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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
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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).
    4. 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.
    5. 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.
    6. 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.
    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.
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    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.
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    4. 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.
    5. 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.

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