Optimal University Course Timetables and the Partial Transversal Polytope

  • Gerald Lach
  • Marco E. Lübbecke
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5038)


University course timetabling is the conflict-free assignment of courses to weekly time slots and rooms subject to various hard and soft constraints. One goal is to meet as closely as possible professors’ preferences. Building on an intuitive integer program (IP), we develop an exact decomposition approach which schedules courses first, and matches courses/times to rooms in a second stage. The subset of constraints which ensures a feasible room assignment defines the well-known partial transversal polytope. We describe it as a polymatroid, and thereby obtain a complete characterization of its facets. This enables us to add only strong valid inequalities to the first stage IP. In fact, for all practical purposes the number of facets is small. We present encouraging computational results on real-world and simulated timetabling data. The sizes of our optimally solvable instances (respecting all hard constraints) are the largest reported in the literature by far.


integer programming partial transversal polytope university course timetabling 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Gerald Lach
    • 1
  • Marco E. Lübbecke
    • 1
  1. 1.Institut für MathematikTechnische Universität BerlinBerlinGermany

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