirements on nonbasic variables are utilized to calculate stronger “penalties” when searching down the solution tree and to give a stronger criterion for abandoning unprofitable branches of the tree when backtracking. This stronger criterion is obtained by making use of Gomory cutting-plane constraints. These modifications have produced considerable reductions of the searching effort required for pure integer and predominantly integer problems, and have the further advantage of being very easy to incorporate.

Suggested Citation

  • J. A. Tomlin, 1971. "Technical Note—An Improved Branch-and-Bound Method for Integer Programming," Operations Research, INFORMS, vol. 19(4), pages 1070-1075, August.
    • Handle: RePEc:inm:oropre:v:19:y:1971:i:4:p:1070-1075
    DOI: 10.1287/opre.19.4.1070
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    Cited by:

    1. Andrew G. Loerch, 1999. "Incorporating learning curve costs in acquisition strategy optimization," Naval Research Logistics (NRL), John Wiley & Sons, vol. 46(3), pages 255-271, April.
    2. Kurt M. Bretthauer, 1994. "A penalty for concave minimization derived from the tuy cutting plane," Naval Research Logistics (NRL), John Wiley & Sons, vol. 41(3), pages 455-463, April.
    3. Ellis L. Johnson & George L. Nemhauser & Martin W.P. Savelsbergh, 2000. "Progress in Linear Programming-Based Algorithms for Integer Programming: An Exposition," INFORMS Journal on Computing, INFORMS, vol. 12(1), pages 2-23, February.
    4. Jeffery L. Kennington & Charles D. Nicholson, 2010. "The Uncapacitated Time-Space Fixed-Charge Network Flow Problem: An Empirical Investigation of Procedures for Arc Capacity Assignment," INFORMS Journal on Computing, INFORMS, vol. 22(2), pages 326-337, May.
    5. 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.
    6. C. Audet & P. Hansen & B. Jaumard & G. Savard, 1997. "Links Between Linear Bilevel and Mixed 0–1 Programming Problems," Journal of Optimization Theory and Applications, Springer, vol. 93(2), pages 273-300, May.
    7. Roberto Roberti & Enrico Bartolini & Aristide Mingozzi, 2015. "The Fixed Charge Transportation Problem: An Exact Algorithm Based on a New Integer Programming Formulation," Management Science, INFORMS, vol. 61(6), pages 1275-1291, June.

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