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

  • 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)

Registered author(s):

    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.

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    File URL: http://dx.doi.org/10.1287/mnsc.49.9.1268.16570
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    Article provided by INFORMS in its journal Management Science.

    Volume (Year): 49 (2003)
    Issue (Month): 9 (September)
    Pages: 1268-1273

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    Handle: RePEc:inm:ormnsc:v:49:y:2003:i:9:p:1268-1273
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    1. 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.
    2. Holmberg, Kaj & Ling, Jonas, 1997. "A Lagrangean heuristic for the facility location problem with staircase costs," European Journal of Operational Research, Elsevier, vol. 97(1), pages 63-74, February.
    3. James E. Falk & Richard M. Soland, 1969. "An Algorithm for Separable Nonconvex Programming Problems," Management Science, INFORMS, vol. 15(9), pages 550-569, May.
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