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Subset Coefficient Reduction Cuts for 0/1 Mixed-Integer Programming

Author

Listed:
  • R. Kipp Martin

    (University of Chicago, Chicago, Illinois)

  • Linus Schrage

    (University of Chicago, Chicago, Illinois)

Abstract

We describe a method for generating cuts for mixed-integer 0/1 programs. These cuts are designed to tighten an integer program prior to applying linear programming based branch and bound algorithms. The method involves two basic ideas: subset selection and coefficient reduction. Coefficient reduction is a process of reducing the coefficients of the 0/1 variables. Subset selection is combined with coefficient reduction by applying the coefficient reduction process to the coefficients of a subset of variables from the constraints in the problem formulation. The paper exploits these two simple ideas to derive a broad class of cuts for integer programs with both 0/1 and continuous variables. It also reports on the use of this methodology in solving a variety of fixed charge problems.

Suggested Citation

  • R. Kipp Martin & Linus Schrage, 1985. "Subset Coefficient Reduction Cuts for 0/1 Mixed-Integer Programming," Operations Research, INFORMS, vol. 33(3), pages 505-526, June.
    • Handle: RePEc:inm:oropre:v:33:y:1985:i:3:p:505-526
    DOI: 10.1287/opre.33.3.505
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    Cited by:

    1. Mahmutoğulları, Özlem & Yaman, Hande, 2023. "A Branch-and-Cut Algorithm for the Inventory Routing Problem with Product Substitution," Omega, Elsevier, vol. 115(C).

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