# Assigning Candidate Tutors to Modules: A Preference Adjustment Matching Algorithm (PAMA)
###### 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 ads slots in web advertising platforms. 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, and the methodology is built on four key assumptions where each module must receive its required number of candidates, candidates can only be assigned to a module once, eligible candidates based on ranking and module capacity must be assigned, and priority is given to mutual first-preference matches with institutional policies guiding alternative strategies when needed. PAMA operates in iterative rounds, dynamically adjusting modules and tutors' preferences while addressing capacity and eligibility constraints. The distinctive innovative element of PAMA is that it combines concepts of maximal and stable matching, pending status and deadlock resolution into a single process for matching tutors to modules to meet the specific requirements of academic institutions and their constraints. This approach achieves balanced assignments by adhering to ranking order and considering preferences on both sides (tutors and institution). PAMA was applied to a real dataset provided by the Hellenic Open University (HOU), in which 3982 tutors competed for 1906 positions within 620 modules. Its performance was tested through various scenarios and proved capable of effectively handling both single-round and multi-round assignments. PAMA effectively handles complex cases, allowing policy-based resolution of deadlocks. While it may lose maximality in such instances, it converges to stability, offering a flexible solution for matching-related problems. tutor assignment; teacher assignment; matching algorithm; preference adjustment matching algorithm +
Footnote †: journal: _Algorithms_  
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various heuristic methods including evolutionary techniques like genetic algorithms. These methods have provided useful frameworks, but they often cannot provide the necessary flexibility that has to be addressed by academic assignments as they lack a dynamic nature and a complex interaction between institutional needs and personal preferences. In that direction, these approaches can fail in cases where an immediate decision may not be the most appropriate, especially when many qualified candidates are competing for the same positions. The aim of the present study is to introduce the preference adjustment matching algorithm (PAMA), a novel matching framework specifically designed to enhance the tutor-module assignment process in academic settings. It seeks to provide a solution for matching tutors to academic modules while balancing various preferences, rankings, and institutional constraints. PAMA relies on both maximal and stable matching principles through an innovative iterative approach. In order to fulfill the unique needs of institutions, PAMA algorithm is novel in the way it integrates the ideas of maximal and stable matching, pending status, and deadlock resolution into a single procedure for matching tutors to modules, and this offers a new contribution to the existing literature. The main advantage of the algorithm is the dynamic processing of multiple rounds that allows for the adjustment of preferences and the introduction of a \"pending\" status. Unlike the traditional stable matching algorithms, which make immediate accept/reject decisions, PAMA temporarily holds promising matches while exploring other possibilities, resulting in assignments that satisfy both institutional and individual preferences. This leads to a fair result as PAMA manages both sides (rankings and preferences) equally, offering overall satisfaction.