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Improved Penalties for Fixed Cost Linear Programs Using Lagrangean Relaxation

Listed author(s):
  • 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.

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Article provided by INFORMS in its journal Management Science.

Volume (Year): 32 (1986)
Issue (Month): 7 (July)
Pages: 856-869

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Handle: RePEc:inm:ormnsc:v:32:y:1986:i:7:p:856-869
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