A gas network has a number of entry and exit points. Shippers independen= tly contract the right to use the network on these points. Only at the time= of actual use, the combination of entries and exits is known. One of the q= uestions is, if all possible future transport use by the shippers can= be met.

**Past. **In the past the situation of gas transport was me=
rely static. So it was possible to take a long period (years) to build expe=
rt knowledge which severe realizations (these are called shipping variants)=
should be considered to see if a new contract can be honoured.**Future. **Although the method works well for=
the current situation it is important to base the method on a firm mathema=
tical basis. Furthermore it would be nice to reduce the number of shipping =
variants even more.

Open questions are:

- Which physical qu=
antities, metrics and techniques should be used to find those transpo=
rt conditions that determine the size of the infrastructure?

- Which tec=
hniques are available to sufficiently reduce the obtained set to find an ex=
haustive subset of which the elements are mutually exclusive, given a requi=
red accuracy?

- What mathematical optimisation tools can be used to maxi=
mise the load and minimise the number of scenarios, given that all transpor=
t paths from entry to exit need to be covered.

**Literature**:

A Systematic Approach to Transmission St=
ress Tests in Entry-Exit Systems Jarig J. Steringa, Marco Hoogwerf, Harry D=
ijkhuis

http://www.oges.info/89799/systematic-approach-transmission-stress-tests-e=
ntry-systems

A stochastic approach to allocation of capacity in =
a gas transmission network D.I. van Huizen

essay.utwente.nl/67166/1/vanhuizen_ma_eemcs.pdf

Comparing se=
vere gas transport situations through the network: Similarity or redu=
ction methods

Kimberley Lindenberg

http://ta.twi.tudelft.nl/nw/users/vuik/numanal/lindenberg_eng=
.html

For the problem a variety of optimization methods have been used: From l=
inear programs to mixed-integer nonlinear programs. The choice of method de=
pends first and foremost on the chosen model for the pressure drop in pipes=
and whether one uses a time-dependent model or not. Among the easy cases a=
re the following: If the network is topologically simple, say a so-called g=
un barrel network, then dynamic programming approaches are the state-of-the=
-art (see the survey of Carter). If one chooses to use a stationary model, =
then it can be reasonable to use an algebraic solution of a simplified syst=
em, a special case of these is known as the so-called Weymouth equation. Th=
e problem then is a mixed-integer nonlinear program which can be tackled di=
rectly with off-theshelf MINLP solvers for small networks or using speciali=
zed methods for larger networks (see e.g. Koch et al. [8]). Popular choices=
for methods include using piecewise linear approximations/linearizations t=
o obtain MIP models [3, 4, 9],

MPEC-based models (see Baumrucker and Bie=
gler [1], Schmidt et al. [11]). Neglecting the discrete decisions leads to =
NLP models which can be solved to local optimality (see Schmidt et al. [12]=
). But also these equations can be simplified even further. One approach is=
to locally linearize them around a working point, an approach that is very=
successful in practice (see van der Hoeven [5]). If one opts to use the fu=
ll Euler equations in the instationary setting one obtains a mixed-integer =
PDAE-constrained optimal control problem that is intractable for current me=
thods except for very simple networks. Another approach with high physical =
accuracy is to use a (sub)gradient-based approach on top of an accurate sim=
ulation tool (see Jen=C3=ADcek [7] and Vostr=C3=BD [13]). One approach to s=
implify the full Euler equations is to only consider the isothermal case. H=
ere using piecewise-linear models leads to MIP models that can be solved fo=
r nontrivial networks (see Domschke et al. [2]).**Data: The GasLib http://gaslib.zib.de provides benchmark instances f=
or planning problems in gas pipeline transmission. The files originate from=
real-world data that was used in a research collaboration with Open Grid E=
urope GmbH [10]. An explanation of the custom XML formats and further refer=
ences can be found in a recent preprint [2]. In addition to the network dat=
a, fixed MINLP models implemented in GAMS are provided for solver developer=
s.**

The GasLib [1] provides benchmark instances for planning problems in gas= pipeline transmission. The files originate from real-world data that was u= sed in a research collaboration with Open Grid Europe GmbH. An explanation = for the file formats and further references can be found in a recent prepri= nt [2]. In addition to the network data, MINLP models implemented in GAMS a= re provided for solver developers.=E2=80=A8

[1] http://gaslib.zib.de=E2=80=A8

[2] http://www.optimization-onlin= e.org/DB_HTML/2015/11/5216.html=E2=80=A8

**References**

[1] B. T. Baumrucker and L. T. Biegle=
r. =E2=80=9CMPEC strategies for cost optimization of pipeline operations=E2=
=80=9D. In: Comp. Chem. Eng. 34.6 (2010), pp. 900=E2=80=93913. issn: 0098-1=
354. doi: 10.1016/j.compchemeng.2009.07.012.

[2] Pia Domschke, Bj=C3=B6r=
n Gei=C3=9Fler, Oliver Kolb, Jens Lang, Alexander Martin, and Antonio Morsi=
. =E2=80=9CCombination of Nonlinear and Linear Optimization of Transient Ga=
s Networks=E2=80=9D. In: INFORMS Journal on Computing 23.4 (2011), pp. 605=
=E2=80=93617.

