<?xml version="1.0" encoding="ISO-8859-1"?><article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
<front>
<journal-meta>
<journal-id>2007-8064</journal-id>
<journal-title><![CDATA[Entreciencias: diálogos en la sociedad del conocimiento]]></journal-title>
<abbrev-journal-title><![CDATA[Entreciencias: diálogos soc. conoc.]]></abbrev-journal-title>
<issn>2007-8064</issn>
<publisher>
<publisher-name><![CDATA[Universidad Nacional Autónoma de México, Escuela Nacional de Estudios Superiores]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S2007-80642020000100201</article-id>
<article-id pub-id-type="doi">10.22201/enesl.20078064e.2020.22.70018</article-id>
<title-group>
<article-title xml:lang="es"><![CDATA[Programación matemática binaria por etapas en la elaboración de un horario universitario]]></article-title>
<article-title xml:lang="en"><![CDATA[Phased binary mathematical programming in the elaboration of a university schedule]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Hernández Vázquez]]></surname>
<given-names><![CDATA[José Israel]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Hernández González]]></surname>
<given-names><![CDATA[Salvador]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Baltazar Flores]]></surname>
<given-names><![CDATA[María del Rosario]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Jiménez García]]></surname>
<given-names><![CDATA[José Alfredo]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Hernández Vázquez]]></surname>
<given-names><![CDATA[José Omar]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Tecnológico Nacional de México  ]]></institution>
<addr-line><![CDATA[León ]]></addr-line>
<country>México</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,Tecnológico Nacional de México  ]]></institution>
<addr-line><![CDATA[Celaya ]]></addr-line>
<country>México</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>12</month>
<year>2020</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>12</month>
<year>2020</year>
</pub-date>
<volume>8</volume>
<numero>22</numero>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_arttext&amp;pid=S2007-80642020000100201&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_abstract&amp;pid=S2007-80642020000100201&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_pdf&amp;pid=S2007-80642020000100201&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen  Objetivo: Establecer una estrategia que permita elaborar un horario universitario en tres etapas, utilizando programación matemática, tomando en cuenta la problemática que enfrentan la mayoría de los centros educativos públicos del nivel superior en México, que incluye la contratación de profesores de forma temporal en cada ciclo escolar.  Método:  La estrategia contempló la descomposición del problema original en tres modelos matemáticos, considerando variables binarias de dos índices, el uso de subconjuntos en el modelado y el empleo de una heurística.  Resultados: Se generaron horarios de clase compactos para estudiantes, en los que se aprovecharon los espacios de las aulas y se empleó de manera eficiente a los profesores de la universidad. La estrategia logró la automatización del proceso en la elaboración de horarios.  Limitaciones:  El trabajo presentado, analiza el caso del Tecnológico Nacional de México en Celaya. Por el momento, no se considera el uso de laboratorios, ni la aleatoriedad de la demanda de grupos y materias.  Principales hallazgos:  La estrategia expuesta, generó una reducción de al menos 98.34 % en el número de variables, permitiendo a la técnica exacta de ramificación y acotamiento alcanzar tiempos eficientes en la búsqueda de una solución, en un problema clasificado como NP-Duro.]]></p></abstract>
<abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract  Purpose: To establish a strategy to develop a three-stage university schedule through mathematical programming taking into account the problems faced by most public higher education centers in Mexico which includes hiring professors on a temporary basis in each school cycle.  Methodology:  The strategy involved the breakdown of the original problem into three mathematical models considering the binary variables of two indexes: the use of both subsets in modeling and heuristics.  Results:  Compact class schedules were generated for students taking advantage of classroom space and efficiently employing university professors. The strategy achieved the automation of the process in the elaboration of schedules.  Limitations:  The work presented only analyses the case of the National Technological Institute of Mexico in Celaya. For the moment, neither the use of laboratories nor the aleatory demand for groups and subjects are considered.  Findings:  The strategy presented generated a reduction of at least 98.34% of the number of variables allowing the exact branch and bound technique to achieve efficient times in the search for a solution in a problem classified as NP-hard.]]></p></abstract>
<kwd-group>
<kwd lng="es"><![CDATA[horario universitario]]></kwd>
<kwd lng="es"><![CDATA[programación entera binaria]]></kwd>
<kwd lng="es"><![CDATA[optimización combinatoria]]></kwd>
<kwd lng="es"><![CDATA[NP- duro]]></kwd>
<kwd lng="en"><![CDATA[University timetabling]]></kwd>
<kwd lng="en"><![CDATA[binary integer programming]]></kwd>
<kwd lng="en"><![CDATA[combinatorial optimization]]></kwd>
<kwd lng="en"><![CDATA[NP-hard]]></kwd>
</kwd-group>
</article-meta>
</front><back>
<ref-list>
<ref id="B1">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Ahmed]]></surname>
<given-names><![CDATA[L. N.]]></given-names>
</name>
<name>
<surname><![CDATA[Özcan]]></surname>
<given-names><![CDATA[E.]]></given-names>
</name>
<name>
<surname><![CDATA[Kheiri]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Solving high school timetabling problems worldwide using selection hyper-heuristics]]></article-title>
<source><![CDATA[Expert Systems with Applications]]></source>
<year>2015</year>
<volume>42</volume>
<numero>13</numero>
<issue>13</issue>
<page-range>5463-71</page-range></nlm-citation>
</ref>
<ref id="B2">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Appleby]]></surname>
<given-names><![CDATA[J. S.]]></given-names>
</name>
<name>
<surname><![CDATA[Blake]]></surname>
<given-names><![CDATA[D. V.]]></given-names>
</name>
<name>
<surname><![CDATA[Newman]]></surname>
<given-names><![CDATA[E. A.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Techniques for producing school timetables on a computer and their application to other scheduling problems]]></article-title>
<source><![CDATA[The Computer Journal]]></source>
<year>1961</year>
<volume>3</volume>
<numero>4</numero>
<issue>4</issue>
<page-range>237-45</page-range></nlm-citation>
</ref>
<ref id="B3">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Babaei]]></surname>
<given-names><![CDATA[H.]]></given-names>
</name>
<name>
<surname><![CDATA[Karimpour]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
<name>
<surname><![CDATA[Hadidi]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[A survey of approaches for university course timetabling problem]]></article-title>
<source><![CDATA[Computers and Industrial Engineering]]></source>
<year>2015</year>
<volume>86</volume>
<page-range>43-59</page-range></nlm-citation>
</ref>
<ref id="B4">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Bakir]]></surname>
<given-names><![CDATA[M. A.]]></given-names>
</name>
<name>
<surname><![CDATA[Aksop]]></surname>
<given-names><![CDATA[C.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[A 0-1 integer programming approach to a university timetabling problem]]></article-title>
<source><![CDATA[Hacettepe Journal of Mathematics and Statistics]]></source>
<year>2008</year>
<volume>37</volume>
<numero>1</numero>
<issue>1</issue>
<page-range>41-55</page-range></nlm-citation>
</ref>
<ref id="B5">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Bardadym]]></surname>
<given-names><![CDATA[V. A.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Computer-aided school and university timetabling: The new wave]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[Burke]]></surname>
<given-names><![CDATA[E.]]></given-names>
</name>
<name>
<surname><![CDATA[Ross]]></surname>
<given-names><![CDATA[P.]]></given-names>
</name>
</person-group>
