IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v295y2020i1d10.1007_s10479-020-03725-2.html
   My bibliography  Save this article

Computing technical capacities in the European entry-exit gas market is NP-hard

Author

Listed:
  • Lars Schewe

    (University of Edinburgh, James Clerk Maxwell Building)

  • Martin Schmidt

    (Trier University)

  • Johannes Thürauf

    (Friedrich-Alexander-Universität Erlangen-Nürnberg
    Energie Campus Nürnberg)

Abstract

As a result of its liberalization, the European gas market is organized as an entry-exit system in order to decouple the trading and transport of natural gas. Roughly summarized, the gas market organization consists of four subsequent stages. First, the transmission system operator (TSO) is obliged to allocate so-called maximal technical capacities for the nodes of the network. Second, the TSO and the gas traders sign mid- to long-term capacity-right contracts, where the capacity is bounded above by the allocated technical capacities. These contracts are called bookings. Third, on a day-ahead basis, gas traders can nominate the amount of gas that they inject or withdraw from the network at entry and exit nodes, where the nominated amount is bounded above by the respective booking. Fourth and finally, the TSO has to operate the network such that the nominated amounts of gas can be transported. By signing the booking contract, the TSO guarantees that all possibly resulting nominations can indeed be transported. Consequently, maximal technical capacities have to satisfy that all nominations that comply with these technical capacities can be transported through the network. This leads to a highly challenging mathematical optimization problem. We consider the specific instantiations of this problem in which we assume capacitated linear as well as potential-based flow models. In this contribution, we formally introduce the problem of Computing Technical Capacities (CTC) and prove that it is NP-complete on trees and NP-hard in general. To this end, we first reduce the Subset Sum problem to CTC for the case of capacitated linear flows in trees. Afterward, we extend this result to CTC with potential-based flows and show that this problem is also NP-complete on trees by reducing it to the case of capacitated linear flow. Since the hardness results are obtained for the easiest case, i.e., on tree-shaped networks with capacitated linear as well as potential-based flows, this implies the hardness of CTC for more general graph classes.

Suggested Citation

  • Lars Schewe & Martin Schmidt & Johannes Thürauf, 2020. "Computing technical capacities in the European entry-exit gas market is NP-hard," Annals of Operations Research, Springer, vol. 295(1), pages 337-362, December.
    • Handle: RePEc:spr:annopr:v:295:y:2020:i:1:d:10.1007_s10479-020-03725-2
    DOI: 10.1007/s10479-020-03725-2
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10479-020-03725-2
    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/s10479-020-03725-2?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. Martin Robinius & Lars Schewe & Martin Schmidt & Detlef Stolten & Johannes Thürauf & Lara Welder, 2019. "Robust optimal discrete arc sizing for tree-shaped potential networks," Computational Optimization and Applications, Springer, vol. 73(3), pages 791-819, July.
    2. DE WOLF, Daniel & SMEERS, Yves, 2000. "The gas transmission problem solved by an extension of the simplex algorithm," LIDAM Reprints CORE 1489, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    3. 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.
    4. M. Collins & L. Cooper & R. Helgason & J. Kennington & L. LeBlanc, 1978. "Solving the Pipe Network Analysis Problem Using Optimization Techniques," Management Science, INFORMS, vol. 24(7), pages 747-760, March.
    5. Veronika Grimm & Lars Schewe & Martin Schmidt & Gregor Zöttl, 2019. "A multilevel model of the European entry-exit gas market," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 89(2), pages 223-255, April.
    6. Björn Geißler & Antonio Morsi & Lars Schewe & Martin Schmidt, 2018. "Solving Highly Detailed Gas Transport MINLPs: Block Separability and Penalty Alternating Direction Methods," INFORMS Journal on Computing, INFORMS, vol. 30(2), pages 309-323, May.
    7. Daniel De Wolf & Yves Smeers, 2000. "The Gas Transmission Problem Solved by an Extension of the Simplex Algorithm," Management Science, INFORMS, vol. 46(11), pages 1454-1465, November.
    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. Lars Schewe & Martin Schmidt & Johannes Thürauf, 2022. "Global optimization for the multilevel European gas market system with nonlinear flow models on trees," Journal of Global Optimization, Springer, vol. 82(3), pages 627-653, March.
    2. Beck, Yasmine & Ljubić, Ivana & Schmidt, Martin, 2023. "A survey on bilevel optimization under uncertainty," European Journal of Operational Research, Elsevier, vol. 311(2), pages 401-426.
    3. Anna Schwele & Christos Ordoudis & Pierre Pinson & Jalal Kazempour, 2021. "Coordination of power and natural gas markets via financial instruments," Computational Management Science, Springer, vol. 18(4), pages 505-538, October.
    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. Qi, Shikun & Zhao, Wei & Qiu, Rui & Liu, Chunying & Li, Zhuochao & Lan, Hao & Liang, Yongtu, 2023. "Capacity allocation method of hydrogen-blending natural gas pipeline network based on bilevel optimization," Energy, Elsevier, vol. 285(C).
    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. Fränk Plein & Johannes Thürauf & Martine Labbé & Martin Schmidt, 2022. "A bilevel optimization approach to decide the feasibility of bookings in the European gas market," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 95(3), pages 409-449, June.

