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  <doc>
    <id>5929</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>2016-04-26</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Makespan and Tardiness in Activity Networks with Lognormal Activity Durations</title>
    <abstract language="eng">We propose an algorithm to approximate the distribution of the completion time (makespan)&#13;
and the tardiness costs of a project, when durations are lognormally distributed. This problem arises naturally for the optimization of surgery scheduling,&#13;
where it is very common to assume lognormal procedure times. We present an analogous of Clark's formulas to compute the moments of the maximum of a set of&#13;
lognormal variables. Then, we use moment matching formulas to approximate the earliest starting time of each activity of the project by a shifted lognormal variable.&#13;
This approach can be seen as a lognormal variant of a state-of-the-art method used for the statistical static timing analysis (SSTA) of digital circuits.&#13;
We carried out numerical experiments with instances based on real data from the application to surgery scheduling. We obtained very&#13;
promising results, especially for the approximation of the mean overtime in operating rooms, &#13;
for which our algorithm yields results of a similar quality to Monte-Carlo simulations&#13;
requiring an amount of computing time several orders of magnitude larger.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-59290</identifier>
    <author>Guillaume Sagnol</author>
    <submitter>Guillaume Sagnol</submitter>
    <author>Felix Balzer</author>
    <author>Ralf Borndörfer</author>
    <author>Claudia Spies</author>
    <author>Falk von Dincklage</author>
    <series>
      <title>ZIB-Report</title>
      <number>16-23</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>scheduling</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>activity network</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>lognormal distribution</value>
    </subject>
    <collection role="msc" number="68M20">Performance evaluation; queueing; scheduling [See also 60K25, 90Bxx]</collection>
    <collection role="msc" number="90B36">Scheduling theory, stochastic [See also 68M20]</collection>
    <collection role="institutes" number="optimization">Mathematical Optimization</collection>
    <collection role="institutes" number="traffic">Mathematics of Transportation and Logistics</collection>
    <collection role="persons" number="borndoerfer">Borndörfer, Ralf</collection>
    <collection role="persons" number="sagnol">Sagnol, Guillaume</collection>
    <collection role="projects" number="Charité-OPOSSUM">Charité-OPOSSUM</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/5929/lognorm_sched_zib_v1.pdf</file>
  </doc>
</export-example>