<source><![CDATA[Practice and Theory of Automated Timetabling]]></source>
<year>1996</year>
<numero>1153</numero>
<issue>1153</issue>
<page-range>22-45</page-range><publisher-loc><![CDATA[Germany ]]></publisher-loc>
<publisher-name><![CDATA[Springer-Verlag Berlin Heidelberg]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B6">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Barták]]></surname>
<given-names><![CDATA[R.]]></given-names>
</name>
<name>
<surname><![CDATA[Müller]]></surname>
<given-names><![CDATA[T.]]></given-names>
</name>
<name>
<surname><![CDATA[Rudová]]></surname>
<given-names><![CDATA[H.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[A New Approach to Modeling and Solving Minimal Perturbation Problems]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[Apt]]></surname>
<given-names><![CDATA[K.]]></given-names>
</name>
<name>
<surname><![CDATA[Fages]]></surname>
<given-names><![CDATA[F.]]></given-names>
</name>
<name>
<surname><![CDATA[Rossi]]></surname>
<given-names><![CDATA[F.]]></given-names>
</name>
<name>
<surname><![CDATA[Szeredi]]></surname>
<given-names><![CDATA[P.]]></given-names>
</name>
<name>
<surname><![CDATA[Váncza]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
</person-group>
<source><![CDATA[Recent Advances in Constraints]]></source>
<year>2004</year>
<numero>3010</numero>
<issue>3010</issue>
<page-range>233-49</page-range><publisher-loc><![CDATA[Germany ]]></publisher-loc>
<publisher-name><![CDATA[Springer-Verlag Berlin Heidelberg]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B7">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Beligiannis]]></surname>
<given-names><![CDATA[G. N.]]></given-names>
</name>
<name>
<surname><![CDATA[Moschopoulos]]></surname>
<given-names><![CDATA[C.]]></given-names>
</name>
<name>
<surname><![CDATA[Likothanassis]]></surname>
<given-names><![CDATA[S. D.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[A genetic algorithm approach to school timetabling]]></article-title>
<source><![CDATA[Journal of the Operational Research Society]]></source>
<year>2009</year>
<volume>60</volume>
<numero>1</numero>
<issue>1</issue>
<page-range>23-42</page-range></nlm-citation>
</ref>
<ref id="B8">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Birbas]]></surname>
<given-names><![CDATA[T.]]></given-names>
</name>
<name>
<surname><![CDATA[Daskalaki]]></surname>
<given-names><![CDATA[S.]]></given-names>
</name>
<name>
<surname><![CDATA[Housos]]></surname>
<given-names><![CDATA[E.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[School timetabling for quality student and teacher schedules]]></article-title>
<source><![CDATA[Journal of Scheduling]]></source>
<year>2009</year>
<volume>12</volume>
<numero>2</numero>
<issue>2</issue>
<page-range>177-97</page-range></nlm-citation>
</ref>
<ref id="B9">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Burke]]></surname>
<given-names><![CDATA[E.]]></given-names>
</name>
<name>
<surname><![CDATA[Jackson]]></surname>
<given-names><![CDATA[K.]]></given-names>
</name>
<name>
<surname><![CDATA[Kingston]]></surname>
<given-names><![CDATA[J. H.]]></given-names>
</name>
<name>
<surname><![CDATA[Weare]]></surname>
<given-names><![CDATA[R.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Automated university timetabling: the state of the art]]></article-title>
<source><![CDATA[The Computer Journal]]></source>
<year>1997</year>
<volume>40</volume>
<numero>9</numero>
<issue>9</issue>
<page-range>565-71</page-range></nlm-citation>
</ref>
<ref id="B10">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Csima]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
<name>
<surname><![CDATA[Gotlieb]]></surname>
<given-names><![CDATA[C.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Tests on a computer method for constructing school timetables]]></article-title>
<source><![CDATA[Communications of the ACM]]></source>
<year>1964</year>
<volume>7</volume>
<numero>3</numero>
<issue>3</issue>
<page-range>160-3</page-range></nlm-citation>
</ref>
<ref id="B11">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Daskalaki]]></surname>
<given-names><![CDATA[S.]]></given-names>
</name>
<name>
<surname><![CDATA[Birbas]]></surname>
