Year: 2025
Type: article
Abstract: Matching problems arise in various settings where two or more entities need to be matched—such as job applicants to positions, students to colleges, organ donors to recipients, and advertisers to ad slots in web advertising platforms. Both offline and online bipartite matching algorithms have been developed for these problems, with online methods being particularly important for real-time applications like internet advertising. This study introduces the Preference Adjustment Matching Algorithm (PAMA), a novel matching framework that pairs elements, which conceptually represent a bipartite graph structure, based on rankings and preferences. In particular, this algorithm is applied to tutor-module assignment in academic settings. Tutor-module assignment is the process of assigning tutors to academic modules while balancing tutor preferences, module rankings, and institutional constraints. Based on the fundamental research theory of matching, PAMA combines both maximal and stability principles within fairness and efficiency criteria to achieve flexible and equitable assignments. PAMA operates in iterative rounds, dynamically adjusting modules and tutors’ preferences while addressing capacity and eligibility constraints. The algorithm operates under two distinct scenarios: in the first case it achieves maximal matching, while in the second one, even if it does not maintain maximality due to deadlock resolution, it guarantees its convergence to a stable solution. PAMA was applied to a real dataset provided by the Hellenic Open University (HOU), in which 3,982 tutors competed for 1,906 positions within 620 modules. Its performance was tested through various scenarios and proved capable of effectively handling both single-round and multi-round assignments. Although PAMA has a maximal matching behavior, this property might be lost in the presence of deadlock(s), but these are resolvable, allowing the algorithm to converge to a stable solution. It also adeptly resolved complex situations, offering flexibility for administrative decision-making that aligned with institutional policies, making PAMA a powerful solution for matching related problems.
Source: Algorithms
DOI: 10.3390/a18050250
Authors: Nikos Karousos, Despoina Pantazi, George Vorvilas, Vassilios S. Verykios
Institution: Hellenic Open University
Language: English
Subfield: Economics and Econometrics
Domain: Social Sciences
SDG: Quality education
Open Access status: gold
Estimated APC paid: $1,930
OpenAlex ID: W4409814026