Ideally, the number of treatments any patient receives is dependent on the type of patient they are, i.e., which treatments they are receiving. Each trial collections period runs for a total of 260 days. Steady state was reached at about 140 days into the simulation, which is the start time for collecting data. Until day 140 an upward trend was apparent.

For our results, we conducted nine total trials. We modified the capacity of total patients ideally allowed to be scheduled for each day of the week Monday through Friday. Due to conflicts in the scheduling process, i.e., no-shows, cancels and patients with bad blood, the total number of patients may exceed these ideal capacities during simulation. From trial to trial, the summation of the capacity for each week remained the same at 300 patients. Our first trial is our baseline, we used this data to examine how close our model matched reality, i.e., our three weeks of infusion center scheduling data. The trials following the first were conducted in effort to improve the scheduling process of the infusion center by manipulating the capacities of each day of the week while maintaining a total capacity of 300 for the week. We conducted the following trials:

Table 2: Scheduling capacity for each day of the week |
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Trial | Total Patients | Monday | Tuesday | Wednesday | Thursday | Friday | Total: |

1 | 7661 | 60 | 60 | 60 | 60 | 60 | 300 |

2 | 7686 | 50 | 50 | 60 | 70 | 70 | 300 |

3 | 7653 | 70 | 70 | 60 | 50 | 50 | 300 |

4 | 7642 | 50 | 65 | 70 | 65 | 50 | 300 |

5 | 7655 | 70 | 55 | 50 | 55 | 70 | 300 |

6 | 7627 | 75 | 55 | 55 | 55 | 60 | 300 |

7 | 7668 | 75 | 60 | 55 | 55 | 55 | 300 |

8 | 7626 | 65 | 59 | 58 | 57 | 61 | 300 |

9 | 7631 | 65 | 59 | 57 | 58 | 61 | 300 |

The above table exhibits two basic metrics: the total number of patients that ran through the system and the scheduling capacity for each day of the week. As demonstrated, the total number of patients that ran through the system was fairly uniform from trial to trial. It is important to have roughly a uniform number of patients from trial to trial, such that results are more comparable. The second metric represents the capacity for each day of the week during the associated trial. These capacities are important measures to remember when examining table 3. Trial 1 is the baseline case with a uniform input. Trial 2 has an input skewed heavily to the end of the week. Trial 3 was tested with an input skewed heavily toward the beginning of the week. Trial 4 has an input of a normal distribution, heavily concentrated on Wednesday. Trial 5 also has a symmetric input, but instead the distribution is skewed toward Friday and Monday with minimal people scheduled for Wednesday. Trials 6-9 were experimentally determined based on the results of the previous trials, with trials 6-9 showing comparable efficiency or improvement from the baseline case.

For each trial, we tracked the patient over and under capacity count from the baseline capacity of 60 for each day of the week, and the total deviation from the minimum value of the over and under capacity counts. The total deviation from the minimum value of the over and under counts was calculated using the following algorithm where x(i+5j) represents the number of patients seen on day i+5j of the simulation from day 1 to day 120 over a 24 week period that excludes weekends:

The following table, table 3, displays the results for each trial including the total number of patients seen and the total deviation from minimum over and under capacity counts. Notice, the actual over and under capacity values per day of the week in relation to the deviation from minimum. The closer the distance between the values of Monday through Friday, the smaller the value of the deviation from the minimum. For example, trial 9 had the smallest deviation from minimum, and the day to day over and under counts are fairly uniform.

Table 3: Total number of patients over capacity or under capacity per day |
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Trial | Monday | Tuesday | Wednesday | Thursday | Friday | Deviation from Minimum |

1 | 68 | 28 | 119 | 101 | 145 | 33.17 |

2 | 220 | -85 | 14 | 85 | 252 | 47.33 |

3 | -9 | 127 | 211 | 150 | -26 | 41.38 |

4 | -63 | -146 | 219 | 200 | 232 | 59.46 |

5 | 172 | 128 | 61 | 4 | 90 | 38.54 |

6 | 67 | 221 | 22 | 54 | 63 | 33.21 |

7 | 50 | 175 | 126 | 62 | 55 | 33.67 |

8 | 106 | 32 | 98 | 132 | 58 | 27.33 |

9 | 76 | 88 | 75 | 107 | 85 | 26.92 |

The above table demonstrates the changes in patient throughput from slight modifications to the ideal capacities for each day of the week. It is important to notice the changes in the deviation from minimum value, which represents the variation of the number of patients over and under capacity from week to week.

In conjunction with this table, to help visualize the deviation in day to day over and under counts, we constructed scatter plots for each trial of the day to day fluctuations in this measure.

The plots for all trials are referenced within the results section of the appendix of this paper. Please reference this section to help visualize the day to day fluctuations in patient over and under counts for each of the associated trials. Additionally, each scatter plot is fitted with a linear line of best fit and a r-squared value that demonstrates how well the linear regression explains the movement in the day to day over and under capacities.