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    <id>780</id>
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    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
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    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2004-02-09</completedDate>
    <publishedDate>2004-02-09</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">A Geometrical Characterization of the Multidimensional Hausdorff and Dale Polytopes with Applications to Exit Time Problems</title>
    <abstract language="eng">We present formulae for the corner points of the multidimensional Hausdorff and Dale Polytopes and show how these results can be used to improve linear programming models for computing e.\,g.\ moments of exit distribution of diffusion processes. Specifically, we compute the mean exit time of twodimensional Brownian motion from the unit square and the unit triangle, as well as higher moments of the exit time of time space Brownian motion from a triangle.</abstract>
    <identifier type="serial">04-05</identifier>
    <identifier type="opus3-id">781</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-7807</identifier>
    <enrichment key="SourceTitle">Part I of the report appeared under the title "A Geometrical Characterization of Multidimensional Hausdorff Polytopes with Applications to Exit Time Problems" in: Mathematics of Operations Research 33(2):315-326, 2008</enrichment>
    <author>Kurt Helmes</author>
    <author>Stefan Röhl</author>
    <series>
      <title>ZIB-Report</title>
      <number>04-05</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>linear programming</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>special polytopes</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>moment problems</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Brownian motion on a triangle</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>numerical methods for exit time problems</value>
    </subject>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="msc" number="44A60">Moment problems</collection>
    <collection role="msc" number="52B12">Special polytopes (linear programming, centrally symmetric, etc.)</collection>
    <collection role="msc" number="60J65">Brownian motion [See also 58J65]</collection>
    <collection role="msc" number="60J70">Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.) [See also 92Dxx]</collection>
    <collection role="msc" number="90C08">Special problems of linear programming (transportation, multi-index, etc.)</collection>
    <collection role="institutes" number="">ZIB Allgemein</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/780/ZR-04-05.ps</file>
    <file>https://opus4.kobv.de/opus4-zib/files/780/ZR-04-05.pdf</file>
  </doc>
  <doc>
    <id>845</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
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    <type>reportzib</type>
    <publisherName/>
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    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2005-01-25</completedDate>
    <publishedDate>2005-01-25</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">A Case Study of Joint Online Truck Scheduling and Inventory Management for Multiple Warehouses</title>
    <abstract language="eng">For a real world problem --- transporting pallets between warehouses in order to guarantee sufficient supply for known and additional stochastic demand --- we propose a solution approach via convex relaxation of an integer programming formulation, suitable for online optimization. The essential new element linking routing and inventory management is a convex piecewise linear cost function that is based on minimizing the expected number of pallets that still need transportation. For speed, the convex relaxation is solved approximately by a bundle approach yielding an online schedule in 5 to 12 minutes for up to 3 warehouses and 40000 articles; in contrast, computation times of state of the art LP-solvers are prohibitive for online application. In extensive numerical experiments on a real world data stream, the approximate solutions exhibit negligible loss in quality; in long term simulations the proposed method reduces the average number of pallets needing transportation due to short term demand to less than half the number observed in the data stream.</abstract>
    <identifier type="serial">05-11</identifier>
    <identifier type="opus3-id">845</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-8454</identifier>
    <enrichment key="SourceTitle">Appeared in: Operations Research 55 (2007) 733-752</enrichment>
    <author>Christoph Helmberg</author>
    <author>Stefan Röhl</author>
    <series>
      <title>ZIB-Report</title>
      <number>05-11</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>convex relaxation</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>integer programming</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>stochastic demand</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>network models</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>large scale problems</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>bundle method</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>logistics</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>vehicle routing</value>
    </subject>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="msc" number="90B05">Inventory, storage, reservoirs</collection>
    <collection role="msc" number="90B06">Transportation, logistics</collection>
    <collection role="msc" number="90C06">Large-scale problems</collection>
    <collection role="msc" number="90C90">Applications of mathematical programming</collection>
    <collection role="institutes" number="">ZIB Allgemein</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/845/ZR-05-11.pdf</file>
    <file>https://opus4.kobv.de/opus4-zib/files/845/ZR-05-11.ps</file>
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