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International Conference on the Practice and Theory of Automated Timetabling

PATAT 2002: Practice and Theory of Automated Timetabling IV pp 100–109Cite as

Solving the Travelling Tournament Problem: A Combined Integer Programming and Constraint Programming Approach

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2740))

Abstract

The Travelling Tournament Problem is a sports timetabling problem requiring production of a minimum distance double round-robin tournament for a group of n teams. Even small instances of this problem seem to be very difficult to solve. In this paper, we present the first provably optimal solution for an instance of eight teams. The solution methodology is a parallel implementation of a branch-and-price algorithm that uses integer programming to solve the master problem and constraint programming to solve the pricing problem. Additionally, constraint programming is used as a primal heuristic.

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References

  1. Applegate, D., Bixby, R., Chvatal, V., Cook, W.: On the Solution of Traveling Salesman Problems. Documenta Mathematica (Journal der Deutschen Mathematiker-Verinigung, International Congress of Mathematicians), 645–656 (1998)

    Google Scholar 

  2. Ball, B.C., Webster, D.B.: Optimal Scheduling for Even-Numbered Team Athletic Conferences. AIIE Trans. 9, 161–169 (1977)

    Google Scholar 

  3. Barnhart, C., Johnson, E.L., Nemhauser, G.L., Savelsbergh, M.W.P., Vance, P.H.: Branch-And-Price: Column Generation for Huge Integer Programs. Oper. Res. 46, 316–329 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  4. Benoist, T., Laburthe, F., Rottembourg, B.: Lagrange Relaxation and Constraint Programming Collaborative Schemes for Traveling Tournament Problems. In: CPAIOR, Wye College, pp. 15–26 (2001)

    Google Scholar 

  5. Easton, K.: Using Integer and Constraint Programming to Solve Sports Scheduling Problems. Doctoral Dissertation, Georgia Institute of Technology, Atlanta (2002)

    Google Scholar 

  6. Easton, K., Nemhauser, G.L., Trick, M.A.: The Traveling Tournament Problem: Description and Benchmarks, Principle and Practices of Constraint Programming. In: Walsh, T. (ed.) CP 2001. LNCS, vol. 2239, pp. 580–585. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  7. Gabow, H.N.: Data Structures for Weighted Matching and Nearest Common Ancestors with Linking. In: Proc. 1st Annu. ACM–SIAM Symp. Discr. Algorithms, pp. 434–443. SIAM, Philadelphia (1990)

    Google Scholar 

  8. Henz, M.: Scheduling a Major College Basketball Conference: Revisted. Oper. Res. 49, 163–168 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  9. Kirkpatrick, D.G., Hell, P.: On the Complexity of a Generalized Matching Problem. In: Proc. 10th Annu. ACM Symp. Theory Computing. Association for Computing Machinery, New York, pp. 240–245 (1978)

    Google Scholar 

  10. Klabjan, D., Johnson, E.L., Nemhauser, G.L.: Solving Large Airline Crew Scheduling Problems: Random Pairing Generation and Strong Branching. Comput. Optim. Appl. 20, 73–91 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  11. Russell, R.A., Leung, J.M.: Devising a Cost Effective Schedule for a Baseball League. Oper. Res. 42, 614–625 (1994)

    Article  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA, 30332, USA

    Kelly Easton & George Nemhauser

  2. Graduate School of Industrial Administration, Carnegie Mellon, Pittsburgh, PA, 15213, USA

    Michael Trick

Authors
  1. Kelly Easton
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  2. George Nemhauser
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  3. Michael Trick
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Editor information

Editors and Affiliations

  1. Automated Scheduling, Optimisation and Planning Group, School of Computer Science & IT, University of Nottingham, NG8 1BB, Nottingham, UK

    Edmund Burke

  2. Information Technology, KaHo St-Lieven, Gebr. Desmetstraat 1, 9000, Gent, Belgium

    Patrick De Causmaecker

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© 2003 Springer-Verlag Berlin Heidelberg

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Easton, K., Nemhauser, G., Trick, M. (2003). Solving the Travelling Tournament Problem: A Combined Integer Programming and Constraint Programming Approach. In: Burke, E., De Causmaecker, P. (eds) Practice and Theory of Automated Timetabling IV. PATAT 2002. Lecture Notes in Computer Science, vol 2740. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45157-0_6

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  • DOI: https://doi.org/10.1007/978-3-540-45157-0_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40699-0

  • Online ISBN: 978-3-540-45157-0

  • eBook Packages: Springer Book Archive

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