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  <doc>
    <id>335</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>683</pageFirst>
    <pageLast>709</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume>292</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2020-10-06</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Solving joint chance constrained problems using regularization and Benders' decomposition</title>
    <abstract language="eng">In this paper we investigate stochastic programs with joint chance constraints. We consider discrete scenario set and reformulate the problem by adding auxiliary variables. Since the resulting problem has a difficult feasible set, we regularize it. To decrease the dependence on the scenario number, we propose a numerical method by iteratively solving a master problem while adding Benders cuts. We find the solution of the slave problem (generating the Benders cuts) in a closed form and propose a heuristic method to decrease the number of cuts. We perform a numerical study by increasing the number of scenarios and compare our solution with a solution obtained by solving the same problem with continuous distribution.</abstract>
    <parentTitle language="eng">Annals of Operations Research</parentTitle>
    <identifier type="doi">10.1007/s10479-018-3091-9</identifier>
    <enrichment key="SubmissionStatus">in press</enrichment>
    <enrichment key="review.accepted_by">2</enrichment>
    <licence>Creative Commons - CC BY-NC-ND - Namensnennung - Nicht kommerziell - Keine Bearbeitungen 4.0 International</licence>
    <author>Lukas Adam</author>
    <author>Martin Branda</author>
    <author>Holger Heitsch</author>
    <author>René Henrion</author>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>chance constrained programming</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>optimality conditions</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>regularization</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Benders cuts</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>gas networks</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/335/ABHH18_Preprint.pdf</file>
  </doc>
</export-example>
