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A linearization approach to solve the natural gas cash-out bilevel problem

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  • Vyacheslav Kalashnikov
  • Gerardo Pérez
  • Nataliya Kalashnykova

Abstract

In this article, we discuss a particular imbalance cash-out problem arising in the natural gas supply chain. This problem was created by the liberalization laws that regulate deals between a natural gas shipping company and a pipeline operator. The problem was first modeled as a bilevel nonlinear mixed-integer problem that considers the cash-out penalization for the final imbalance occurring in the system. We extend the original problem’s upper level objective function by including additional terms accounting for the gas shipping company’s daily actions aimed at taking advantage of the price variations. Then we linearize all the constraints at both levels in an equivalent way so as to make easier their numerical solution. The results of numerical experiments are compared with those obtained by the inexact penalization method proposed by the authors in previous papers. Copyright Springer Science+Business Media, LLC 2010

Suggested Citation

  • Vyacheslav Kalashnikov & Gerardo Pérez & Nataliya Kalashnykova, 2010. "A linearization approach to solve the natural gas cash-out bilevel problem," Annals of Operations Research, Springer, vol. 181(1), pages 423-442, December.
    • Handle: RePEc:spr:annopr:v:181:y:2010:i:1:p:423-442:10.1007/s10479-010-0740-z
    DOI: 10.1007/s10479-010-0740-z
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    References listed on IDEAS

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    1. Dussault, Jean-Pierre & Marcotte, Patrice & Roch, Sebastien & Savard, Gilles, 2006. "A smoothing heuristic for a bilevel pricing problem," European Journal of Operational Research, Elsevier, vol. 174(3), pages 1396-1413, November.
    2. Kalashnikov, Vyacheslav V. & Pérez-Valdés, Gerardo A. & Tomasgard, Asgeir & Kalashnykova, Nataliya I., 2010. "Natural gas cash-out problem: Bilevel stochastic optimization approach," European Journal of Operational Research, Elsevier, vol. 206(1), pages 18-33, October.
    3. Dempe, Stephan & Kalashnikov, Vyacheslav & Rios-Mercado, Roger Z., 2005. "Discrete bilevel programming: Application to a natural gas cash-out problem," European Journal of Operational Research, Elsevier, vol. 166(2), pages 469-488, October.
    4. Chiou, Suh-Wen, 2005. "Bilevel programming for the continuous transport network design problem," Transportation Research Part B: Methodological, Elsevier, vol. 39(4), pages 361-383, May.
    5. Benoît Colson & Patrice Marcotte & Gilles Savard, 2007. "An overview of bilevel optimization," Annals of Operations Research, Springer, vol. 153(1), pages 235-256, September.
    6. Wen, U. P. & Huang, A. D., 1996. "A simple Tabu Search method to solve the mixed-integer linear bilevel programming problem," European Journal of Operational Research, Elsevier, vol. 88(3), pages 563-571, February.
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    Cited by:

    1. Leonardo Lozano & J. Cole Smith, 2017. "A Value-Function-Based Exact Approach for the Bilevel Mixed-Integer Programming Problem," Operations Research, INFORMS, vol. 65(3), pages 768-786, June.
    2. Liu, Shaonan & Wang, Mingzheng & Kong, Nan & Hu, Xiangpei, 2021. "An enhanced branch-and-bound algorithm for bilevel integer linear programming," European Journal of Operational Research, Elsevier, vol. 291(2), pages 661-679.
    3. Dempe, Stephan & Kalashnikov, Vyacheslav V. & Pérez-Valdés, Gerardo A. & Kalashnykova, Nataliya I., 2011. "Natural gas bilevel cash-out problem: Convergence of a penalty function method," European Journal of Operational Research, Elsevier, vol. 215(3), pages 532-538, December.

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