Advertisement

An Integer Programming Approach to the Student-Project Allocation Problem with Preferences over Projects

  • David Manlove
  • Duncan Milne
  • Sofiat OlaosebikanEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10856)

Abstract

The Student-Project Allocation problem with preferences over Projects (SPA-P) involves sets of students, projects and lecturers, where the students and lecturers each have preferences over the projects. In this context, we typically seek a stable matching of students to projects (and lecturers). However, these stable matchings can have different sizes, and the problem of finding a maximum stable matching (MAX-SPA-P) is NP-hard. There are two known approximation algorithms for MAX-SPA-P, with performance guarantees of 2 and \(\frac{3}{2}\). In this paper, we describe an Integer Programming (IP) model to enable MAX-SPA-P to be solved optimally. Following this, we present results arising from an empirical analysis that investigates how the solution produced by the approximation algorithms compares to the optimal solution obtained from the IP model, with respect to the size of the stable matchings constructed, on instances that are both randomly-generated and derived from real datasets. Our main finding is that the \(\frac{3}{2}\)-approximation algorithm finds stable matchings that are very close to having maximum cardinality.

References

  1. 1.
    Abraham, D.J., Irving, R.W., Manlove, D.F.: Two algorithms for the Student-Project allocation problem. J. Discrete Algorithms 5(1), 79–91 (2007)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Anwar, A.A., Bahaj, A.S.: Student project allocation using integer programming. IEEE Trans. Educ. 46(3), 359–367 (2003)CrossRefGoogle Scholar
  3. 3.
    Calvo-Serrano, R., Guillén-Gosálbez, G., Kohn, S., Masters, A.: Mathematical programming approach for optimally allocating students’ projects to academics in large cohorts. Educ. Chem. Eng. 20, 11–21 (2017)CrossRefGoogle Scholar
  4. 4.
    Chiarandini, M., Fagerberg, R., Gualandi, S.: Handling preferences in student-project allocation. In: Annals of Operations Research (2018, to appear)Google Scholar
  5. 5.
    Gale, D., Shapley, L.S.: College admissions and the stability of marriage. Am. Mathe. Mon. 69, 9–15 (1962)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Harper, P.R., de Senna, V., Vieira, I.T., Shahani, A.K.: A genetic algorithm for the project assignment problem. Comput. Oper. Res. 32, 1255–1265 (2005)CrossRefGoogle Scholar
  7. 7.
    Iwama, K., Miyazaki, S., Yanagisawa, H.: Improved approximation bounds for the student-project allocation problem with preferences over projects. J. Discrete Algorithms 13, 59–66 (2012)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Kazakov, D.: Co-ordination of student-project allocation. Manuscript, University of York, Department of Computer Science (2001). http://www-users.cs.york.ac.uk/kazakov/papers/proj.pdf. Accessed 8 Mar 2018
  9. 9.
    Király, Z.: Better and simpler approximation algorithms for the stable marriage problem. Algorithmica 60, 3–20 (2011)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Kwanashie, A., Irving, R.W., Manlove, D.F., Sng, C.T.S.: Profile-based optimal matchings in the student/project allocation problem. In: Kratochvíl, J., Miller, M., Froncek, D. (eds.) IWOCA 2014. LNCS, vol. 8986, pp. 213–225. Springer, Cham (2015).  https://doi.org/10.1007/978-3-319-19315-1_19CrossRefGoogle Scholar
  11. 11.
    Manlove, D.F.: Algorithmics of Matching Under Preferences. World Scientific (2013)Google Scholar
  12. 12.
    Manlove, D.F., O’Malley, G.: Student project allocation with preferences over projects. J. Discrete Algorithms 6, 553–560 (2008)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Manlove, D.F., Milne, D., Olaosebikan, S.: An integer programming approach to the student-project allocation problem with preferences over projects. CoRR abs/1804.09993 (2018). https://arxiv.org/abs/1804.09993
  14. 14.
    Proll, L.G.: A simple method of assigning projects to students. Oper. Res. Q. 23(2), 195–201 (1972)CrossRefGoogle Scholar
  15. 15.
    Roth, A.E.: The evolution of the labor market for medical interns and residents: a case study in game theory. J. Polit. Econ. 92(6), 991–1016 (1984)CrossRefGoogle Scholar
  16. 16.
    Teo, C.Y., Ho, D.J.: A systematic approach to the implementation of final year project in an electrical engineering undergraduate course. IEEE Trans. Educ. 41(1), 25–30 (1998)CrossRefGoogle Scholar
  17. 17.
    Gurobi Optimization website. http://www.gurobi.com. Accessed 09 Jan 2018
  18. 18.
    GNU Linear Proramming Kit. https://www.gnu.org/software/glpk. Accessed 09 Jan 2018
  19. 19.
    CPLEX Optimization Studio. http://www-03.ibm.com/software/products/en/ibmilogcpleoptistud/. Accessed 19 May 2017

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Computing ScienceUniversity of GlasgowGlasgowScotland

Personalised recommendations