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The Set-Covering Problem: A New Implicit Enumeration Algorithm

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  • Javier Etcheberry

    (University of Chile, Santiago, Chile)

Abstract

The set-covering problem is to minimize cx subject to A x ≧ e n over all binary n -vectors x . A is an m × n binary matrix and e n is an n -vector of 1's. We develop a new implicit enumeration strategy to solve this problem. The branching strategy is similar to the row partitioning strategy used by other authors in the partitioning problem. Simple and sharp bounds are obtained by relaxing the constraints of the associated linear program by attaching nonnegative multipliers to them. Good multipliers are obtained by using the subgradient optimization technique. Computational experience shows that these bounds are at least one order of magnitude more efficient than the ones obtained by solving the associated linear program with the simplex method. Computational results with this new implicit enumeration algorithm are encouraging. Problems with as many as 50 constraints and 100 variables were solved in the order of 100 seconds of CPU time on an IBM 360-67.

Suggested Citation

  • Javier Etcheberry, 1977. "The Set-Covering Problem: A New Implicit Enumeration Algorithm," Operations Research, INFORMS, vol. 25(5), pages 760-772, October.
    • Handle: RePEc:inm:oropre:v:25:y:1977:i:5:p:760-772
    DOI: 10.1287/opre.25.5.760
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    Cited by:

    1. Kraft, Edwin R., 2002. "Scheduling railway freight delivery appointments using a bid price approach," Transportation Research Part A: Policy and Practice, Elsevier, vol. 36(2), pages 145-165, February.
    2. Chiou, Yu-Chiun & Lan, Lawrence W., 2001. "Genetic clustering algorithms," European Journal of Operational Research, Elsevier, vol. 135(2), pages 413-427, December.
    3. Marshall L. Fisher, 2004. "The Lagrangian Relaxation Method for Solving Integer Programming Problems," Management Science, INFORMS, vol. 50(12_supple), pages 1861-1871, December.

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