    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. 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.
    2. Lars Schewe & Martin Schmidt & Johannes Thürauf, 2022. "Global optimization for the multilevel European gas market system with nonlinear flow models on trees," Journal of Global Optimization, Springer, vol. 82(3), pages 627-653, March.
    3. Ralf Lenz & Kai Helge Becker, 2022. "Optimization of capacity expansion in potential-driven networks including multiple looping: a comparison of modelling approaches," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 44(1), pages 179-224, March.
    4. Yijiang Li & Santanu S. Dey & Nikolaos V. Sahinidis, 2024. "A reformulation-enumeration MINLP algorithm for gas network design," Journal of Global Optimization, Springer, vol. 90(4), pages 931-963, December.
    5. Mengying Xue & Tianhu Deng & Zuo‐Jun Max Shen, 2019. "Optimizing natural gas pipeline transmission with nonuniform elevation: A new initialization approach," Naval Research Logistics (NRL), John Wiley & Sons, vol. 66(7), pages 547-564, October.
    6. Hong, Sung-Pil & Kim, Taegyoon & Lee, Subin, 2019. "A precision pump schedule optimization for the water supply networks with small buffers," Omega, Elsevier, vol. 82(C), pages 24-37.
    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. Jesco Humpola & Armin Fügenschuh, 2015. "Convex reformulations for solving a nonlinear network design problem," Computational Optimization and Applications, Springer, vol. 62(3), pages 717-759, December.
    9. Beyza, Jesus & Ruiz-Paredes, Hector F. & Garcia-Paricio, Eduardo & Yusta, Jose M., 2020. "Assessing the criticality of interdependent power and gas systems using complex networks and load flow techniques," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    10. Daniel de Wolf, 2017. "Mathematical Properties of Formulations of the Gas Transmission Problem," Post-Print halshs-02396747, HAL.
    11. Conrado Borraz-Sánchez & Dag Haugland, 2013. "Optimization methods for pipeline transportation of natural gas with variable specific gravity and compressibility," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(3), pages 524-541, October.
    12. Zhou, Li & Liao, Zuwei & Wang, Jingdai & Jiang, Binbo & Yang, Yongrong & Du, Wenli, 2015. "Energy configuration and operation optimization of refinery fuel gas networks," Applied Energy, Elsevier, vol. 139(C), pages 365-375.
    13. repec:cty:dpaper:1464 is not listed on IDEAS
    14. Dieckhoener, Caroline, 2010. "Simulating security of supply effects of the Nabucco and South Stream projects for the European natural gas market," EWI Working Papers 2010-7, Energiewirtschaftliches Institut an der Universitaet zu Koeln (EWI), revised 21 Jan 2012.
    15. Song, Chenhui & Xiao, Jun & Zu, Guoqiang & Hao, Ziyuan & Zhang, Xinsong, 2021. "Security region of natural gas pipeline network system: Concept, method and application," Energy, Elsevier, vol. 217(C).
    16. Fränk Plein & Johannes Thürauf & Martine Labbé & Martin Schmidt, 2022. "A bilevel optimization approach to decide the feasibility of bookings in the European gas market," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 95(3), pages 409-449, June.
    17. Daniel de Wolf & Yves Smeers, 2021. "Generalized derivatives of the optimal value of a linear program with respect to matrix coefficients," Post-Print halshs-02396708, HAL.
    18. Shabanpour-Haghighi, Amin & Seifi, Ali Reza, 2015. "Multi-objective operation management of a multi-carrier energy system," Energy, Elsevier, vol. 88(C), pages 430-442.
    19. Jin, Xiaolong & Mu, Yunfei & Jia, Hongjie & Wu, Jianzhong & Xu, Xiandong & Yu, Xiaodan, 2016. "Optimal day-ahead scheduling of integrated urban energy systems," Applied Energy, Elsevier, vol. 180(C), pages 1-13.
    20. Tian, Xingtao & Lin, Xiaojie & Zhong, Wei & Zhou, Yi, 2023. "Analytical sensitivity analysis of radial natural gas networks," Energy, Elsevier, vol. 263(PC).
    21. R. Navarro & H. Rojas & Izabelly S. De Oliveira & J. E. Luyo & Y. P. Molina, 2022. "Optimization Model for the Integration of the Electric System and Gas Network: Peruvian Case," Energies, MDPI, vol. 15(10), pages 1-32, May.

    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:295:y:2020:i:1:d:10.1007_s10479-020-03725-2. 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.