Advertisement

Annals of Operations Research

, Volume 181, Issue 1, pp 423–442 | Cite as

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

  • Vyacheslav V. KalashnikovEmail author
  • Gerardo A. Pérez
  • Nataliya I. Kalashnykova
Article

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.

Keywords

Natural gas cash-out problem Bi-level programming Linearization 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Anandalingam, G., & Friesz, T. L. (2005). Hierarchical optimization: an introduction. Annals of Operations Research, 31(1), 1–11. Google Scholar
  2. Chiou, S. W. (2005). Bilevel programming for the continuous transport network design problem. Transportation Research Part B, 39(2005), 361–383. Google Scholar
  3. Colson, B., Marcotte, P., & Savard, G. (2007). An overview of bilevel optimization. Annals of Operations Research, 151(1), 235–256. CrossRefGoogle Scholar
  4. Dempe, S., Kalashnikov, V. V., & Ríos-Mercado, R. Z. (2005). Discrete bilevel programming: application to a natural gas cash-out problem. European Journal of Operational Research, 166(2), 469–488. CrossRefGoogle Scholar
  5. Dempe, S., Kalashnikov, V. V., & Perez-Valdes, G. A. (2006). Mixed-integer bilevel programming: application to an extended gas cash-out problem. In: R. P. Clute (Ed.), Proceedings of the 2006 international business and economics research conference, Las Vegas, NV, USA, 02–06 October 2006. Google Scholar
  6. Dussalt, J. P., Marcotte, P., Roch, S., & Savard, G. (2006). A smoothing heuristic for a bilevel pricing problem. European Journal of Operational Research, 174(24), 1396–1413. CrossRefGoogle Scholar
  7. Energy Information Administration (2005). Natural gas summary. http://tonto.eia.doe.gov/dnav/ng/ng_sum_lsum_dcu_nus_m.htm. Accessed 02 November 2008.
  8. Energy Information Administration (2008a). FERC policy on system ownership since 1992. http://www.eia.doe.gov/cneaf/electricity/2008forms/consolidate_923.html. Retrieved June 21 2008.
  9. Energy Information Administration (2008b). FERC order 636: the restructuring rule. http://www.eia.doe.gov/cneaf/electricity/2008forms/consolidate_923.html. Accessed 21 June 2008.
  10. Environmental Protection Agency (2008). The Impacts of FERC order 636 on coal gas project development. http://epa.gov/cmop/docs/pol004.pdf. Accessed 21 June 2008.
  11. IHS Engineering (2007). EC proposes new legislation for European energy policy. http://engineers.ihs.com/news/eu-en-energy-policy-9-07.html. Accessed 21 June 2007.
  12. Kalashnikov, V. V., & Ríos-Mercado, R. Z. (2001). A penalty-function approach to a mixed-integer bilevel programming problem. In: Proceedings of the 3rd international meeting on computer science (Vol. 2, pp. 1045–1054). Aguascalientes, Mexico, 16–19 September 2001. Google Scholar
  13. Kalashnikov, V. V., & Ríos-Mercado, R. Z. (2002). An algorithm to solve a natural gas cash-out problem. In: R. P. Clute (Ed.), Proceedings of the 2002 international applied business research conference, Puerto Vallarta, Mexico, 14–19 March 2002. Google Scholar
  14. Kalashnikov, V. V., & Ríos-Mercado, R. Z. (2006). A natural gas cash-out problem: a bilevel programming framework and a penalty function method. Optimization and Engineering, 7(4), 403–420. CrossRefGoogle Scholar
  15. Kalashnikov, V. V., Kalashnikova, N. I., & Perez, G. A. (2007). Natural gas cash-out problem with price predictions. In: R. P. Clute (Ed.), Proceedings of the 2007 international applied business research conference, Mazatlán, Mexico, 26–29 March 2007. Google Scholar
  16. Kalashnikov, V. V., Pérez-Valdés, G. A., Tomasgard, A., & Kalashnykova, N. I. (2010). Natural gas cash-out problem: bilevel stochastic optimization approach. European Journal of Operational Research, 206(1), 18–33. CrossRefGoogle Scholar
  17. Kuo, R. J., & Huang, C. C. (2009). Application of particle swarm optimization algorithm for solving bi-level linear programming problem. Computers and Mathematics with Applications, 58(2009), 678–685. CrossRefGoogle Scholar
  18. Liu, Y. H., & Spencer, T. H. (1995). Solving a bilevel linear program when the inner decision maker controls few variables. European Journal of Operational Research, 81(10), 644–651. CrossRefGoogle Scholar
  19. Naturalgas.org (2004). The market under regulation. http://naturalgas.org/fegulation/market.asp. Accessed 21 June 2008.
  20. Soto, A. (2008). FERC order 636 & 637. http://www.aga.org/Legislative/issuesummaries/FERCOrder636637.html. Accessed 21 June 2008.
  21. Wen, U. P., & Hsu, S. T. (1991). Linear bi-level programming problems—a review. Journal of the Operational Research Society, 42(2), 125–133. Google Scholar
  22. 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, 88(9), 563–571. CrossRefGoogle Scholar
  23. White, D. J., & Anandalingam, G. (1993). A penalty function approach for solving bi-level linear programs. Journal of Global Optimization, 3(4), 397–419. CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • Vyacheslav V. Kalashnikov
    • 1
    • 2
    Email author
  • Gerardo A. Pérez
    • 3
  • Nataliya I. Kalashnykova
    • 4
  1. 1.Department of Systems & Industrial EngineeringITESM (Tec de Monterrey)MonterreyMexico
  2. 2.Central Economics & Mathematics Institute (CEMI)Russian Academy of Sciences (RAS)MoscowRussia
  3. 3.Centro de Calidad y ManufacturaITESM (Tec de Monterrey)MonterreyMexico
  4. 4.Facultad de Ciencias Físico-Matemáticas (FCFM)Universidad Autónoma de Nuevo León (UANL)San Nicolás de los GarzaMexico

Personalised recommendations