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Improved Penalties for Fixed Cost Linear Programs Using Lagrangean Relaxation

Author

Listed:
  • A. Victor Cabot

    (School of Business, Indiana University, Bloomington, Indiana 47405)

  • S. Selcuk Erenguc

    (University of Florida, Gainesville, Florida 32611)

Abstract

The most commonly used penalty in branch and bound approaches to integer programming is the Driebeek--Tomlin penalty. It has been used successfully in solving fixed cost linear programs by Kennington and Unger and by Barr, Glover and Klingman. It is well known that the Driebeek--Tomlin penalty can be derived from a Lagrangean relaxation of the integer programming problem. We show, however, that the Lagrangean relaxation for fixed cost problems not only yields the Driebeek--Tomlin penalty, but two penalties which sometimes dominate it. We show the strength of the new penalties by solving a series of text problems and comparing the number of nodes generated on the branch and bound tree and the total computer time needed to solve each problem.

Suggested Citation

  • A. Victor Cabot & S. Selcuk Erenguc, 1986. "Improved Penalties for Fixed Cost Linear Programs Using Lagrangean Relaxation," Management Science, INFORMS, vol. 32(7), pages 856-869, July.
    • Handle: RePEc:inm:ormnsc:v:32:y:1986:i:7:p:856-869
    DOI: 10.1287/mnsc.32.7.856
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    Cited by:

    1. Sun, Minghe & Aronson, Jay E. & McKeown, Patrick G. & Drinka, Dennis, 1998. "A tabu search heuristic procedure for the fixed charge transportation problem," European Journal of Operational Research, Elsevier, vol. 106(2-3), pages 441-456, 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. Klose, Andreas & Drexl, Andreas, 2001. "Combinatorial optimisation problems of the assignment type and a partitioning approach," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 545, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.
    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. Erika Buson & Roberto Roberti & Paolo Toth, 2014. "A Reduced-Cost Iterated Local Search Heuristic for the Fixed-Charge Transportation Problem," Operations Research, INFORMS, vol. 62(5), pages 1095-1106, October.
    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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