# Assigning Candidate Tutors to Modules: A Preference Adjustment Matching Algorithm (PAMA)
## 4 The Preference Adjustment Matching Algorithm (PAMA)
### The PAMA Logic
In the remaining two cases, there were similar observations; however, it is worth mentioning that when a deadlock is addressed by applying the solution for the first teacher that is being examined, the next step is to re-execute the entire first stage of the algorithm. That means that the rest of the pending candidates that are related to a particular deadlock are most likely to be automatically assigned to a module according to the initial principles of the algorithm (commitment from both sides). In simple words, by handling only one of the pending candidates of a deadlock, the rest of the candidates involved in the same deadlock are likely to be automatically assigned to the next rounds of the algorithm. In general, the appliance of the algorithm to the Institute teacher assignment problem was helpful in terms of time and errors. The 3 cases in which the algorithm detected no maximal matching were indicated, and the Institute was able to monitor the final assignments in any different available policy. In this assignment period, the institute decided to use the user preference priority since, firstly, it has been ensured that the modules will not lose any critical educational quality level by not picking up the first available candidate. To evaluate the effectiveness of the algorithm and to control the time required for its execution, assignment data from previous years, in which the final assignment had been carried out manually, were used. In addition, to compare PAMA with other algorithms, a classic example of the deferred acceptance (DA) algorithm was chosen, the Gale-Shapley (GS), which seems to be the most suitable for solving the specific problem. The execution results of the two algorithms are shown in Table 6. Compared to the GS algorithm, PAMA produces almost the same assignments. In the last column, \"Differences\" are defined as the number of different matches between the two algorithms. The differences that arise in some academic periods are due to deadlock cases. In such cases, depending on HOU's resolution policy, the outcome may be the exact same result (if candidate's preferences are first considered) or a different one (if module rankings or the candidate's current position, if they are already employed at the institution, are taken into account). These deadlocks in the GS algorithm are typically resolved by assigning candidates to their top preferences, not to the best-ranked tutors. The key difference between the two algorithms is that PAMA does not prioritize the proposing side (tutors' preferences). For instance, in the academic year 2021-2022, the two differences between the two algorithms in GS refer to assignments made to tutors who had the module as their first choice. This illustrates that PAMA operates successfully and fulfills its intended purpose: making assignments and identifying special cases where the Hellenic Open University (HOU) may intervene in the assignment process. The execution time of PAMA is very short for the datasets related to assignments at HOU but appears significantly longer compared to the execution time of the G-S algorithm. The choice of round-based execution, as well as the re-execution of the entire first phase after resolving each deadlock, seems to have a significant impact on execution time. Nevertheless, the application of the algorithm in this specific use case is considered to have a negligible execution time. ## 6 Conclusions

The PAMA algorithm offers a novel solution to the tutor-module assignment problem by integrating maximal and stable matching principles with pending status and deadlock resolution in a unified process. This approach reframes deadlocks from being mere obstacles to serving as strategic tools for enforcing institutional policies while maintaining fairness by honoring ranking orders and balancing preferences, ultimately enhancing satisfaction for both tutors and the institution.