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A Comparison of Mixed-Integer Programming Models for Nonconvex Piecewise Linear Cost Minimization Problems

Author

Listed:
  • Keely L. Croxton

    (Fisher College of Business, The Ohio State University, Columbus, Ohio 43210)

  • Bernard Gendron

    (Département d'informatique, et de recherche opérationnelle, and Centre de recherche sur les transports, Université de Montréal, Montréal, Quebec H3C 3J7, Canada)

  • Thomas L. Magnanti

    (School of Engineering, and Sloan School of Management, Massachusetts Institute of Technology, Cambridge, Massachusetts)

Abstract

We study a generic minimization problem with separable nonconvex piecewise linear costs, showing that the linear programming (LP) relaxation of three textbook mixed-integer programming formulations each approximates the cost function by its lower convex envelope. We also show a relationship between this result and classical Lagrangian duality theory.

Suggested Citation

  • Keely L. Croxton & Bernard Gendron & Thomas L. Magnanti, 2003. "A Comparison of Mixed-Integer Programming Models for Nonconvex Piecewise Linear Cost Minimization Problems," Management Science, INFORMS, vol. 49(9), pages 1268-1273, September.
    • Handle: RePEc:inm:ormnsc:v:49:y:2003:i:9:p:1268-1273
    DOI: 10.1287/mnsc.49.9.1268.16570
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    References listed on IDEAS

    as
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    3. Holmberg, Kaj, 1994. "Solving the staircase cost facility location problem with decomposition and piecewise linearization," European Journal of Operational Research, Elsevier, vol. 75(1), pages 41-61, May.
    4. Thomas L. Magnanti & Prakash Mirchandani & Rita Vachani, 1995. "Modeling and Solving the Two-Facility Capacitated Network Loading Problem," Operations Research, INFORMS, vol. 43(1), pages 142-157, February.
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