Annals of Operations Research

, Volume 275, Issue 1, pp 39–78 | Cite as

Handling preferences in student-project allocation

  • Marco ChiarandiniEmail author
  • Rolf Fagerberg
  • Stefano Gualandi
S.I.: PATAT 2016


We consider the problem of allocating students to project topics satisfying side constraints and taking into account students’ preferences. Students rank projects according to their preferences for the topic and side constraints limit the possibilities to team up students in the project topics. The goal is to find assignments that are fair and that maximize the collective satisfaction. Moreover, we consider issues of stability and envy from the students’ viewpoint. This problem arises as a crucial activity in the organization of a first year course at the Faculty of Science of the University of Southern Denmark. We formalize the student-project allocation problem as a mixed integer linear programming problem and focus on different ways to model fairness and utilitarian principles. On the basis of real-world data, we compare empirically the quality of the allocations found by the different models and the computational effort to find solutions by means of a state-of-the-art commercial solver. We provide empirical evidence about the effects of these models on the distribution of the student assignments, which could be valuable input for policy makers in similar settings. Building on these results we propose novel combinations of the models that, for our case, attain feasible, stable, fair and collectively satisfactory solutions within a minute of computation. Since 2010, these solutions are used in practice at our institution.


Bipartite matching with one-sided preferences Student-project allocation problem Mixed integer linear programming Fair assignment Lexicographic optimization Ordered weighted averaging Profile-based optimization Envy-free division 


