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    <completedDate>2011-09-29</completedDate>
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    <title language="eng">Solving steel mill slab design problems</title>
    <abstract language="eng">The steel mill slab design problem from the CSPLIB is a combinatorial&#13;
optimization problem motivated by an application of the steel industry. It&#13;
has been widely studied in the constraint programming community.  Several&#13;
methods were proposed to solve this problem. A steel mill slab library was&#13;
created which contains 380 instances. A closely related binpacking problem&#13;
called the multiple knapsack problem with color constraints, originated&#13;
from the same industrial problem, was discussed in the integer programming&#13;
community. In particular, a simple integer program for this problem has&#13;
been given by Forrest et al. The aim of this paper is to bring these&#13;
different studies together. Moreover, we adapt the model of Forrest et&#13;
al. for the steel mill slab design problem. Using this model and a&#13;
state-of-the-art integer program solver all instances of the steel mill&#13;
slab library can be solved efficiently to optimality.  We improved,&#13;
thereby, the solution values of 76 instances compared to previous results.&#13;
Finally, we consider a recently introduced variant of the steel mill slab&#13;
design problem, where within all solutions which minimize the leftover one&#13;
is interested in a solution which requires a minimum number of slabs. For&#13;
that variant we introduce two approaches and solve all instances of the&#13;
steel mill slab library with this slightly changed objective function to&#13;
optimality.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="serial">11-38</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-14089</identifier>
    <identifier type="doi">10.1007/s10601-011-9113-8</identifier>
    <enrichment key="SourceTitle">Appeared in: Constraints 17 (2012) 39-50</enrichment>
    <author>Stefan Heinz</author>
    <submitter>Stefan Heinz</submitter>
    <author>Thomas Schlechte</author>
    <author>Rüdiger Stephan</author>
    <author>Michael Winkler</author>
    <series>
      <title>ZIB-Report</title>
      <number>11-38</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>steel mill slab design problem</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>multiple knapsack problem with color constraints</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>integer programming</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>set partitioning</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>binpacking with side constraints</value>
    </subject>
    <collection role="msc" number="90-XX">OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING</collection>
    <collection role="msc" number="90Cxx">Mathematical programming [See also 49Mxx, 65Kxx]</collection>
    <collection role="msc" number="90C90">Applications of mathematical programming</collection>
    <collection role="institutes" number="optimization">Mathematical Optimization</collection>
    <collection role="persons" number="heinz">Heinz, Stefan</collection>
    <collection role="persons" number="schlechte">Schlechte, Thomas</collection>
    <collection role="persons" number="michael.winkler">Winkler, Michael</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/1408/ZR-11-38.pdf</file>
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  <doc>
    <id>4731</id>
    <completedYear/>
    <publishedYear>2012</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>39</pageFirst>
    <pageLast>50</pageLast>
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    <issue>1</issue>
    <volume>17</volume>
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    <title language="eng">Solving steel mill slab design problems</title>
    <abstract language="eng">The steel mill slab design problem from the CSPLIB is a combinatorial optimization problem motivated by an application of the steel industry. It has been widely studied in the constraint programming community. Several methods were proposed to solve this problem. A steel mill slab library was created which contains 380 instances. A closely related binpacking problem called the multiple knapsack problem with color constraints, originated from the same industrial problem, was discussed in the integer programming community. In particular, a simple integer program for this problem has been given by Forrest et al. (INFORMS J Comput 18:129–134, 2006). The aim of this paper is to bring these different studies together. Moreover, we adapt the model of Forrest et al. (INFORMS J Comput 18:129–134, 2006) for the steel mill slab design problem. Using this model and a state-of-the-art integer program solver all instances of the steel mill slab library can be solved efficiently to optimality. We improved, thereby, the solution values of 76 instances compared to previous results (Schaus et al., Constraints 16:125–147, 2010). Finally, we consider a recently introduced variant of the steel mill slab design problem, where within all solutions which minimize the leftover one is interested in a solution which requires a minimum number of slabs. For that variant we introduce two approaches and solve all instances of the steel mill slab library with this slightly changed objective function to optimality.</abstract>
    <parentTitle language="eng">Constraints</parentTitle>
    <identifier type="doi">10.1007/s10601-011-9113-8</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-14089</enrichment>
    <author>Stefan Heinz</author>
    <submitter>Gerald Gamrath</submitter>
    <author>Thomas Schlechte</author>
    <author>Rüdiger Stephan</author>
    <author>Michael Winkler</author>
    <collection role="institutes" number="optimization">Mathematical Optimization</collection>
    <collection role="institutes" number="mip">Mathematical Optimization Methods</collection>
    <collection role="persons" number="heinz">Heinz, Stefan</collection>
    <collection role="persons" number="schlechte">Schlechte, Thomas</collection>
    <collection role="persons" number="michael.winkler">Winkler, Michael</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
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    <language>eng</language>
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    <completedDate>2009-04-29</completedDate>
    <publishedDate>2009-04-29</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Solving Steel Mill Slab Problems with Branch and Price</title>
    <abstract language="eng">The steel mill slab design problem from the CSPLib is a binpacking problem that is motivated by an application of the steel industry and that has been widely studied in the constraint programming community. Recently, several people proposed new models and methods to solve this problem. A steel mill slab library was created which contains 380 instances. A closely related binpacking problem called multiple knapsack problem with color constraints, originated from the same industrial problem, were discussed in the integer programming community. In particular, a simple integer programming for this problem has been given by Forrest et al. [3]. The aim of this paper is to bring these different studies together. Moreover, we adopt the model of [3] for the steel mill slab problem. Using a state of the art integer program solver, this model is capable to solve all instances of the steel mill slab library, mostly in less than one second, to optimality. We improved, thereby, the solution value of 76 instances.</abstract>
    <identifier type="serial">09-14</identifier>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="opus3-id">1175</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-11260</identifier>
    <author>Stefan Heinz</author>
    <submitter>unknown unknown</submitter>
    <author>Rüdiger Stephan</author>
    <author>Thomas Schlechte</author>
    <series>
      <title>ZIB-Report</title>
      <number>09-14</number>
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    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>steel mill slab problem</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>branch-and-price</value>
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    <subject>
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      <value>integer programming</value>
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    <collection role="ddc" number="510">Mathematik</collection>
    <collection role="msc" number="90C10">Integer programming</collection>
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    <collection role="institutes" number="optimization">Mathematical Optimization</collection>
    <collection role="persons" number="heinz">Heinz, Stefan</collection>
    <collection role="persons" number="schlechte">Schlechte, Thomas</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
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