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Improved Combinatorial Programming Algorithms for a Class of All-Zero-One Integer Programming Problems

Author

Listed:
  • John F. Pierce

    (Management Decisions Development Corporation, Cincinnati, Ohio)

  • Jeffrey S. Lasky

    (Northeastern University)

Abstract

In an earlier paper [Pierce, J. F. 1968. Application of combinatorial programming to a class of all-zero-one integer programming problems. Management Sci. 15 (3, November) 191-209.] combinatorial programming procedures were presented for solving a class of integer programming problems in which all elements are zero or one. By representing the problem elements in a binary computer as bits in a word and employing logical "and" and "or" operations in the problem-solving process, a number of problems involving several hundred integer variables were solved in a matter of seconds. In the present paper a number of improvements in these earlier algorithms are presented, including a new search strategy, methods for reducing the original problem, and mechanisms for feasibility filtering in multi-word problems. With these improvements problem-solving efficiency has been increased in many instances by an order of magnitude. In addition, the present paper contains computational experience obtained in solving problems for the k-best solutions.

Suggested Citation

  • John F. Pierce & Jeffrey S. Lasky, 1973. "Improved Combinatorial Programming Algorithms for a Class of All-Zero-One Integer Programming Problems," Management Science, INFORMS, vol. 19(5), pages 528-543, January.
    • Handle: RePEc:inm:ormnsc:v:19:y:1973:i:5:p:528-543
    DOI: 10.1287/mnsc.19.5.528
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    Cited by:

    1. Sarin, Subhash C. & Aggarwal, Sanjay, 2001. "Modeling and algorithmic development of a staff scheduling problem," European Journal of Operational Research, Elsevier, vol. 128(3), pages 558-569, February.
    2. Dolgui, A. & Ihnatsenka, I., 2009. "Branch and bound algorithm for a transfer line design problem: Stations with sequentially activated multi-spindle heads," European Journal of Operational Research, Elsevier, vol. 197(3), pages 1119-1132, September.

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