The doctor starts his practice at 8:00 AM and desires to leave his office for the hospital by 1:30 pm or 2:00pm at the latest. He also prefers to eat lunch before he leaves for the hospital. Also note that the doctor is experiencing a no-show rate of 10% in his practice. The data on patient arrival time and the doctor idle time is shown below

The first table below shows the patient arrival time distribution (i.e., the number of minutes earlier/later than the scheduled appointment). For example, in the table, 4 of the 100 patients arrived 10 minutes earlier than their appointment times, and 2 patients arrived 3 minutes late. For simplicity, it is assumed that this arrival distribution is identical throughout the day and for any appointment schedule. The table shows the distribution of arrival times of the 100 patients, with a range of 10 minutes early to 5 minutes late.

The second table shows his MD Service Time Distribution (i.e., the distribution of number of minutes the doctor spends examining each patient). For example, 16 percent of patients required 14 minutes of examining time.

Help the doctor decide which appointment schedule is best suited for his practice, both in terms of reducing patient waiting time as well as minimizing the doctor's idle time. Each group will examine the effects of scheduling appointments by a particular time interval. That is, the effect of scheduling patient appointments every 30 minutes.

Calculate the frequency distributions (probability) for patient arrival time and MD service time (based on the frequencies given in the Excel sheet). Note: the frequency distribution is the number of occurrences in each category divided by the total number (i.e., the probability of a 16 min. MD service time is .18).

Convert the frequency distributions to cumulative probability distributions for patient arrival time and MD service time (based on the frequency distribution calculated in Step 1). For example, the cumulative probability of a 16 min. MD service time is .80).

calculate the simulated patient arrival time (using col. 3) and simulated MD service time (using col. 5) for each of the 20 patients and display the totals for the last 4 columns. If a random occurs which is exactly equal to a cumulative percent, select the next lower value. (The simulated patient arrival time, MD service time, patient wait time, MD idle time is calculated for the first patient to get you started).

Assume that the doctor is ready to start seeing patients at 8:00 AM.

List the appointment times for your assigned appointment interval (i.e., 5-30 mins.) in column 2 in place of the 15 min. appt. interval shown.

Assume that there is NO lag time between the time the doctor finishes seeing one patient and begins examining the next patient. (e.g. if the doctor finishes seeing the first patient at 8:16 am, the next patient begins at 8:16am IF a patient is waiting for him).

Assume the arrival distribution is applicable for any appointment time interval throughout the day.

Calculate Patient Total time in Clinic (i.e., total time spent by the patient at the clinic since arrival till the doctor finishes examining him). For the first patient - the patient arrives at 7:52 AM and the doctor finishes with her at 8:16 AM. Thus, the patient spends a total of 24 minutes within the system.

Calculate Patient Wait time (i.e., number of minutes the patient waited since arriving at the clinic before being able to see the doctor). The first patient arrives at 7:52 AM but can see the doctor only at 8:00 AM, thus total patient wait time is 8 minutes.

Calculate Patient Wait Time Post-Appt (i.e., the number of minutes the patient waited to see the doctor after his/her appointment time has passed). For example, for the first patient it is ZERO since the doctor saw the patient at the scheduled time of 8:00am.

Calculate MD Idle time (i.e., the number of minutes the doctor waits for the patient - if any). If the second patient arrives at 8:20am, but the doctor was available to see the patient 8:16 AM, then 4 minutes of doctor idle time is experienced.

MD SERVICE TIME DISTRIBUTION

MINUTES	FREQUENCY
10	2
11	4
12	8
13	12
14	16
15	20
16	18
17	12
18	6
19	2
Total	100

PATIENT ARRIVAL TIME DISTRIBUTION

MINUTES EARLY	FREQUENCY
10	4
9	6
8	8
7	10
6	12
5	13
4	11
3	9
2	7
1	6
0	5
1	3
2	2
3	2
4	1
5	1
Total	10