IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v181y2010i1p423-44210.1007-s10479-010-0740-z.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10479-010-0740-z
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10479-010-0740-z?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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. 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.
    3. 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.
    4. Benoît Colson & Patrice Marcotte & Gilles Savard, 2007. "An overview of bilevel optimization," Annals of Operations Research, Springer, vol. 153(1), pages 235-256, September.
    5. 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.
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Di, Zhen & Yang, Lixing, 2020. "Reversible lane network design for maximizing the coupling measure between demand structure and network structure," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 141(C).
    3. 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.
    4. Richard Oberdieck & Nikolaos A. Diangelakis & Styliani Avraamidou & Efstratios N. Pistikopoulos, 2017. "On unbounded and binary parameters in multi-parametric programming: applications to mixed-integer bilevel optimization and duality theory," Journal of Global Optimization, Springer, vol. 69(3), pages 587-606, November.
    5. Deniz Aksen & Nuray Piyade & Necati Aras, 2010. "The budget constrained r-interdiction median problem with capacity expansion," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 18(3), pages 269-291, September.
    6. M. Hosein Zare & Osman Y. Özaltın & Oleg A. Prokopyev, 2018. "On a class of bilevel linear mixed-integer programs in adversarial settings," Journal of Global Optimization, Springer, vol. 71(1), pages 91-113, May.
    7. Junlong Zhang & Osman Y. Özaltın, 2021. "Bilevel Integer Programs with Stochastic Right-Hand Sides," INFORMS Journal on Computing, INFORMS, vol. 33(4), pages 1644-1660, October.
    8. Carvalho, Margarida & Lodi, Andrea, 2023. "A theoretical and computational equilibria analysis of a multi-player kidney exchange program," European Journal of Operational Research, Elsevier, vol. 305(1), pages 373-385.
    9. Andreas Lanz & Gregor Reich & Ole Wilms, 2022. "Adaptive grids for the estimation of dynamic models," Quantitative Marketing and Economics (QME), Springer, vol. 20(2), pages 179-238, June.
    10. Shi, Yi & Deng, Yawen & Wang, Guoan & Xu, Jiuping, 2020. "Stackelberg equilibrium-based eco-economic approach for sustainable development of kitchen waste disposal with subsidy policy: A case study from China," Energy, Elsevier, vol. 196(C).
    11. Lucio Bianco & Massimiliano Caramia & Stefano Giordani & Veronica Piccialli, 2016. "A Game-Theoretic Approach for Regulating Hazmat Transportation," Transportation Science, INFORMS, vol. 50(2), pages 424-438, May.
    12. M. Köppe & M. Queyranne & C. T. Ryan, 2010. "Parametric Integer Programming Algorithm for Bilevel Mixed Integer Programs," Journal of Optimization Theory and Applications, Springer, vol. 146(1), pages 137-150, July.
    13. Cerulli, Martina & Serra, Domenico & Sorgente, Carmine & Archetti, Claudia & Ljubić, Ivana, 2023. "Mathematical programming formulations for the Collapsed k-Core Problem," European Journal of Operational Research, Elsevier, vol. 311(1), pages 56-72.
    14. Chan Y. Han & Brian J. Lunday & Matthew J. Robbins, 2016. "A Game Theoretic Model for the Optimal Location of Integrated Air Defense System Missile Batteries," INFORMS Journal on Computing, INFORMS, vol. 28(3), pages 405-416, August.
    15. Lorenzo Lampariello & Simone Sagratella, 2015. "It is a matter of hierarchy: a Nash equilibrium problem perspective on bilevel programming," DIAG Technical Reports 2015-07, Department of Computer, Control and Management Engineering, Universita' degli Studi di Roma "La Sapienza".
    16. R. Paulavičius & C. S. Adjiman, 2020. "New bounding schemes and algorithmic options for the Branch-and-Sandwich algorithm," Journal of Global Optimization, Springer, vol. 77(2), pages 197-225, June.
    17. Grimm, Veronika & Schewe, Lars & Schmidt, Martin & Zöttl, Gregor, 2017. "Uniqueness of market equilibrium on a network: A peak-load pricing approach," European Journal of Operational Research, Elsevier, vol. 261(3), pages 971-983.
    18. Liang, Jinpeng & Wu, Jianjun & Gao, Ziyou & Sun, Huijun & Yang, Xin & Lo, Hong K., 2019. "Bus transit network design with uncertainties on the basis of a metro network: A two-step model framework," Transportation Research Part B: Methodological, Elsevier, vol. 126(C), pages 115-138.
    19. Wei Jiang & Huiqiang Wang & Bingyang Li & Haibin Lv & Qingchuan Meng, 2020. "A multi-user multi-operator computing pricing method for Internet of things based on bi-level optimization," International Journal of Distributed Sensor Networks, , vol. 16(1), pages 15501477199, January.
    20. Martin Weibelzahl & Alexandra Märtz, 2020. "Optimal storage and transmission investments in a bilevel electricity market model," Annals of Operations Research, Springer, vol. 287(2), pages 911-940, April.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:annopr:v:181:y:2010:i:1:p:423-442:10.1007/s10479-010-0740-z. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.