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Capacity Management

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2. Flow rate or capacity of each resource. a. Receptionist: capacity = (1 patient / 3 min) (60 min/hr) = 20 patients / hr

b. Changing Rooms: Each patient requires 5 min in step 2 as well as 5 minutes in step 6 for a total of ten minutes. capacity = (1 patient / 10 min) (60 min/hr) (3 changing rooms) = 18 patients / hr

c. Nurse 1: capacity = (1 patient / 6min) (60 min / hr) = 10 patients / hr

d. Nurse 2: capacity = [1 patient / (3 + 1 min)] (60 min / hr) = 15 patients /hr

e. Nurse 3 / MRI Machine: capacity = (1 patient / 10 min) (60 min / hr) = 6 patients / hr

3. Bottleneck is Nurse 3/MRI Machine because that resource’s capacity is least. The process capacity is the bottleneck because the maximum number of patients this setup can handle is 6 patients per hour, no more.

4. The best case lead time for one patient without delays is 33 minutes, calculated by the time it takes without delays to go through all six steps- 3 min (step1) + 5 min (step2) + 6 min (step3) + 4 min (step 4) + 10 min (step 5) + 5 min (step 6) = 33 minutes.

5. If a patient could start at step 6 to begin the day, the bottleneck of 6 patients per hour should be multiplied by 12 hours to determine that 72 patients should be scheduled in a day. However, with a patient required to begin at step 1 at 8am, patient #1 does not reach step 5 (the bottleneck of 10 min) till 8:19am. Therefore, from 8:19 am to 7:49pm, Nurse 3 / MRI Machine can serve 69 patients, allowing for the last patient to finish in the changing room by 7:54pm. 69 patients should be scheduled in a 12 hour day.

6. Steady-state utilization of each resource.

a. Receptionist: Util of Resource = (6 patients / hr) / (20 patients / hr) = .3 or 30%

b. Changing Rooms: Util of Resource = (6 patients / hr) / (18 patients / hr) = .33… or 33.33%

c. Nurse 1: Util of Resource = (6 patients / hr) / (10 patients / hr) = .6 or 60%

d. Nurse 2: Util of Resource = (6 patients / hr) / (15 patients / hr) = .4 or 40%

e. Nurse 3 / MRI Machine: Util of Resource = (6 patients / hr) / (6 patients / hr) = 1 or 100%

7. At most, there will be 4 patients in the system at any one time, assuming they arrive at the rate of the bottleneck.

8. On average, there will be in the system at any one time, assuming they arrive at the rate of the bottleneck. Little’s Law tell us that the average # of patients in the system at any one time is the effective arrival rate, in this case 6 patients per hour times the average time the patients spends in the system in the system.

9. At most, 2 valve apparatuses are needed in the system.

10. At 69 patients per day, the process generates $345,000 per day. With another scan, the bottleneck now becomes nurse 1 at 10 patients per hour. The total number of new patients the hospital can serve increases by 46 or a price of $23,000 per hour I‘d willing to rent the machine for.

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