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  <doc>
    <id>386</id>
    <completedYear>2021</completedYear>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>preprint</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2021-05-13</completedDate>
    <publishedDate>2021-05-13</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Value at risk approach to producer's best response in electricity market with uncertain demand</title>
    <abstract language="eng">We deal with several sources of uncertainty in electricity markets. The independent system operator (ISO) maximizes the social welfare using chance constraints to hedge against discrepancies between the estimated and real electricity demand. We find an explicit solution of the ISO problem, and use it to tackle the problem of a producer. In our model, production as well as income of a producer are determined based on the estimated electricity demand predicted by the ISO, that is unknown to producers. Thus, each producer is hedging against the uncertainty of prediction of the demand using the value-at-risk approach. To illustrate our results, a numerical study of a producer's best response given a historical distribution of both estimated and real electricity demand is provided.</abstract>
    <enrichment key="SubmissionStatus">under review</enrichment>
    <enrichment key="opus.source">publish</enrichment>
    <enrichment key="review.accepted_by">2</enrichment>
    <licence>Creative Commons - CC BY - Namensnennung 4.0 International</licence>
    <author>Martin Branda</author>
    <author>René Henrion</author>
    <author>Miroslav Pištěk</author>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>electricity market</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>multi-leader-common-follower game</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>stochastic demand</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>day-ahead bidding</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>chance constraints</value>
    </subject>
    <collection role="institutes" number="">Weierstraß-Institut für Angewandte Analysis und Stochastik</collection>
    <collection role="subprojects" number="">B04</collection>
    <file>https://opus4.kobv.de/opus4-trr154/files/386/wias_preprints_2831.pdf</file>
  </doc>
  <doc>
    <id>371</id>
    <completedYear>2021</completedYear>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber>34</pageNumber>
    <edition/>
    <issue/>
    <volume/>
    <type>preprint</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>1</belongsToBibliography>
    <completedDate>2021-02-26</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">On Convex Lower-Level Black-Box Constraints in Bilevel Optimization   with an Application to Gas Market Models with Chance Constraints</title>
    <abstract language="eng">Bilevel optimization is an increasingly important tool to model hierarchical decision making. However, the ability of modeling such settings makes bilevel problems hard to solve in theory and practice. In this paper, we add on the general difficulty of this class of problems by further incorporating convex black-box constraints in the lower level. For this setup, we develop a cutting-plane algorithm that computes approximate bilevel-feasible points. We apply this method to a bilevel model of the European gas market in which we use a joint chance constraint to model uncertain loads. Since the chance constraint is not available in closed form, this fits into the black-box setting studied before. For the applied model, we use further problem-specific insights to derive bounds on the objective value of the bilevel problem. By doing so, we are able to show that we solve the application problem to approximate global optimality. In our numerical case study we are thus able to evaluate the welfare sensitivity in dependence of the achieved safety level of uncertain load coverage.</abstract>
    <enrichment key="SubmissionStatus">under review</enrichment>
    <enrichment key="opus.source">publish</enrichment>
    <licence>Creative Commons - CC BY - Namensnennung 4.0 International</licence>
    <author>Holger Heitsch</author>
    <author>René Henrion</author>
    <author>Thomas Kleinert</author>
    <author>Martin Schmidt</author>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Bilevel optimization</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Black-box constraints</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Chance constraints</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Cutting planes</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>European gas market</value>
    </subject>
    <collection role="institutes" number="">Friedrich-Alexander-Universität Erlangen-Nürnberg</collection>
    <collection role="institutes" number="">Weierstraß-Institut für Angewandte Analysis und Stochastik</collection>
    <collection role="subprojects" number="">A05</collection>
    <collection role="subprojects" number="">B04</collection>
    <collection role="subprojects" number="">B08</collection>
    <collection role="institutes" number="">Universität Trier</collection>
    <file>https://opus4.kobv.de/opus4-trr154/files/371/bilevel_chance_constraint_preprint.pdf</file>
  </doc>
  <doc>
    <id>285</id>
    <completedYear>2019</completedYear>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber>8</pageNumber>
    <edition/>
    <issue/>
    <volume/>
    <type>preprint</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>1</belongsToBibliography>
    <completedDate>2019-11-08</completedDate>
    <publishedDate>2019-11-08</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Capacity Evaluation for Large-Scale Gas Networks</title>
    <abstract language="eng">Natural gas is important for the energy turnaround in many countries like in Germany, where it serves as a "bridging energy" towards a fossil-free energy supply in the future. About 20% of the total German energy demand is provided by natural gas, which is transported through a complex pipeline network with a total length of about 30000 km and the efficient use of the given transport infrastructure for natural gas is of political, economic, and societal importance.&#13;
&#13;
As a consequence of the liberalization of the European gas market in the last decades, gas trading and transport have been decoupled. This has led to new challenges for gas transport companies, and mathematical optimization is perfectly suited for tackling many of these challenges. However, the underlying mathematical problems are by far too hard to be solved by today's general-purpose software so that novel mathematical theory and algorithms are needed. The industrial research project "ForNe: Research Cooperation Network   Optimization" has been initiated and funded by Open Grid Europe in 2009 and brought together experts in mathematical optimization from seven German universities and research institutes, which cover almost the entire range of mathematical optimization: integer and nonlinear optimization as well as optimization under uncertainty.&#13;
&#13;
The mathematical research results have been put together in a software package that has been delivered to Open Grid Europe at the end of the project. Moreover, the research is still continuing - e.g., in the Collaborative Research Center/Transregio 154 "Mathematical Modelling, Simulation and Optimization using the Example of Gas Networks" funded by the German Research Foundation.</abstract>
    <enrichment key="SubmissionStatus">under review</enrichment>
    <enrichment key="review.accepted_by">2</enrichment>
    <licence>Creative Commons - CC BY - Namensnennung 4.0 International</licence>
    <author>Martin Schmidt</author>
    <author>Benjamin Hiller</author>
    <author>Thorsten Koch</author>
    <author>Marc Pfetsch</author>
    <author>Björn Geißler</author>
    <author>René Henrion</author>
    <author>Imke Joormann</author>
    <author>Alexander Martin</author>
    <author>Antonio Morsi</author>
    <author>Werner Römisch</author>
    <author>Lars Schewe</author>
    <author>Rüdiger Schultz</author>
    <author>Marc C. Steinbach</author>
    <collection role="institutes" number="">Friedrich-Alexander-Universität Erlangen-Nürnberg</collection>
    <collection role="institutes" number="">Technische Universität Darmstadt</collection>
    <collection role="institutes" number="">Humboldt-Universität zu Berlin</collection>
    <collection role="institutes" number="">Zuse-Institut Berlin (ZIB)</collection>
    <collection role="institutes" number="">Weierstraß-Institut für Angewandte Analysis und Stochastik</collection>
    <collection role="institutes" number="">Universität Duisburg-Essen</collection>
    <collection role="subprojects" number="">A01</collection>
    <collection role="subprojects" number="">A05</collection>
    <collection role="subprojects" number="">A07</collection>
    <collection role="subprojects" number="">B04</collection>
    <collection role="subprojects" number="">B05</collection>
    <collection role="subprojects" number="">B07</collection>
    <collection role="subprojects" number="">B08</collection>
    <collection role="institutes" number="">Universität Trier</collection>
    <collection role="institutes" number="">University of Edinburgh</collection>
    <file>https://opus4.kobv.de/opus4-trr154/files/285/forne-komso.pdf</file>
  </doc>
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