# Assigning Candidate Tutors to Modules: A Preference Adjustment Matching Algorithm (PAMA)
## 2 Matching Problems and the Teacher Assignment Problem (TAP): A Review of Related Work  
The process of assigning teachers to courses has been a research topic since 1976, when [PERSON] (1976) introduced the so-called Faculty Assignment Problem, later known as the TAP. According to the recent literature review of [PERSON] et al. [PERSON] et al. (2002), the research has gained consistent attention since 2002, and the main approaches can generally be divided into two major categories: optimization-based methods, particularly integer programming, which has dominated the field since its inception, and a diverse range of heuristic approaches, including evolutionary algorithms such as genetic algorithms. Pioneer work on such methods is attributed to [PERSON] in 1976 using linear programming with constraints via the simplex algorithm. Later, [PERSON] and [PERSON] and [PERSON] (2003), starting from a MIP formulation of the problem of minimizing the average number of different courses assigned to each teacher, have shown that their model can be transformed into a special case of the Fixed Charge Transportation Problem solvable by linear programming. Their approach was based on finding a maximally degenerate basic solution to the transportation problem. Following this direction, [PERSON] and [PERSON] [4] also proposed a mixed integer linear programming (MILP) model that balances teacher workload while considering teacher preferences, based on academic ranks such as professor or lecturer, with the unique ability to parameterize optimization criteria through weights for different institutional needs. A more recent study conducted by [PERSON] et al. [5] has extended the integer programming approach a step further and developed a binary integer programming model for resolving the faculty-course assignment problem. The overall objective is the maximization of faculty satisfaction in accordance with preferences for teaching specific courses. Time, course assignment, qualification, workload, and time block constraints are incorporated into the model. Their implementation, tested on real data from a university department, successfully generated feasible schedules that respected all constraints while maximizing instructor preferences in a very short time, demonstrating the practical effectiveness of modern integer programming approaches to the TAP. An interesting approach has been suggested by [PERSON] and [PERSON] [6], who have given a two-stage solution to the teacher-course assignments. In the first stage, rather than collecting teacher preferences directly (which can be time-consuming), they infer these preferences from the frequency of assignment in the past, performance scores, course description, and teacher specialization similarity, qualifications, and academic rank. In the second stage, they apply an integer linear programming model that maximizes satisfaction of these estimated preferences while reducing deviation from target teaching workloads. This approach significantly reduced the time taken for assignment generation from 5 weeks to a much smaller time, while also producing assignments with smaller deviation from workload targets than those generated manually. In the domain of evolutionary techniques, genetic algorithms represent the other major approach to TAP. [PERSON] [7] demonstrated the application of genetic algorithms to solve the teaching assignment problem while considering teacher preferences. A novel quantum-inspired approach was presented by [PERSON] [8], in which he developed new operators for the quantum evolutionary algorithm (QEA) to solve timetabling issues. QEA combines the principles of quantum computing with evolutionary algorithms, using quantum bits and superposition of states as basic principles to search the problem space.