R. K. Ahuja, T. L. Magnanti, and J. B. Orlin, Network Flows: Theory, Algorithms, and Applications, 1993.

D. Aßmann, F. Liers, and M. Stingl, Decomposable Robust Two-Stage Optimization: An Application to Gas Network Operations under Uncertainty, vol.74, pp.40-61, 2019.

D. Aßmann, F. Liers, M. Stingl, and J. C. Vera, Deciding Robust Feasibility and Infeasibility Using a Set Containment Approach: An Application to Stationary Passive Gas Network Operations, In: SIAM Journal on Optimization, vol.28, pp.2489-2517, 2018.

B. Bakhouya and D. Wolf, The Gas Transmission Problem When the Merchant and the Transport Functions Are Disconnected, 2007.

S. Basu, R. Pollack, and M. Coste-roy, Algorithms in Real Algebraic Geometry, vol.10, 2007.

A. Ben-tal, L. E. Ghaoui, and A. Nemirovski, Robust optimization, 2009.

A. Ben-tal, A. Goryashko, E. Guslitzer, and A. Nemirovski, Adjustable robust solutions of uncertain linear programs, Mathematical Programming, vol.99, pp.351-376, 2004.

M. Collins, L. Cooper, R. Helgason, J. Kennington, and L. Leblanc, Solving the Pipe Network Analysis Problem Using Optimization Techniques, Management Science, vol.24, pp.747-760, 1978.

D. , D. Wolf, and Y. Smeers, The Gas Transmission Problem Solved by an Extension of the Simplex Algorithm, Management Science, vol.46, pp.1454-1465, 2000.

A. Fügenschuh, B. Geißler, R. Gollmer, C. Hayn, R. Henrion et al., Mathematical Optimization for Challenging Network Planning Problems in Unbundled Liberalized Gas Markets, In: Energy Systems, vol.5, pp.449-473, 2013.

A. Fügenschuh, K. Junosza-szaniawski, and S. Kwasiborski, The Reservation-Allocation Network Flow Problem, 2014.

B. Geißler, Towards Globally Optimal Solutions for MINLPs by Discretization Techniques with Applications in Gas Network Optimization, 2011.

B. Geißler, A. Morsi, and L. Schewe, A New Algorithm for MINLP Applied to Gas Transport Energy Cost Minimization, pp.321-353, 2013.

B. Geißler, A. Morsi, L. Schewe, and M. Schmidt, Solving Highly Detailed Gas Transport MINLPs: Block Separability and Penalty Alternating Direction Methods, In: INFORMS Journal on Computing, vol.30, pp.309-323, 2018.

C. Gotzes, H. Heitsch, R. Henrion, and R. Schultz, On the quantification of nomination feasibility in stationary gas networks with random load, In: Mathematical Methods of Operations Research, vol.84, pp.427-457, 2016.

M. Gross, M. E. Pfetsch, L. Schewe, M. Schmidt, and M. Skutella, Algorithmic Results for Potential-Based Flows: Easy and Hard Cases, vol.73, pp.306-324, 2019.

M. Grötschel, L. Lovász, and A. Schrijver, Geometric Algorithms and Combinatorial Optimization, Algorithms and Combinatorics, vol.2, 1988.

C. Hayn, Computing maximal entry and exit capacities of transportation networks, 2016.

C. Hewicker and S. Kesting, The New Entry-Exit Model in the EU and Its Consequences for Gas Supply Companies

, , pp.477-491, 2009.

J. Humpola, Gas Network Optimization by MINLP, 2017.

T. Koch, B. Hiller, M. Pfetsch, and L. Schewe, Evaluating Gas Network Capacities, 2015.

M. Labbé, F. Plein, and M. Schmidt, Bookings in the European Gas Market: Characterisation of Feasibility and Computational Complexity Results, In: Optimization and Engineering, 2019.

A. Martin, B. Geißler, C. Hayn, A. Morsi, L. Schewe et al., Optimierung Technischer Kapazitäten in Gasnetzen, Optimierung in der Energiewirtschaft. VDI-Berichte 2157, pp.105-114, 2011.

A. Martin, M. Möller, and S. Moritz, Mixed Integer Models for the Stationary Case of Gas Network Optimization, Mathematical Programming, vol.105, issue.2, pp.563-582, 2006.

J. J. Maugis, Étude de réseaux de transport et de distribution de fluide, In: RAIRO -Operations Research, vol.11, issue.2, pp.243-248, 1977.

, concerning common rules for the internal market in natural gas and repealing Directive 98/30/EC (OJ L, vol.176, pp.57-78, 2003.

, Directive 2009/73/EC of the European Parliament and of the Council concerning common rules for the internal market in natural gas and repealing Directive, vol.55, pp.36-54, 2003.

, concerning common rules for the internal market in natural gas, OJ L, vol.204, pp.1-12, 1998.

R. Z. Ríos-mercado and C. Borraz-sánchez, Optimization Problems in Natural Gas Transportation Systems: A State-of-the-Art Review, In: Applied Energy, vol.147, pp.536-555

R. Z. Ríos-mercado, S. Wu, L. R. Scott, and E. A. Boyd, A Reduction Technique for Natural Gas Transmission Network Optimization Problems, In: Annals of Operations Research, vol.117, issue.1, pp.217-234, 2002.

M. Robinius, L. Schewe, M. Schmidt, D. Stolten, J. Thürauf et al., Robust Optimal Discrete Arc Sizing for Tree-Shaped Potential Networks, Computational Optimization and Applications, vol.73, pp.791-819, 2019.

L. Schewe, M. Schmidt, and J. Thürauf, Structural Properties of Feasible Bookings in the European Entry-Exit Gas Market System, p.4, 2019.

M. Schmidt, M. C. Steinbach, and B. M. Willert, High Detail Stationary Optimization Models for Gas Networks, In: Optimization and Engineering, vol.16, issue.1, pp.131-164, 2015.

B. Willert, Validation of Nominations in Gas Networks and Properties of Technical Capacities, 2014.

?. Yan?ko?lu, B. L. Gorissen, and D. Den-hertog, In analogy to Case 1, the modification decreases f 4 , which contradicts the optimality of the original solution, 08.031. d), vol.277, p.1050, 2018.

G. Trier and . Email, Fürther Str. 250, 90429 Nürnberg, p.91058