<given-names><![CDATA[T.]]></given-names>
</name>
<name>
<surname><![CDATA[Housos]]></surname>
<given-names><![CDATA[E.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[An integer programming formulation for a case study in university timetabling]]></article-title>
<source><![CDATA[European Journal of Operational Research]]></source>
<year>2004</year>
<volume>153</volume>
<numero>1</numero>
<issue>1</issue>
<page-range>117-35</page-range></nlm-citation>
</ref>
<ref id="B12">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[De Werra]]></surname>
<given-names><![CDATA[D.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[An introduction to timetabling]]></article-title>
<source><![CDATA[European Journal of Operational Research]]></source>
<year>1985</year>
<volume>19</volume>
<numero>2</numero>
<issue>2</issue>
<page-range>151-62</page-range></nlm-citation>
</ref>
<ref id="B13">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[De Werra]]></surname>
<given-names><![CDATA[D.]]></given-names>
</name>
<name>
<surname><![CDATA[Asratian]]></surname>
<given-names><![CDATA[A. S.]]></given-names>
</name>
<name>
<surname><![CDATA[Durand]]></surname>
<given-names><![CDATA[S.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Complexity of some special types of timetabling problems]]></article-title>
<source><![CDATA[Journal of Scheduling]]></source>
<year>2002</year>
<volume>5</volume>
<numero>2</numero>
<issue>2</issue>
<page-range>171-83</page-range></nlm-citation>
</ref>
<ref id="B14">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Demirovi&#263;]]></surname>
<given-names><![CDATA[E.]]></given-names>
</name>
<name>
<surname><![CDATA[Musliu]]></surname>
<given-names><![CDATA[N.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[MaxSAT-based large neighborhood search for high school timetabling]]></article-title>
<source><![CDATA[Computers and Operations Research]]></source>
<year>2017</year>
<volume>78</volume>
<page-range>172-80</page-range></nlm-citation>
</ref>
<ref id="B15">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Even]]></surname>
<given-names><![CDATA[S.]]></given-names>
</name>
<name>
<surname><![CDATA[Itai]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
<name>
<surname><![CDATA[Shamir]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[On the complexity of timetable and multicommodity flow problems]]></article-title>
<source><![CDATA[SIAM Journal on Computing]]></source>
<year>1976</year>
<volume>5</volume>
<numero>4</numero>
<issue>4</issue>
<page-range>691-703</page-range></nlm-citation>
</ref>
<ref id="B16">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Feng]]></surname>
<given-names><![CDATA[X.]]></given-names>
</name>
<name>
<surname><![CDATA[Lee]]></surname>
<given-names><![CDATA[Y.]]></given-names>
</name>
<name>
<surname><![CDATA[Moon]]></surname>
<given-names><![CDATA[I.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[An integer program and a hybrid genetic algorithm for the university timetabling problem]]></article-title>
<source><![CDATA[Optimization Methods and Software]]></source>
<year>2017</year>
<volume>32</volume>
<numero>3</numero>
<issue>3</issue>
<page-range>625-49</page-range></nlm-citation>
</ref>
<ref id="B17">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Fonseca]]></surname>
<given-names><![CDATA[G. H.]]></given-names>
</name>
<name>
<surname><![CDATA[Santos]]></surname>
<given-names><![CDATA[H. G.]]></given-names>
</name>
<name>
<surname><![CDATA[Carrano]]></surname>
<given-names><![CDATA[E. G.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Late acceptance hill-climbing for high school timetabling]]></article-title>
<source><![CDATA[Journal of Scheduling]]></source>
<year>2016</year>
<volume>19</volume>
<numero>4</numero>
<issue>4</issue>
<page-range>453-65</page-range></nlm-citation>
</ref>
<ref id="B18">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Goh]]></surname>
<given-names><![CDATA[S. L.]]></given-names>
</name>
<name>
<surname><![CDATA[Kendall]]></surname>
<given-names><![CDATA[G.]]></given-names>
</name>
<name>
<surname><![CDATA[Sabar]]></surname>
