Our methodology started with conducting a baseline trial to compare our simulated results with our realistic data. To ensure accuracy of results, the simulation is considered to accurately model the actual infusion clinic when the output distribution of the average number of patients seen per day in the simulation matches the distribution of the average number of patients seen per day in reality.
|Table 4: Total number of patients|
While the baseline simulation is higher than each actual day, the distribution remains the same, noting that the day with the most patients seen occurred on Friday while the day with the least patients seen occurred on Tuesday in both cases. The Weekly Average for the simulation is likely higher given that our baseline input is rounded up for simplicity.
Presented below is a visualization of the day to day over and under fluctuations in patient counts from the ideal, baseline capacity value of 60. Notice, there is a slight upwards trend, not only within this plot, but also within the remaining scatter plots referenced within our appendix. This is validated from the very small, but positive value of the slope from the linear trend line on trial 1. This may be associated with the large percentage of patients looping through the system for multiple treatments. Although our discrete distribution of patient number of treatments is quite simplified, compared to reality, the number of treatments a patient receives may extend far beyond the reach of a total of seven treatments. Given the limitations of the quantity of our data, we were pleased with how comparable our results of trial 1 were in regards to examining simulation versus reality.
After running a number of simulations, changing the capacity of each day by multiples of 5, it became apparent that the system is quite sensitive to slight capacity perturbations. Trials with a value higher than the established baseline deviation from minimum measurement are deemed less favorable, i.e. trials 2-7. Trials 8 and 9 required minimal capacity adjustment but returned a significantly lower deviation from minimum measurement. Although Tuesday usually sees a deficit in a number of people who arrive for their appointments, the best scenario, trial 9, overbooks Monday by 5 people and Friday by 1 person. From the baseline case, trial 1 above, the maximum number of patients observed that were over capacity were 19 while the minimum observed that were under capacity were 12. In the optimal scenario, the maximum decreased over capacity decreased to 18 patients, while the minimum under capacity decreased to 9.
Presented below is trial 9, our best trial in terms of the minimum variation of day to day over and under capacity, one of our key measurements. From simple visual observation, it is clear the peak to peak spikes are not as sharp as pictured in trial 1. Additionally, the deviation from minimum value, referenced in the results section of this paper, exhibits a value of 26.92 compared to the deviation from minimum value of trial 1 at 33.17. This asserts that there is less variation in the day to day fluctuations compared to the baseline trial. Examining the day of week capacities, heavily overbooking the beginning of the week and the end of the week seems to decrease the variation in day to day over and under counts.