## 5 Numerical Results  
The simulations have been conducted considering the following main indicators to study process behavior:  
* Average time to complete the publication for the public selection, denoted as \"_Publication.Average Time in System_\";
* Average time to complete the comparative evaluation, denoted as \"_Comparative.Average Time in System_\";
* Average time to assign the activity, denoted as \"_Assingment.Average Time in System_\";
* Average time to complete the activity, denoted as \"_complete.Average Time in System_\";
* Average time to complete the entire process until the payment, denoted as \"_Payment.Average Time in System_\";
* Standard deviation of the average time to complete the publication for the public selection, denoted as \"_Publication.St Dev_\";
* Standard deviation of the average time to complete the comparative evaluation, denoted as \"_Comparative.St Dev_\";
* Standard deviation of the average time to assign the activity, denoted as \"_Assingment.St Dev_\";
* Standard deviation of the average time to complete the activity, denoted as \"_complete.St Dev_\";
* Standard deviation of the average time to complete the entire process until the payment, denoted as \"_Payment.St Dev_\";
* The average utilization of the Academic Office, denoted as \"_Academic office.Utilization \(\%\)_\";
* The average utilization of the UAC Office, denoted as \"_UAC.Utilization \(\%\)_\";
* The average utilization of the UAC Secretariat Office, denoted as \"_UAC secretariat.Utilization \(\%\)_\";
* The average utilization of the Director's Office, denoted as \"_Director.Utilization \(\%\)_\";
* The average utilization of the Evaluation Committee, denoted as \"_Evaluation committee.Utilization \(\%\)_\";
* The number of assignments completed related to teaching activities, denoted as \"_complete.Number Completed_\";
* The number of assignments completed related to payment, denoted as \"_Payment.Number Completed_\". The simulations are conducted following the terminating simulation approach. For each experimental class, a number of replications able to ensure a 5% confidence interval and a 95% confidence level for each performance measure has been conducted. Table 2 reports the simulation conducted with different availabilities of the academic office, which is the most used resource of the process, to test the effect on all of the performance measures tested. The sensitivity analysis concerns the availability of the academic office resource from 100% to 30%. The simulation analysis, conducted using Simul8, quantified the efficiency gains of the redesigned teaching assignment process against the baseline (\"AS-IS\") model. Key performance indicators (KPIs) included end-to-end process duration, resource utilization rates, and throughput. The model assumed an 8 h workday and a 5-day workweek and incorporated stochastic elements, such as exponential and normal distributions for activity delays, reflecting real-world variability in administrative workflows. The main key findings are the following. Process Time Reduction: The optimized \"TO-BE\" model reduced the average end-to-end processing time by 35%, from 46,200 min (\(\approx\)96 working days) at baseline to 30,040 min (\(\approx\)62.5 working days). Sub-processes, such as the publication of public selections and comparative evaluations, saw the most significant improvements, with delays reduced by 42% and 38%, respectively. Resource Utilization: Administrative staff utilization improved by 22%, from 7.2% at baseline to 9.1% in the optimized model, indicating better workload distribution. The Academic Affairs Office, previously a bottleneck, achieved a balanced utilization rate of 58.8% under 50% resource availability scenarios, demonstrating scalability. Throughput and Consistency: The redesigned process increased monthly throughput by 28%, with the number of completed assignments rising from 6.9 to 7.7 per cycle. Standard deviations in process duration decreased by 12-18%, highlighting enhanced predictability.