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    <id>5850</id>
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    <language>eng</language>
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    <publishedDate>2016-03-24</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Robust Allocation of Operating Rooms: a Cutting Plane Approach to handle Lognormal Case Durations</title>
    <abstract language="eng">The problem of allocating operating rooms (OR) to surgical cases is a challenging task, involving both combinatorial aspects&#13;
and uncertainty handling. We formulate this problem as a parallel machines scheduling problem, in which job durations follow a lognormal distribution,&#13;
and a fixed assignment of jobs to machines must be computed.&#13;
We propose a cutting-plane approach to solve the robust counterpart of this optimization problem.&#13;
To this end, we develop an algorithm based on fixed-point iterations that identifies worst-case scenarios and generates cut inequalities.&#13;
The main result of this article uses Hilbert's projective geometry to prove the convergence of this procedure under mild conditions.&#13;
We also propose two exact solution methods for a similar problem, but with a polyhedral uncertainty set, for which&#13;
only approximation approaches were known. Our model can&#13;
be extended to balance the load over several planning periods in a rolling horizon.&#13;
We present extensive numerical experiments for instances based on real data from a major hospital in Berlin. In particular, we find that:&#13;
(i) our approach performs well compared to a previous model that ignored the distribution of case durations; &#13;
(ii) compared to an alternative stochastic programming approach, robust optimization yields solutions that are more robust against uncertainty, at a small price in terms of average cost;&#13;
(iii) the \emph{longest expected processing time first} (LEPT) heuristic performs well and efficiently protects against extreme scenarios, but only if a good prediction model for the durations is available.&#13;
Finally, we draw a number of managerial implications from these observations.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-58502</identifier>
    <identifier type="doi">10.1016/j.ejor.2018.05.022</identifier>
    <enrichment key="SourceTitle">Appeared in: European Journal of Operational Research 271(2):420-435</enrichment>
    <author>Guillaume Sagnol</author>
    <submitter>Guillaume Sagnol</submitter>
    <author>Christoph Barner</author>
    <author>Ralf Borndörfer</author>
    <author>Mickaël Grima</author>
    <author>Matthes Seeling</author>
    <author>Claudia Spies</author>
    <author>Klaus Wernecke</author>
    <series>
      <title>ZIB-Report</title>
      <number>16-18</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>robust optimization</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>lognormal duration</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Hilbert's projective metric</value>
    </subject>
    <collection role="msc" number="90Cxx">Mathematical programming [See also 49Mxx, 65Kxx]</collection>
    <collection role="institutes" number="optimization">Mathematical Optimization</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="projects" number="BMBF-IBOSS">BMBF-IBOSS</collection>
    <collection role="institutes" number="healthcare">Mathematics of Health Care</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/5850/robust_alloc_lognorm_v1_zib.pdf</file>
    <file>https://opus4.kobv.de/opus4-zib/files/5850/robust_alloc_lognorm_v3_zib.pdf</file>
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  <doc>
    <id>5849</id>
    <completedYear/>
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    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
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    <completedDate>--</completedDate>
    <publishedDate>2016-03-24</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Robust Allocation of Operating Rooms with Lognormal case Durations</title>
    <abstract language="eng">The problem of allocating operating rooms (OR) to surgical cases is a challenging task,&#13;
involving both combinatorial aspects and uncertainty handling. In this article,&#13;
we formulate this problem as a job shop scheduling problem, in which the job durations follow a lognormal distribution.&#13;
We propose to use a cutting-plane approach to solve a robust version of this optimization problem. To this end, &#13;
we develop an algorithm based on fixed-point iterations to solve the subproblems that&#13;
identify worst-case scenarios and generate cut inequalities. The procedure is illustrated with numerical experiments based&#13;
on real data from a major hospital in Berlin.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-58497</identifier>
    <identifier type="url">http://www.pms2016.com/congreso/ficha.en.html</identifier>
    <enrichment key="SourceTitle">Proceedings of the 15th International Conference on Project Management and Scheduling (PMS 2016), pp.52-55</enrichment>
    <author>Guillaume Sagnol</author>
    <submitter>Guillaume Sagnol</submitter>
    <author>Ralf Borndörfer</author>
    <author>Mickaël Grima</author>
    <author>Matthes Seeling</author>
    <author>Claudia Spies</author>
    <series>
      <title>ZIB-Report</title>
      <number>16-16</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>robust optimization</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>lognormal duration</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Hilbert's projective metric</value>
    </subject>
    <collection role="msc" number="90Cxx">Mathematical programming [See also 49Mxx, 65Kxx]</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>
    <thesisPublisher>Zuse Institute Berlin (ZIB)</thesisPublisher>
    <thesisGrantor>Freie Universität Berlin</thesisGrantor>
    <file>https://opus4.kobv.de/opus4-zib/files/5849/PMS2016_zib.pdf</file>
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