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Modeling fixed-charge problems with polynomials

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  • Lev, Benjamin
  • Kowalski, Krzysztof

Abstract

In this paper we formulate fixed-charge problems with polynomials. Using polynomial formulations we show structural similarity between different kinds of linear and fixed charge formulations. We also show the benefits of applying polynomial formulation for finding an approximate solution for problems where no algorithms exist and in some cases for developing a method to provide direct solutions to those problems. The main benefit of this paper is better understanding of the fixed-charge function structure and better explanation of the local and global minima phenomena. We present a numerical example to illustrate applications of the proposed method.

Suggested Citation

  • Lev, Benjamin & Kowalski, Krzysztof, 2011. "Modeling fixed-charge problems with polynomials," Omega, Elsevier, vol. 39(6), pages 725-728, December.
  • Handle: RePEc:eee:jomega:v:39:y:2011:i:6:p:725-728
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    References listed on IDEAS

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    1. Sun, Minghe & Aronson, Jay E. & McKeown, Patrick G. & Drinka, Dennis, 1998. "A tabu search heuristic procedure for the fixed charge transportation problem," European Journal of Operational Research, Elsevier, vol. 106(2-3), pages 441-456, April.
    2. Kowalski, Krzysztof & Lev, Benjamin, 2008. "On step fixed-charge transportation problem," Omega, Elsevier, vol. 36(5), pages 913-917, October.
    3. Adlakha, Veena & Kowalski, Krzysztof & Lev, Benjamin, 2010. "A branching method for the fixed charge transportation problem," Omega, Elsevier, vol. 38(5), pages 393-397, October.
    4. Fagerholt, Kjetil & Christiansen, Marielle & Magnus Hvattum, Lars & Johnsen, Trond A.V. & Vabø, Thor J., 2010. "A decision support methodology for strategic planning in maritime transportation," Omega, Elsevier, vol. 38(6), pages 465-474, December.
    5. Warren E. Walker, 1976. "A Heuristic Adjacent Extreme Point Algorithm for the Fixed Charge Problem," Management Science, INFORMS, vol. 22(5), pages 587-596, January.
    6. Caramia, M. & Guerriero, F., 2009. "A heuristic approach to long-haul freight transportation with multiple objective functions," Omega, Elsevier, vol. 37(3), pages 600-614, June.
    7. Udatta S. Palekar & Mark H. Karwan & Stanley Zionts, 1990. "A Branch-and-Bound Method for the Fixed Charge Transportation Problem," Management Science, INFORMS, vol. 36(9), pages 1092-1105, September.
    8. Adlakha, Veena & Kowalski, Krzysztof, 2003. "A simple heuristic for solving small fixed-charge transportation problems," Omega, Elsevier, vol. 31(3), pages 205-211, June.
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    Cited by:

    1. Kowalski, Krzysztof & Lev, Benjamin & Shen, Wenjing & Tu, Yan, 2014. "A fast and simple branching algorithm for solving small scale fixed-charge transportation problem," Operations Research Perspectives, Elsevier, vol. 1(1), pages 1-5.

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