  1. Abdulkadirolu, A., Pathak, P. A., & Roth, A. E. (2009). Strategy-proofness versus efficiency in matching with indifferences: Redesigning the NYC high school match. American Economic Review, 99(5), 1954–78. Scholar
  2. Abraham, D. J., Irving, R. W., & Manlove, D. F. (2007). Two algorithms for the student-project allocation problem. Journal of Discrete Algorithms, 5(1), 73–90. Scholar
  3. Anwar, A. A., & Bahaj, A. (2003). Student project allocation using integer programming. IEEE Transactions on Education, 46(3), 359–367. Scholar
  4. Arulselvan, A., Cseh, Á., Groß, M., Manlove, D.F., & Matuschke, J. (2016). Matchings with lower quotas: Algorithms and complexity. CoRR arXiv:1412.0325. Preliminary version appeared at ISAAC 2015.
  5. Ashlagi, I., & Shi, P. (2014). Improving community cohesion in school choice via correlated-lottery implementation. Working paper.Google Scholar
  6. Atkinson, A. B. (1970). On the measurement of inequality. Journal of Economic Theory, 2(3), 244–263.CrossRefGoogle Scholar
  7. Bertsimas, D., Farias, V. F., & Trichakis, N. (2012). On the efficiency-fairness trade-off. Management Science, 58(12), 2234–2250. Scholar
  8. Biró, P., Fleiner, T., Irving, R. W., & Manlove, D. F. (2010). The college admissions problem with lower and common quotas. Theoretical Computer Science, 411(34), 3136–3153. Scholar
  9. Biró, P., & McDermid, E. (2014). Matching with sizes (or scheduling with processing set restrictions). Discrete Applied Mathematics, 164(Part 1), 61–67. Scholar
  10. Bogomolnaia, A., & Moulin, H. (2001). A new solution to the random assignment problem. Journal of Economic Theory, 100(2), 295–328. Scholar
  11. Bouveret, S., & Lang, J. (2008). Efficiency and envy-freeness in fair division of indivisible goods: Logical representation and complexity. Journal of Artificial Intelligence Research, 32, 525–564. Scholar
  12. Brams, S. J., & Taylor, A. D. (1996). Fair division: From cake-cutting to dispute resolution. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  13. Budish, E. (2011). The combinatorial assignment problem: Approximate competitive equilibrium from equal incomes. Journal of Political Economy, 119(6), 1061–1103. Scholar
  14. Budish, E., & Cantillon, E. (2012). The multi-unit assignment problem: Theory and evidence from course allocation at Harvard. American Economic Review, 102(5), 2237–71. Scholar
  15. Dye, J. (2001). A constraint logic programming approach to the stable marriage problem and its application to student-project allocation. In Proceedings of the sixth international workshop on computer-aided software engineering.Google Scholar
  16. El-Atta, A., & Moussa, M.I. (2009). Student project allocation with preference lists over (student, project) pairs. In Second international conference on computer and electrical engineering, 2009. ICCEE ’09 (Vol. 1, pp. 375–379).
  17. Fragiadakis, D. E., & Troyan, P. (2014). Improving welfare in assignment problems: An experimental investigation. Working paper at Economic Research Laboratory, Texas A&M University.
  18. Garg, N., Kavitha, T., Kumar, A., Mehlhorn, K., & Mestre, J. (2010). Assigning papers to referees. Algorithmica, 58(1), 119–136. Scholar
  19. Geiger, M. J., & Wenger, W. (2010). On the assignment of students to topics: A variable neighborhood search approach. Socio-Economic Planning Sciences, 44(1), 25–34. Scholar
  20. Gusfield, D., & Irving, R. (1989). The stable marriage problem: Structure and algorithms. Cambridge: MIT Press.Google Scholar
  21. Harper, P. R., de Senna, V., Vieira, I. T., & Shahani, A. K. (2005). A genetic algorithm for the project assignment problem. Computers & Operations Research, 32(5), 1255–1265. Scholar
  22. Hooker, J. N., & Williams, H. P. (2012). Combining equity and utilitarianism in a mathematical programming model. Management Science, 58(9), 1682–1693. Scholar
  23. Iwama, K., & Miyazaki, S. (2008). A survey of the stable marriage problem and its variants. In International conference on informatics education and research for knowledge-circulating society (ICKS 2008) (pp. 131–136).
  24. Iwama, K., Miyazaki, S., & Yanagisawa, H. (2012). Improved approximation bounds for the student-project allocation problem with preferences over projects. Journal of Discrete Algorithms, 13, 59–66. Scholar
  25. Kagel, J. H., & Roth, A. E. (Eds.). (1997). The handbook of experimental economics. Princeton: Princeton University Press.Google Scholar
  26. Lu, T., & Boutilier, C.E. (2012). Matching models for preference-sensitive group purchasing. In Proceedings of the 13th ACM conference on electronic commerce, EC ’12 (pp. 723–740). ACM, New York, NY, USA.
  27. Manlove, D. F. (2013). Algorithmics of matching under preferences. Series on theoretical computer science (Vol. 2). Singapore: World Scientific.CrossRefGoogle Scholar
  28. Manlove, D. F., & O’Malley, G. (2008). Student-project allocation with preferences over projects. Journal of Discrete Algorithms, 6(4), 553–560. Scholar
  29. Moulin, H. (2003). Fair division and collective welfare. Cambridge: The MIT Press.CrossRefGoogle Scholar
  30. Ogryczak, W., Pióro, M., & Tomaszewski, A. (2005). Telecommunications network design and max–min optimization problem. Journal of Telecommunications and Information Technology, 3, 43–56.Google Scholar
  31. Perach, N., Polak, J., & Rothblum, U. G. (2008). A stable matching model with an entrance criterion applied to the assignment of students to dormitories at the technion. International Journal of Game Theory, 36(3), 519–535. Scholar
  32. Proll, L. G. (1972). A simple method of assigning projects to students. Operational Research Quarterly (1970–1977), 23(2), 195–201.Google Scholar
  33. Rawls, J. (1971). A theory of justice. Cambridge, MA: Harvard University Press.Google Scholar
  34. Roth, A. E. (1984). The evolution of the labor market for medical interns and residents: A case study in game theory. Journal of Political Economy, 92(6), 991–1016.CrossRefGoogle Scholar
  35. Srinivasan, D., & Rachmawati, L. (2008). Efficient fuzzy evolutionary algorithm-based approach for solving the student project allocation problem. IEEE Transactions on Education, 51(4), 439–447. Scholar
  36. Tempkin, L. (1993). Inequality. New York: Oxford University Press.Google Scholar
  37. Teo, C., & Ho, D. J. (1998). A systematic approach to the implementation of final year project in an electrical engineering undergraduate course. IEEE Transactions on Education, 41(1), 25–30. Scholar
  38. Williams, H. P. (2013). Model building in mathematical programming (5th ed.). Chichester: Wiley.Google Scholar
  39. Yager, R. R. (1996). Constrained OWA aggregation. Fuzzy Sets and Systems, 81(1), 89–101. Scholar
  40. Yager, R. R. (1997). On the analytic representation of the leximin ordering and its application to flexible constraint propagation. European Journal of Operational Research, 102(1), 176–192. Scholar
  41. Young, P. (1995). Equity: In theory and practice. Princeton, NJ: Princeton University Press.Google Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2017

Authors and Affiliations

  1. 1.Department of Mathematics and Computer ScienceUniversity of Southern DenmarkOdense MDenmark
  2. 2.Department of MathematicsUniversity of PaviaPaviaItaly

Personalised recommendations