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On the Value of Binary Expansions for General Mixed-Integer Linear Programs

Author

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  • Jonathan H. Owen

    (General Motors Research and Development Center, 30500 Mound Road, MC #480-106-359, Warren, Michigan 48090)

  • Sanjay Mehrotra

    (Department of Industrial Engineering and Management Sciences, Robert R. McCormick School of Engineering, Northwestern University, Evanston, Illinois 60208)

Abstract

We study the use of binary variables in reformulating general mixed-integer linear programs. We show that binary reformulations result in problems for which almost all the binary variables replacing a general integer variable need to be explored during branching. We also give computational results on the performance of such reformulations in solving the mixed-integer programs, which support our theoretical results.

Suggested Citation

  • Jonathan H. Owen & Sanjay Mehrotra, 2002. "On the Value of Binary Expansions for General Mixed-Integer Linear Programs," Operations Research, INFORMS, vol. 50(5), pages 810-819, October.
    • Handle: RePEc:inm:oropre:v:50:y:2002:i:5:p:810-819
    DOI: 10.1287/opre.50.5.810.370
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    References listed on IDEAS

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    1. Egon Balas & Sebastián Ceria & Gérard Cornuéjols, 1996. "Mixed 0-1 Programming by Lift-and-Project in a Branch-and-Cut Framework," Management Science, INFORMS, vol. 42(9), pages 1229-1246, September.
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    Cited by:

    1. Binyuan Chen & Simge Küçükyavuz & Suvrajeet Sen, 2011. "Finite Disjunctive Programming Characterizations for General Mixed-Integer Linear Programs," Operations Research, INFORMS, vol. 59(1), pages 202-210, February.
    2. Liu, Bingqian & Bissuel, Côme & Courtot, François & Gicquel, Céline & Quadri, Dominique, 2024. "A generalized Benders decomposition approach for the optimal design of a local multi-energy system," European Journal of Operational Research, Elsevier, vol. 318(1), pages 43-54.
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    4. Yongchun Li & Weijun Xie, 2025. "Exact and Approximation Algorithms for Sparse Principal Component Analysis," INFORMS Journal on Computing, INFORMS, vol. 37(3), pages 582-602, May.

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