IDEAS home Printed from https://ideas.repec.org/a/spr/comgts/v14y2017i3d10.1007_s10287-017-0284-7.html
   My bibliography  Save this article

A joint model of probabilistic/robust constraints for gas transport management in stationary networks

Author

Listed:
  • T. González Grandón

    (Humboldt University Berlin)

  • H. Heitsch

    (Weierstrass Institute for Applied Analysis and Stochastics)

  • R. Henrion

    (Weierstrass Institute for Applied Analysis and Stochastics)

Abstract

We present a novel mathematical algorithm to assist gas network operators in managing uncertainty, while increasing reliability of transmission and supply. As a result, we solve an optimization problem with a joint probabilistic constraint over an infinite system of random inequalities. Such models arise in the presence of uncertain parameters having partially stochastic and partially non-stochastic character. The application that drives this new approach is a stationary network with uncertain demand (which are stochastic due to the possibility of fitting statistical distributions based on historical measurements) and with uncertain roughness coefficients in the pipes (which are uncertain but non-stochastic due to a lack of attainable measurements). We study the sensitivity of local uncertainties in the roughness coefficients and their impact on a highly reliable network operation. In particular, we are going to answer the question, what is the maximum uncertainty that is allowed (shaping a ’maximal’ uncertainty set) around nominal roughness coefficients, such that random demands in a stationary gas network can be satisfied at given high probability level for no matter which realization of true roughness coefficients within the uncertainty set. One ends up with a constraint, which is probabilistic with respect to the load of gas and robust with respect to the roughness coefficients. We demonstrate how such constraints can be dealt with in the framework of the so-called spheric-radial decomposition of multivariate Gaussian distributions. The numerical solution of a corresponding optimization problem is illustrated. The results might assist the network operator with the implementation of cost-intensive roughness measurements.

Suggested Citation

  • T. González Grandón & H. Heitsch & R. Henrion, 2017. "A joint model of probabilistic/robust constraints for gas transport management in stationary networks," Computational Management Science, Springer, vol. 14(3), pages 443-460, July.
    • Handle: RePEc:spr:comgts:v:14:y:2017:i:3:d:10.1007_s10287-017-0284-7
    DOI: 10.1007/s10287-017-0284-7
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10287-017-0284-7
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10287-017-0284-7?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. Claudia Gotzes & Holger Heitsch & René Henrion & Rüdiger Schultz, 2016. "On the quantification of nomination feasibility in stationary gas networks with random load," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 84(2), pages 427-457, October.
    2. W. Ackooij & A. Frangioni & W. Oliveira, 2016. "Inexact stabilized Benders’ decomposition approaches with application to chance-constrained problems with finite support," Computational Optimization and Applications, Springer, vol. 65(3), pages 637-669, December.
    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. Holger Berthold & Holger Heitsch & René Henrion & Jan Schwientek, 2022. "On the algorithmic solution of optimization problems subject to probabilistic/robust (probust) constraints," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 96(1), pages 1-37, August.
    2. Farrokhifar, Meisam & Nie, Yinghui & Pozo, David, 2020. "Energy systems planning: A survey on models for integrated power and natural gas networks coordination," Applied Energy, Elsevier, vol. 262(C).
    3. Lukáš Adam & Martin Branda & Holger Heitsch & René Henrion, 2020. "Solving joint chance constrained problems using regularization and Benders’ decomposition," Annals of Operations Research, Springer, vol. 292(2), pages 683-709, September.
    4. Wim Ackooij & Pedro Pérez-Aros, 2020. "Gradient Formulae for Nonlinear Probabilistic Constraints with Non-convex Quadratic Forms," Journal of Optimization Theory and Applications, Springer, vol. 185(1), pages 239-269, April.
    5. W. Ackooij & S. Demassey & P. Javal & H. Morais & W. Oliveira & B. Swaminathan, 2021. "A bundle method for nonsmooth DC programming with application to chance-constrained problems," Computational Optimization and Applications, Springer, vol. 78(2), pages 451-490, March.

