<?xml version="1.0" encoding="utf-8"?>
<export-example>
  <doc>
    <id>7059</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>1</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>2018-09-27</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Calculation of clinch and elimination numbers for sports leagues with multiple tiebreaking criteria</title>
    <abstract language="eng">The clinch (elimination) number is a minimal number of future wins (losses) needed to clinch (to be eliminated from) a specified place in a sports league. Several optimization models and computational results are shown in this paper for calculating clinch and elimination numbers in the presence of predefined multiple tiebreaking criteria. The main subject of this paper is to provide a general algorithmic framework based on integer programming with utilizing possibly multilayered upper and lower bounds.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-70591</identifier>
    <author>Satoshi Ito</author>
    <submitter>Yuji Shinano</submitter>
    <author>Yuji Shinano</author>
    <series>
      <title>ZIB-Report</title>
      <number>18-51</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Sports league</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Round-robin tournament</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Tiebreaking criteria</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Clinch number</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Elimination number</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Combinatorial optimization</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Integer programming</value>
    </subject>
    <collection role="ccs" number="I.">Computing Methodologies</collection>
    <collection role="pacs" number="00.00.00">GENERAL</collection>
    <collection role="msc" number="68-XX">COMPUTER SCIENCE (For papers involving machine computations and programs in a specific mathematical area, see Section -04 in that area)</collection>
    <collection role="msc" number="90-XX">OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING</collection>
    <collection role="institutes" number="optimization">Mathematical Optimization</collection>
    <collection role="persons" number="shinano">Shinano, Yuji</collection>
    <collection role="projects" number="MODAL-SynLab">MODAL-SynLab</collection>
    <collection role="projects" number="MODAL-Gesamt">MODAL-Gesamt</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
    <thesisPublisher>Zuse Institute Berlin (ZIB)</thesisPublisher>
    <file>https://opus4.kobv.de/opus4-zib/files/7059/ZIB-Report-18-51.pdf</file>
  </doc>
</export-example>
