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Improved Penalties for Fixed Cost Linear Programs Using Lagrangean Relaxation


  • A. Victor Cabot

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

  • S. Selcuk Erenguc

    (University of Florida, Gainesville, Florida 32611)


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

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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. 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.


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