    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. W. Ackooij & S. Demassey & P. Javal & H. Morais & W. Oliveira & B. Swaminathan, 2021. "A bundle method for nonsmooth DC programming with application to chance-constrained problems," Computational Optimization and Applications, Springer, vol. 78(2), pages 451-490, March.
    2. Martina Kuchlbauer & Frauke Liers & Michael Stingl, 2022. "Outer Approximation for Mixed-Integer Nonlinear Robust Optimization," Journal of Optimization Theory and Applications, Springer, vol. 195(3), pages 1056-1086, December.
    3. Lukáš Adam & Martin Branda & Holger Heitsch & René Henrion, 2020. "Solving joint chance constrained problems using regularization and Benders’ decomposition," Annals of Operations Research, Springer, vol. 292(2), pages 683-709, September.
    4. Johannes Thürauf, 2022. "Deciding the feasibility of a booking in the European gas market is coNP-hard," Annals of Operations Research, Springer, vol. 318(1), pages 591-618, November.
    5. Daniel Baena & Jordi Castro & Antonio Frangioni, 2020. "Stabilized Benders Methods for Large-Scale Combinatorial Optimization, with Application to Data Privacy," Management Science, INFORMS, vol. 66(7), pages 3051-3068, July.
    6. Zhao, Wei & Liao, Qi & Qiu, Rui & Liu, Chunying & Xu, Ning & Yu, Xiao & Liang, Yongtu, 2024. "Pipe sharing: A bilevel optimization model for the optimal capacity allocation of natural gas network," Applied Energy, Elsevier, vol. 359(C).
    7. Lars Schewe & Martin Schmidt & Johannes Thürauf, 2020. "Structural properties of feasible bookings in the European entry–exit gas market system," 4OR, Springer, vol. 18(2), pages 197-218, June.
    8. Luo, Tao & Pan, Junting & Fu, Lintao & Mei, Zili & Kong, Cuixue & Huang, Hailong, 2017. "Reducing biogas emissions from village-scale plant with optimal floating-drum biogas storage tank and operation parameters," Applied Energy, Elsevier, vol. 208(C), pages 312-318.
    9. Holger Berthold & Holger Heitsch & René Henrion & Jan Schwientek, 2022. "On the algorithmic solution of optimization problems subject to probabilistic/robust (probust) constraints," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 96(1), pages 1-37, August.
    10. Grimm, Veronika & Grübel, Julia & Schewe, Lars & Schmidt, Martin & Zöttl, Gregor, 2019. "Nonconvex equilibrium models for gas market analysis: Failure of standard techniques and alternative modeling approaches," European Journal of Operational Research, Elsevier, vol. 273(3), pages 1097-1108.
    11. Xiao Liu & Simge Küçükyavuz, 2018. "A polyhedral study of the static probabilistic lot-sizing problem," Annals of Operations Research, Springer, vol. 261(1), pages 233-254, February.
    12. Wim Ackooij & Welington Oliveira & Yongjia Song, 2019. "On level regularization with normal solutions in decomposition methods for multistage stochastic programming problems," Computational Optimization and Applications, Springer, vol. 74(1), pages 1-42, September.
    13. Wim Ackooij & Pedro Pérez-Aros, 2020. "Gradient Formulae for Nonlinear Probabilistic Constraints with Non-convex Quadratic Forms," Journal of Optimization Theory and Applications, Springer, vol. 185(1), pages 239-269, April.
    14. Shuai Liu, 2019. "A simple version of bundle method with linear programming," Computational Optimization and Applications, Springer, vol. 72(2), pages 391-412, March.
    15. Martina Kuchlbauer & Frauke Liers & Michael Stingl, 2022. "Adaptive Bundle Methods for Nonlinear Robust Optimization," INFORMS Journal on Computing, INFORMS, vol. 34(4), pages 2106-2124, July.

    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:comgts:v:14:y:2017:i:3:d:10.1007_s10287-017-0284-7. 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.