<given-names><![CDATA[N. R.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Improved local search approaches to solve the post enrolment course timetabling problem]]></article-title>
<source><![CDATA[European Journal of Operational Research]]></source>
<year>2017</year>
<volume>261</volume>
<numero>1</numero>
<issue>1</issue>
<page-range>17-29</page-range></nlm-citation>
</ref>
<ref id="B19">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Junn]]></surname>
<given-names><![CDATA[K. Y.]]></given-names>
</name>
<name>
<surname><![CDATA[Obit]]></surname>
<given-names><![CDATA[J. H.]]></given-names>
</name>
<name>
<surname><![CDATA[Alfred]]></surname>
<given-names><![CDATA[R.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[The study of genetic algorithm approach to solving university course timetabling problem]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[Alfred]]></surname>
<given-names><![CDATA[R.]]></given-names>
</name>
<name>
<surname><![CDATA[Iida]]></surname>
<given-names><![CDATA[H.]]></given-names>
</name>
<name>
<surname><![CDATA[Ag. Ibrahim]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
<name>
<surname><![CDATA[Lim]]></surname>
<given-names><![CDATA[Y.]]></given-names>
</name>
</person-group>
<source><![CDATA[Computational Science and Technology]]></source>
<year>2018</year>
<numero>488</numero>
<issue>488</issue>
<page-range>454-63</page-range><publisher-loc><![CDATA[Singapore ]]></publisher-loc>
<publisher-name><![CDATA[Springer]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B20">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Junn]]></surname>
<given-names><![CDATA[K. Y.]]></given-names>
</name>
<name>
<surname><![CDATA[Obit]]></surname>
<given-names><![CDATA[J. H.]]></given-names>
</name>
<name>
<surname><![CDATA[Alfred]]></surname>
<given-names><![CDATA[R.]]></given-names>
</name>
<name>
<surname><![CDATA[Bolongkikit]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[A formal Model of Multi-agent System for University Course Timetabling Problems]]></article-title>
<person-group person-group-type="editor">
<name>
<surname><![CDATA[Alfred]]></surname>
<given-names><![CDATA[R.]]></given-names>
</name>
<name>
<surname><![CDATA[Lim]]></surname>
<given-names><![CDATA[Y.]]></given-names>
</name>
<name>
<surname><![CDATA[Ibrahim]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
<name>
<surname><![CDATA[Anthony]]></surname>
<given-names><![CDATA[P.]]></given-names>
</name>
</person-group>
<source><![CDATA[Computational Science and Technology]]></source>
<year>2019</year>
<numero>481</numero>
<issue>481</issue>
<page-range>215-25</page-range><publisher-loc><![CDATA[Singapore ]]></publisher-loc>
<publisher-name><![CDATA[Springer]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B21">
<nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Khonggamnerd]]></surname>
<given-names><![CDATA[P.]]></given-names>
</name>
<name>
<surname><![CDATA[Innet]]></surname>
<given-names><![CDATA[S.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[On improvement of effectiveness in automatic university timetabling arrangement with applied genetic algorithm]]></article-title>
<source><![CDATA[Fourth International Conference on Computer Sciences and Convergence Information Technology]]></source>
<year>2009</year>
<page-range>1266-70</page-range></nlm-citation>
</ref>
<ref id="B22">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Kristiansen]]></surname>
<given-names><![CDATA[S.]]></given-names>
</name>
<name>
<surname><![CDATA[Sørensen]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Stidsen]]></surname>
<given-names><![CDATA[T. R.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Integer programming for the generalized high school timetabling problem]]></article-title>
<source><![CDATA[Journal of Scheduling]]></source>
<year>2015</year>
<volume>18</volume>
<numero>4</numero>
<issue>4</issue>
<page-range>377-92</page-range></nlm-citation>
</ref>
<ref id="B23">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Lawrie]]></surname>
<given-names><![CDATA[N. L.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[An integer linear programming model of a school timetabling problem]]></article-title>
<source><![CDATA[The Computer Journal]]></source>
<year>1969</year>
