Flow Formulations for Curriculum-based Course Timetabling

Niels-Christian Fink Bagger*, Simon Kristiansen, Matias Sørensen, Thomas Jacob Riis Stidsen

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review

Abstract

In this paper we present two mixed-integer programming formulations for the curriculum based course timetabling problem (CTT). We show that the formulations contain underlying network structures by dividing the CTT into two separate models and then connect the two models using flow formulation techniques. The first mixed-integer programming formulation is based on an underlying minimum cost flow problem, which decreases the number of integer variables significantly and improves the performance compared to an intuitive mixed-integer programming formulation. The second formulation is based on a multi-commodity flow problem which in general is NP-hard, however, we prove that it suffices to solve the linear programming relaxation of the model. The formulations show competitiveness with other approaches based on mixed-integer programming from the literature and improve the currently best known lower bound on one data instance in the benchmark data set from the second international timetabling competition. Regarding upper bounds, the formulation based on the minimum cost flow problem performs better on average than other mixed integer programming approaches for the CTT.
Original languageEnglish
JournalAnnals of Operations Research
Volume280
Issue number1-2
Pages (from-to)121-150
Number of pages30
ISSN0254-5330
DOIs
Publication statusPublished - 2019

Keywords

  • Universe course timetabling
  • Integer programming
  • Minimum cost flow
  • Multi-commodity flow

Cite this

Bagger, Niels-Christian Fink ; Kristiansen, Simon ; Sørensen, Matias ; Stidsen, Thomas Jacob Riis. / Flow Formulations for Curriculum-based Course Timetabling. In: Annals of Operations Research. 2019 ; Vol. 280, No. 1-2. pp. 121-150.
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title = "Flow Formulations for Curriculum-based Course Timetabling",
abstract = "In this paper we present two mixed-integer programming formulations for the curriculum based course timetabling problem (CTT). We show that the formulations contain underlying network structures by dividing the CTT into two separate models and then connect the two models using flow formulation techniques. The first mixed-integer programming formulation is based on an underlying minimum cost flow problem, which decreases the number of integer variables significantly and improves the performance compared to an intuitive mixed-integer programming formulation. The second formulation is based on a multi-commodity flow problem which in general is NP-hard, however, we prove that it suffices to solve the linear programming relaxation of the model. The formulations show competitiveness with other approaches based on mixed-integer programming from the literature and improve the currently best known lower bound on one data instance in the benchmark data set from the second international timetabling competition. Regarding upper bounds, the formulation based on the minimum cost flow problem performs better on average than other mixed integer programming approaches for the CTT.",
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year = "2019",
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Flow Formulations for Curriculum-based Course Timetabling. / Bagger, Niels-Christian Fink; Kristiansen, Simon; Sørensen, Matias; Stidsen, Thomas Jacob Riis.

In: Annals of Operations Research, Vol. 280, No. 1-2, 2019, p. 121-150.

Research output: Contribution to journalJournal articleResearchpeer-review

TY - JOUR

T1 - Flow Formulations for Curriculum-based Course Timetabling

AU - Bagger, Niels-Christian Fink

AU - Kristiansen, Simon

AU - Sørensen, Matias

AU - Stidsen, Thomas Jacob Riis

PY - 2019

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N2 - In this paper we present two mixed-integer programming formulations for the curriculum based course timetabling problem (CTT). We show that the formulations contain underlying network structures by dividing the CTT into two separate models and then connect the two models using flow formulation techniques. The first mixed-integer programming formulation is based on an underlying minimum cost flow problem, which decreases the number of integer variables significantly and improves the performance compared to an intuitive mixed-integer programming formulation. The second formulation is based on a multi-commodity flow problem which in general is NP-hard, however, we prove that it suffices to solve the linear programming relaxation of the model. The formulations show competitiveness with other approaches based on mixed-integer programming from the literature and improve the currently best known lower bound on one data instance in the benchmark data set from the second international timetabling competition. Regarding upper bounds, the formulation based on the minimum cost flow problem performs better on average than other mixed integer programming approaches for the CTT.

AB - In this paper we present two mixed-integer programming formulations for the curriculum based course timetabling problem (CTT). We show that the formulations contain underlying network structures by dividing the CTT into two separate models and then connect the two models using flow formulation techniques. The first mixed-integer programming formulation is based on an underlying minimum cost flow problem, which decreases the number of integer variables significantly and improves the performance compared to an intuitive mixed-integer programming formulation. The second formulation is based on a multi-commodity flow problem which in general is NP-hard, however, we prove that it suffices to solve the linear programming relaxation of the model. The formulations show competitiveness with other approaches based on mixed-integer programming from the literature and improve the currently best known lower bound on one data instance in the benchmark data set from the second international timetabling competition. Regarding upper bounds, the formulation based on the minimum cost flow problem performs better on average than other mixed integer programming approaches for the CTT.

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