Advertisement

Central European Journal of Operations Research

, Volume 23, Issue 3, pp 547–562 | Cite as

Modelling practical placement of trainee teachers to schools

  • Katarína CechlárováEmail author
  • Tamás Fleiner
  • David F. Manlove
  • Iain McBride
  • Eva Potpinková
Original Paper

Abstract

Several countries successfully use centralized matching schemes for assigning students to study places or fresh graduates to their first positions. In this paper we explore the computational aspects of a possible similar scheme for assigning trainee teachers to schools. Our model is motivated by the situation characteristic for Slovak and Czech education system where each pre-service teacher specializes in two subjects. We show that if the two subjects can be performed independently in two different schools, then a feasible assignment can be found efficiently by employing network flow techniques. By contrast, the requirement to perform both subjects at the same school leads to intractable problems even under several strict restrictions concerning the total number of subjects, partial capacities of schools and the number of acceptable schools each teacher is allowed to list. Finally, we report on an integer programming model for solving the ‘inseparable subjects’ case of the teachers assignment problem and the results of its application to real data.

Keywords

Assignment Algorithm NP-completeness  Linear programming 

Notes

Acknowledgments

We would like to thank R. Orosová, N. Kocová, T. Bušová, R. Soták (UPJŠ Košice), I. Kohanová (Comenius University Bratislava) and N. Vondrová (Charles University Prague) for detailed explanations of practical aspects of student assignment and for providing us with the data.

References

  1. Abdulkadiroglu A, Pathak PA, Roth AE (2005a) The New York City high school match. Am Econ Rev 95(2):364–367Google Scholar
  2. Abdulkadiroglu A, Pathak PA, Roth AE, Sönmez T (2005b) The Boston public school match. Am Econ Rev 95(2):368–371Google Scholar
  3. Ahuja RK, Magnanti TL, Orlin JB (1993) Network flows: theory, algorithms, and applications. Prentice Hall, Upper Saddle RiverGoogle Scholar
  4. Abraham D, Cechlárová K, Manlove D, Mehlhorn K (2004) Pareto optimality in house allocation problems. LNCS 3341:3–15Google Scholar
  5. Berman P, Karpinski M, Scott AD (2003) Approximation hardness of short symmetric instances of MAX-3SAT, Electronic Colloquium on Computational Complexity Report, number 49Google Scholar
  6. Biró P, Fleiner T, Irving RW, Manlove DF (2010) The college admissions problem with lower and common quotas. Theoret Comput Sci 411(34–36):3136–3153CrossRefGoogle Scholar
  7. Biró P, Kiselgof S (2013) College admissions with stable score-limits. Cent Eur J Oper Res. doi: 10.1007/s10100-013-0320-9
  8. Biró P and Klijn F (2013) Matching with couples: a multidisciplinary survey. Int Game Theory Rev 15(2) article number 1340008Google Scholar
  9. Biró P, McDermid E (2014) Matching with sizes (or scheduling with processing set restrictions). Discret Appl Math 164/1, 61–67Google Scholar
  10. Biró P, Manlove DF and McBride I (2013)The hospitals/residents problem with couples: complexity and integer programming models. Tech Rep arXiv:1308.4534, Computing Research Repository, Cornell University Library
  11. Biró P, Irving RW, Schlotter I (2011) Stable matching with couples: an empirical study. ACM J Exp Algorithmics. 16/1, Article 1.2Google Scholar
  12. Gale D, Shapley LS (1962) College admissions and the stability of marriage. Am Math Mon 69(1):9–15CrossRefGoogle Scholar
  13. Garey MR, Johnson DS (1979) Computers and intractability. Freeman, San FranciscoGoogle Scholar
  14. Gusfield D, Irving RW (1989) The stable marriage problem: structure and algorithms, foundations od computing. MIT Press, CambridgeGoogle Scholar
  15. Hefner A, Kleinschmidt P (1995) A constrained matching problem. Ann OR 57:135–145CrossRefGoogle Scholar
  16. Irving RW (1998) Matching medical students to pairs of hospitals: a new variation on an old theme. LNCS 1461:381–392Google Scholar
  17. McDermid E, Manlove DF (2010) Keeping partners together: algorithmic results for the hospitals/residents problem with couples. J Comb Optim 19(3):279–303CrossRefGoogle Scholar
  18. Manlove DF (2013) Algorithmics of matching under preferences. World Scientific, SingaporeCrossRefGoogle Scholar
  19. Roth AE (1984) The evolution of the labor market for medical interns and residents: a case study in game theory. J Polit Econ 6(4):991–1016CrossRefGoogle Scholar
  20. Schrijver A (2003) Combinatorial optimization: polyhedra and efficiency. Algorithms and Combinatorics, vol 24. Springer, Berlin, HeidelbergGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Katarína Cechlárová
    • 1
    Email author
  • Tamás Fleiner
    • 2
    • 3
  • David F. Manlove
    • 4
  • Iain McBride
    • 4
  • Eva Potpinková
    • 1
  1. 1.Institute of Mathematics, Faculty of ScienceP.J. Šafárik UniversityKošiceSlovakia
  2. 2.Department of Computer Science and Information TheoryBudapest University of Technology and EconomicsBudapestHungary
  3. 3.MTA-ELTE Egerváry Research Group, Operations Research DepartmentEötvös UniversityBudapestHungary
  4. 4.School of Computing ScienceUniversity of GlasgowGlasgowUK

Personalised recommendations