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Deciding the feasibility of a booking in the European gas market is coNP-hard

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  • Johannes Thürauf

    (Trier University)

Abstract

We show that deciding the feasibility of a booking (FB) in the European entry-exit gas market is coNP-hard if a nonlinear potential-based flow model is used. The feasibility of a booking can be characterized by polynomially many load flow scenarios with maximum potential-difference, which are computed by solving nonlinear potential-based flow models. We use this existing characterization of the literature to prove that FB is coNP-hard by reducing Partition to the infeasibility of a booking. We further prove that computing a potential-difference maximizing load flow scenario is $${\textsc {NP}}$$ NP -hard even if we can determine the flow direction a priori. From the literature, it is known that FB can be decided in polynomial time on trees and a single cycle. Thus, our hardness result draws the first line that separates the easy from the hard variants of FB and finally answers that FB is hard in general.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:annopr:v:318:y:2022:i:1:d:10.1007_s10479-022-04732-1
    DOI: 10.1007/s10479-022-04732-1
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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. T. D. Chuong & V. Jeyakumar, 2017. "An Exact Formula for Radius of Robust Feasibility of Uncertain Linear Programs," Journal of Optimization Theory and Applications, Springer, vol. 173(1), pages 203-226, April.
    3. 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.
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    5. 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.
    6. 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.
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