IDEAS home Printed from https://ideas.repec.org/a/kap/netspa/v13y2013i2p205-227.html

An SOS1-Based Approach for Solving MPECs with a Natural Gas Market Application

Author

Listed:
  • S. Siddiqui

  • S. Gabriel

Abstract

This paper presents a new method for solving mathematical programs with equilibrium constraints. The approach uses a transformation of the original problem via Schur’s decomposition coupled with two separate formulations for modeling related absolute value functions. The first formulation, based on SOS1 variables, when solved to optimality will provide a global solution to the MPEC. The second, penalty-based formulation is used to heuristically obtain local solutions to large-scale MPECs. The advantage of these methods over disjunctive constraints for solving MPECs is that computational time is much lower, which is corroborated by numerical examples. Finally, an application of the method to an MPEC representing the United States natural gas market is given. Copyright Springer Science+Business Media, LLC 2013

Suggested Citation

  • S. Siddiqui & S. Gabriel, 2013. "An SOS1-Based Approach for Solving MPECs with a Natural Gas Market Application," Networks and Spatial Economics, Springer, vol. 13(2), pages 205-227, June.
    • Handle: RePEc:kap:netspa:v:13:y:2013:i:2:p:205-227
    DOI: 10.1007/s11067-012-9178-y
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s11067-012-9178-y
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s11067-012-9178-y?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

    for a different version of it.

    References listed on IDEAS

    as
    1. Gabriel, S.A. & Rosendahl, K.E. & Egging, Ruud & Avetisyan, H.G. & Siddiqui, S., 2012. "Cartelization in gas markets: Studying the potential for a “Gas OPEC”," Energy Economics, Elsevier, vol. 34(1), pages 137-152.
    2. Holger Scheel & Stefan Scholtes, 2000. "Mathematical Programs with Complementarity Constraints: Stationarity, Optimality, and Sensitivity," Mathematics of Operations Research, INFORMS, vol. 25(1), pages 1-22, February.
    3. S A Gabriel & R García-Bertrand & P Sahakij & A J Conejo, 2006. "A practical approach to approximate bilinear functions in mathematical programming problems by using Schur's decomposition and SOS type 2 variables," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 57(8), pages 995-1004, August.
    4. Gabriel, Steven A. & Leuthold, Florian U., 2010. "Solving discretely-constrained MPEC problems with applications in electric power markets," Energy Economics, Elsevier, vol. 32(1), pages 3-14, January.
    5. repec:aen:journl:1995v16-01-a06 is not listed on IDEAS
    6. Alexander Mitsos, 2010. "Global solution of nonlinear mixed-integer bilevel programs," Journal of Global Optimization, Springer, vol. 47(4), pages 557-582, August.
    7. Yihsu Chen & Benjamin Hobbs & Sven Leyffer & Todd Munson, 2006. "Leader-Follower Equilibria for Electric Power and NO x Allowances Markets," Computational Management Science, Springer, vol. 3(4), pages 307-330, September.
    Full references (including those not matched with items on IDEAS)