<volume>12</volume>
<numero>4</numero>
<issue>4</issue>
<page-range>307-16</page-range></nlm-citation>
</ref>
<ref id="B24">
<nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Lindahl]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Mason]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Room planning at universities]]></article-title>
<source><![CDATA[11th International Conference on Practice and Theory of Automated Timetabling]]></source>
<year>2016</year>
<page-range>515-9</page-range></nlm-citation>
</ref>
<ref id="B25">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Lindahl]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Stidsen]]></surname>
<given-names><![CDATA[T.]]></given-names>
</name>
<name>
<surname><![CDATA[Sørensen]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Quality recovering of university timetables]]></article-title>
<source><![CDATA[European Journal of Operational Research]]></source>
<year>2019</year>
<volume>276</volume>
<numero>2</numero>
<issue>2</issue>
<page-range>422-35</page-range></nlm-citation>
</ref>
<ref id="B26">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Lindahl]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Sørensen]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Stidsen]]></surname>
<given-names><![CDATA[T. R.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[A fix-and-optimize matheuristic for university timetabling]]></article-title>
<source><![CDATA[Journal of Heuristics]]></source>
<year>2018</year>
<volume>24</volume>
<numero>4</numero>
<issue>4</issue>
<page-range>645-65</page-range></nlm-citation>
</ref>
<ref id="B27">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Lü]]></surname>
<given-names><![CDATA[Z.]]></given-names>
</name>
<name>
<surname><![CDATA[Hao]]></surname>
<given-names><![CDATA[J. K.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Adaptive tabu search for course timetabling]]></article-title>
<source><![CDATA[European Journal of Operational Research]]></source>
<year>2010</year>
<volume>200</volume>
<numero>1</numero>
<issue>1</issue>
<page-range>235-44</page-range></nlm-citation>
</ref>
<ref id="B28">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Phillips]]></surname>
<given-names><![CDATA[A. E.]]></given-names>
</name>
<name>
<surname><![CDATA[Walker]]></surname>
<given-names><![CDATA[C. G.]]></given-names>
</name>
<name>
<surname><![CDATA[Ehrgott]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Ryan]]></surname>
<given-names><![CDATA[D. M.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Integer programming for minimal perturbation problems in university course timetabling]]></article-title>
<source><![CDATA[Annals of Operations Research]]></source>
<year>2017</year>
<volume>252</volume>
<numero>2</numero>
<issue>2</issue>
<page-range>283-304</page-range></nlm-citation>
</ref>
<ref id="B29">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Sánchez-Partida]]></surname>
<given-names><![CDATA[D.]]></given-names>
</name>
<name>
<surname><![CDATA[Martínez-Flores]]></surname>
<given-names><![CDATA[J. L.]]></given-names>
</name>
<name>
<surname><![CDATA[Cabrera-Ríos]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Olivares-Benítez]]></surname>
<given-names><![CDATA[E.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Case Study: A Comprehensive Integer Programming Model for Improving an Educational Timetable]]></article-title>
<source><![CDATA[International Journal of Combinatorial Optimization Problems and Informatics]]></source>
<year>2017</year>
<volume>8</volume>
<numero>3</numero>
<issue>3</issue>
<page-range>71-82</page-range></nlm-citation>
</ref>
<ref id="B30">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Saviniec]]></surname>
<given-names><![CDATA[L.]]></given-names>
</name>
<name>
<surname><![CDATA[Santos]]></surname>
<given-names><![CDATA[M. O.]]></given-names>
</name>
<name>
<surname><![CDATA[Costa]]></surname>
<given-names><![CDATA[A. M.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Effective local search algorithms for high school timetabling problems]]></article-title>
<source><![CDATA[Applied Soft Computing]]></source>
<year>2017</year>
<volume>60</volume>
