Data604 Homework 9

Problem 6 page 245

Problem Description:
A small free clinic has a single doctor who see patients between 8:00 AM 12:00 noon.
The doctor spend 6 to 14 minutes (average 10 minutes) to see the patient. So in theory, seeing 6 patients/hour with total of 24 patients a day.
Staff is currently scheduling patients every 10 minutes but found out that patients can arrive up to 15 minutes early and up to 30 minutes late. In addition 10% of patients do not show up for the scheduled appointment.

Staff would like to evuate a different scheduling scheme to maximize doctor time; scheduling 2-3 arrivals every 20 minutes

The doctor will stay until all the scheduled patients have been seen for a day but is very unhappy if has to stay beyond 12:30 PM.

First we will model the current system and then we will make the schedule change and see the impact on the doctor’s utilization and number of patients for the day.

Model Considerations
Doctor(Server):
The server in this system (doctor) has single capacity and we wil model the service time as a triangular distribution (4,10,14).
Since the doctor see patients until done, we will not model the end of day in the schedule but we cannot assume that the doctor will be there prior to 8:00 AM or ready to see patient prior to 8:00 AM (in some patients may show up early)

We will assume that the clinic is open Monday - Friday.

We will model a work schedule M-F with hours 8:00 AM - 2:00 PM to allow for patients at clinic to be process, with capacity 1 for each day/time. We are also assuming that the doctor is not stopping for a lunch break as well.

Patients (source):
Arrival time will be model using an Arrival time table, with appointment schedule every 10 minutes from 8:00 AM to 12:00PM.
We will model this with arrival table, using real number to be an offset from 8:00 AM every 10 minutes (in hours fraction).
We will also specify a disruption on random uniform distribution with minimu = -0.25 (patients show up 15 minutes early) and maximum = 0.5 (patients show up 30 minutes late)
We will also specify the no show probability to be 0.10.

Arrival Time Specification

The model:

Model as is

We will now look at the results: we can see that doctor is utilized about 83% of time with minimum 56% and maximum 98%. The doctor processed about 21 patients per day.

Results

We will now change the model by changing the arrivaltime table, we will schedule the appointment every 20 minutes and set a capacity alternate between 2 and 3 patients for each.

Arrival Time Specifications new model

The model:

Model as is

We will now look at the results: We are now achieving 26 patients a day. The doctor’s utilization is also higher. The doctor’s day is slightly longer.

Results