[3] Bj=C3=B6rn Gei=C3=9Fler, Alexander Martin, Antonio Mor=
si, and Lars Schewe. =E2=80=9CThe MILP-relaxation approach=E2=80=9D. In: Ev=
aluating Gas Network Capacities. Ed. by Thorsten Koch, Benjamin Hiller, Mar=
c E. Pfetsch, and Lars Schewe.

SIAM-MOS series on Optimization. SIAM, Ma=
r. 2015. Chap. 7. isbn: 978-1-611973-68-6.

[4] Bj=C3=B6rn Gei=C3=9Fler, =
Antonio Morsi, Lars Schewe, and Martin Schmidt. =E2=80=9CSolving Power-Cons=
trained Gas Transportation Problems using an Alternating Direction Method=
=E2=80=9D. In: Computers & Chemical Engineering 82.2 (2015), pp. 303=E2=
=80=93317. doi: 10.1016/j.compchemeng.2015.07.005.

[5] Tom van der Hoeve=
n. =E2=80=9CMath in Gas and the art of linearization=E2=80=9D. PhD thesis. =
Rijksuniversiteit Groningen, 2004.

[6] Jesco Humpola, Imke Joormann, Dja=
mal Oucherif, Marc E. Pfetsch, Lars Schewe, Martin Schmidt, and Robert Schw=
arz. GasLib =E2=80=93 A Library of Gas Network Instances. Nov. 2015. url: <=
a href=3D"http://www.optimization-online" class=3D"external-link" rel=3D"no=
follow">http://www.optimization-online. org/DB_HTML/2015/11/5216.html.<=
br>[7] Tom=C3=A1=C5=A1 Jen=C3=ADcek. =E2=80=9CSteady-State Optimization of =
Gas Transport=E2=80=9D. In: Proceedings of 2nd International Workshop SIMON=
E on Innovative Approaches to Modeling and Optimal Control of Large Scale P=
ipeline Networks.

Prague, 1993, pp. 26=E2=80=9338.

[8] Thorsten Koch,=
Benjamin Hiller, Marc E. Pfetsch, and Lars Schewe, eds. Evaluating Gas Net=
work Capacities. SIAM-MOS series on Optimization. SIAM, Mar. 2015. xvi + 37=
6. isbn: 978-1-611973-68-6.

[9] Alexander Martin, M. M=C3=B6ller, and S.=
Moritz. =E2=80=9CMixed Integer Models for the Stationary Case of Gas Netwo=
rk Optimization=E2=80=9D. In: Mathematical Programming, Series B 105 (2006)=
, pp. 563=E2=80=93582.

[10] Marc E. Pfetsch, Armin F=C3=BCgenschuh, Bj=
=C3=B6rn Gei=C3=9Fler, Nina Gei=C3=9Fler, Ralf Gollmer, Benjamin Hiller, Je=
ssica R=C3=B6vekamp, Jesco Humpola, Thorsten Koch, Thomas Lehmann, Alexande=
r Martin, Antonio Morsi, Lars Schewe,Martin Schmidt, Robert Schwarz, R=C3=
=BCdiger Schultz, Jonas Schweiger, Claudia Stangl, Marc C. Steinbach, Stefa=
n Vigerske, and Bernhard M. Willert. =E2=80=9CValidation of Nominations in =
Gas Network Optimization: Models, Methods, and Solutions=E2=80=9D. In: Opti=
m. Methods Softw. 30.1 (2015), pp.15=E2=80=9353. doi: 10.1080/10556788.2014=
.888426.

[11] Martin Schmidt, Marc C. Steinbach, and Bernhard M. Willert=
. =E2=80=9CAn MPEC based heuristic=E2=80=9D. In: ed. by Thorsten Koch, Benj=
amin Hiller, Marc E. Pfetsch, and Lars Schewe. SIAM-MOS series on Optimizat=
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doi: 10.1137/1.9781611973693.ch9.

[12] Martin Schmidt, Marc C. Steinbac=
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. by Thorsten Koch, Benjamin Hiller, Marc E. Pfetsch, and Lars Schewe. SIAM=
-MOS series on Optimization. SIAM,Mar.2015. Chap. 10, pp. 181=E2=80=93210. =
isbn: 978-1-611973-68-6. doi: 10.1137/1.9781611973693.ch10.

[13] Zdenek =
Vostr=C3=BD. =E2=80=9CTransient Optimization of Gas Transport and Distribut=
ion=E2=80=9D. In: Proceedings of 2nd International Workshop SIMONE on Innov=
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Approaches to Modeling and Optimal Control of Large Scale Pipeline=
Networks. Prague, Sept. 1993, pp. 53=E2=80=9362.

**Contributors**:

Prof. Kees Vuik, Delft University of Technology

Dr Lars Schewe, Universit=C3=A4t E=
rlangen-N=C3=BCrnberg