Handling preferences in student-project allocation
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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.
KeywordsBipartite 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
- 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.
- Ashlagi, I., & Shi, P. (2014). Improving community cohesion in school choice via correlated-lottery implementation. Working paper.Google Scholar
- 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
- 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). https://doi.org/10.1109/ICCEE.2009.63.
- Fragiadakis, D. E., & Troyan, P. (2014). Improving welfare in assignment problems: An experimental investigation. http://erl.tamu.edu/working-papers/. Working paper at Economic Research Laboratory, Texas A&M University.
- Gusfield, D., & Irving, R. (1989). The stable marriage problem: Structure and algorithms. Cambridge: MIT Press.Google Scholar
- 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). https://doi.org/10.1109/ICKS.2008.7.
- Kagel, J. H., & Roth, A. E. (Eds.). (1997). The handbook of experimental economics. Princeton: Princeton University Press.Google Scholar
- 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. https://doi.org/10.1145/2229012.2229068.
- 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
- Rawls, J. (1971). A theory of justice. Cambridge, MA: Harvard University Press.Google Scholar
- Tempkin, L. (1993). Inequality. New York: Oxford University Press.Google Scholar
- Williams, H. P. (2013). Model building in mathematical programming (5th ed.). Chichester: Wiley.Google Scholar
- Young, P. (1995). Equity: In theory and practice. Princeton, NJ: Princeton University Press.Google Scholar