<page-range>363-73</page-range></nlm-citation>
</ref>
<ref id="B31">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Saviniec]]></surname>
<given-names><![CDATA[L.]]></given-names>
</name>
<name>
<surname><![CDATA[Santos]]></surname>
<given-names><![CDATA[M. O.]]></given-names>
</name>
<name>
<surname><![CDATA[Costa]]></surname>
<given-names><![CDATA[A. M.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Parallel local search algorithms for high school timetabling problems]]></article-title>
<source><![CDATA[Applied Soft Computing]]></source>
<year>2018</year>
<volume>265</volume>
<numero>1</numero>
<issue>1</issue>
<page-range>81-98</page-range></nlm-citation>
</ref>
<ref id="B32">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Schimmelpfeng]]></surname>
<given-names><![CDATA[K.]]></given-names>
</name>
<name>
<surname><![CDATA[Helber]]></surname>
<given-names><![CDATA[S.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Application of a real-world university-course timetabling model solved by integer programming]]></article-title>
<source><![CDATA[OR Spectrum]]></source>
<year>2007</year>
<volume>29</volume>
<numero>4</numero>
<issue>4</issue>
<page-range>783-803</page-range></nlm-citation>
</ref>
<ref id="B33">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Song]]></surname>
<given-names><![CDATA[T.]]></given-names>
</name>
<name>
<surname><![CDATA[Liu]]></surname>
<given-names><![CDATA[S.]]></given-names>
</name>
<name>
<surname><![CDATA[Tang]]></surname>
<given-names><![CDATA[X.]]></given-names>
</name>
<name>
<surname><![CDATA[Peng]]></surname>
<given-names><![CDATA[X.]]></given-names>
</name>
<name>
<surname><![CDATA[Chen]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[An iterated local search algorithm for the university course timetabling problem]]></article-title>
<source><![CDATA[Applied Soft Computing]]></source>
<year>2018</year>
<volume>68</volume>
<page-range>597-608</page-range></nlm-citation>
</ref>
<ref id="B34">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Sørensen]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Dahms]]></surname>
<given-names><![CDATA[F. H. W.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[A Two-stage decomposition of high school timetabling applied to cases in Denmark]]></article-title>
<source><![CDATA[Computers and Operations Research]]></source>
<year>2014</year>
<volume>43</volume>
<numero>1</numero>
<issue>1</issue>
<page-range>36-49</page-range></nlm-citation>
</ref>
<ref id="B35">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Tripathy]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[School timetabling-A case in large binary integer linear programming]]></article-title>
<source><![CDATA[Management Science]]></source>
<year>1984</year>
<volume>30</volume>
<numero>12</numero>
<issue>12</issue>
<page-range>1473-89</page-range></nlm-citation>
</ref>
<ref id="B36">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Welsh]]></surname>
<given-names><![CDATA[D. J.]]></given-names>
</name>
<name>
<surname><![CDATA[Powell]]></surname>
<given-names><![CDATA[M. B.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[An upper bound to the chromatic number of a graph and its application to timetabling problem]]></article-title>
<source><![CDATA[The Computer Journal]]></source>
<year>1967</year>
<volume>10</volume>
<numero>1</numero>
<issue>1</issue>
<page-range>85-6</page-range></nlm-citation>
</ref>
<ref id="B37">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Yasari]]></surname>
<given-names><![CDATA[P.]]></given-names>
</name>
<name>
<surname><![CDATA[Ranjbar]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Jamili]]></surname>
<given-names><![CDATA[N.]]></given-names>
</name>
<name>
<surname><![CDATA[Shaelaie]]></surname>
<given-names><![CDATA[M. H.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[A two-stage stochastic programming approach for a multi-objective course timetabling problem with courses cancelation risk]]></article-title>
<source><![CDATA[Computers and Industrial Engineering]]></source>
<year>2019</year>
<volume>130</volume>
<page-range>650-60</page-range></nlm-citation>
</ref>
</ref-list>
</back>
</article>