    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. Feijoo, Felipe & Das, Tapas K., 2014. "Design of Pareto optimal CO2 cap-and-trade policies for deregulated electricity networks," Applied Energy, Elsevier, vol. 119(C), pages 371-383.
    2. Christos N. Dimitriadis & Evangelos G. Tsimopoulos & Michael C. Georgiadis, 2021. "A Review on the Complementarity Modelling in Competitive Electricity Markets," Energies, MDPI, vol. 14(21), pages 1-27, November.
    3. Trüby, Johannes, 2013. "Strategic behaviour in international metallurgical coal markets," Energy Economics, Elsevier, vol. 36(C), pages 147-157.
    4. Arriet, Andrea & Matis, Timothy I. & Feijoo, Felipe, 2024. "Electricity sector impacts of water taxation for natural gas supply under high renewable generation," Energy, Elsevier, vol. 294(C).
    5. Meng Xu & Guangmin Wang & Susan Grant-Muller & Ziyou Gao, 2017. "Joint road toll pricing and capacity development in discrete transport network design problem," Transportation, Springer, vol. 44(4), pages 731-752, July.
    6. Yohan Shim & Marte Fodstad & Steven Gabriel & Asgeir Tomasgard, 2013. "A branch-and-bound method for discretely-constrained mathematical programs with equilibrium constraints," Annals of Operations Research, Springer, vol. 210(1), pages 5-31, November.
    7. Huppmann, Daniel, 2013. "Endogenous shifts in OPEC market power - A Stackelberg oligopoly with fringe," VfS Annual Conference 2013 (Duesseldorf): Competition Policy and Regulation in a Global Economic Order 79758, Verein für Socialpolitik / German Economic Association.
    8. J. S. Pang, 2007. "Partially B-Regular Optimization and Equilibrium Problems," Mathematics of Operations Research, INFORMS, vol. 32(3), pages 687-699, August.
    9. Anne Neumann & Juan Rosellón & Hannes Weigt, 2015. "Removing Cross-Border Capacity Bottlenecks in the European Natural Gas Market—A Proposed Merchant-Regulatory Mechanism," Networks and Spatial Economics, Springer, vol. 15(1), pages 149-181, March.
    10. Atsushi Hori & Masao Fukushima, 2019. "Gauss–Seidel Method for Multi-leader–follower Games," Journal of Optimization Theory and Applications, Springer, vol. 180(2), pages 651-670, February.
    11. S A Gabriel & P Sahakij & M Ramirez & C Peot, 2007. "A multiobjective optimization model for processing and distributing biosolids to reuse fields," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 58(7), pages 850-864, July.
    12. Wolf-Peter Schill & Juan Rosellón & Jonas Egerer, 2011. "Regulated Expansion of Electricity Transmission Networks: The Effects of Fluctuating Demand and Wind Generation," Discussion Papers of DIW Berlin 1109, DIW Berlin, German Institute for Economic Research.
    13. Stefan Scholtes, 2004. "Nonconvex Structures in Nonlinear Programming," Operations Research, INFORMS, vol. 52(3), pages 368-383, June.
    14. Virasjoki, Vilma & Siddiqui, Afzal S. & Oliveira, Fabricio & Salo, Ahti, 2020. "Utility-scale energy storage in an imperfectly competitive power sector," Energy Economics, Elsevier, vol. 88(C).
    15. Rintamäki, Tuomas & Siddiqui, Afzal S. & Salo, Ahti, 2020. "Strategic offering of a flexible producer in day-ahead and intraday power markets," European Journal of Operational Research, Elsevier, vol. 284(3), pages 1136-1153.
    16. Stein, Oliver, 2012. "How to solve a semi-infinite optimization problem," European Journal of Operational Research, Elsevier, vol. 223(2), pages 312-320.
    17. Birbil, S.I. & Bouza, G. & Frenk, J.B.G. & Still, G.J., 2003. "Equilibrium Constrained Optimization Problems," Econometric Institute Research Papers ERS-2003-085-LIS, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    18. Zhang, Fang & Lu, Jian & Hu, Xiaojian & Meng, Qiang, 2023. "Integrated deployment of dedicated lane and roadside unit considering uncertain road capacity under the mixed-autonomy traffic environment," Transportation Research Part B: Methodological, Elsevier, vol. 174(C).
    19. Mehdi Ansari & Juan S. Borrero & Leonardo Lozano, 2023. "Robust Minimum-Cost Flow Problems Under Multiple Ripple Effect Disruptions," INFORMS Journal on Computing, INFORMS, vol. 35(1), pages 83-103, January.
    20. Gui-Hua Lin & Mei-Ju Luo & Jin Zhang, 2016. "Smoothing and SAA method for stochastic programming problems with non-smooth objective and constraints," Journal of Global Optimization, Springer, vol. 66(3), pages 487-510, November.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    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:kap:netspa:v:13:y:2013:i:2:p:205-227. 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.