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In an outpatient clinic there are only one nurse and one doctor, and they visit patients by appointment. Yesterday, there were 5 patients scheduled to arrive, one every hour from 8am to noon. Each patient received an assessment visit (triage) of exactly 15 minutes from the nurse, and then a visit of 45 minutes from the doctor. As always, all patients showed on time, all service times were constant, and nurse and doctor worked at capacity when busy. As expected, nurse and doctor were able to close the clinic at 1pm. Please determine (i) total busy time, total idle time and utilization rate of the nurse, and (ii) the system utilization rate. Also, draw (iii) a cumulated inflow/outflow diagram and an inventory diagram of the doctor’s room. Then, (iv) apply the Little’s law to the doctors room over the five hours to find the doctor’s throughput. Today, the clinic has 6 patients to see and has scheduled them to arrive from 8am and every 48 minutes, such that the last patient’s appointment is still at noon. Nurse and doctor will still work at capacity when busy, but they will not be gone by 1pm. In fact, most patients will have to wait. Please draw (v) the Gantt chart and (vi) the inventory diagram of the system from 8am to when the clinic closes, and determine (vii) the total service and wait time of the last patient and (viii) the total busy and idle time of the doctor. Finally, using the Little’s law, (ix) determine the average patient flow time. Suppose now we can pay a lease of $50/day for an online prescription tool that shortens the doctor service time from 45 to 35 minutes, and suppose we value every minute waited by our patients $1 in loss of goodwill. Is the tool worth its cost? Please (x) motivate your answer and show your calculations.
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