Case $5-2$: Health Maintenance Organization $($B$)$

The administrator of the Life$-$Time Insurance Company HMO, Ms$.$ Taylor, was anxious to solve potential problems before the new clinic opened in Austin, Texas. In Buffalo, New York, where the original clinic is located, the pharmacy had been extremely busy from the beginning, and long waiting times for prescriptions to be filled presented a very real problem.

The Buffalo HMO pharmacy was modern, spacious, and well designed. The peak time for prescriptions was between $10$ AM and $3$ PM$.$ During this period, prescriptions would back up$,$ and the waiting time would increase. After $5$ PM$,$ the staff would be reduced to one pharmacist and one technician, butthe two had no trouble providing very timely service throughout the evening.

Ms$.$ Taylor became acutely aware of the long waiting times after several complaints had been lodged. Each stated that the waiting time had exceeded $1$ hour. The pharmacy is staffed with five persons on duty until $5$ PM$.$

Ms$.$ Taylor personally studied the tasks of all the pharmacy personnel. She noted the time required to accomplish each task, and her results are listed below. The prescriptions were filled in an assembly$-$line fashion by two technicians and three pharmacists, and each person performed only one task.

Activity Time in Seconds

Receive prescriptions $24$

Type labels $120$

Fill prescriptions $60$

Check prescriptions $40$

Dispense prescriptions $30$

Note: The activities of filling, checking, and dispensing prescriptions must be performed by a registered pharmacist.

Questions

a$)$ Draw the diagram of the current service line. Identify the bottleneck activity. What is the cycle time and capacity of the current process?

b$)$ Show how capacity can be increased by using only two pharmacists and two technicians. Draw the diagram of the revised line layout. What are the cycle time and capacity of the revised process?

c$)$ In addition to savings in personnel costs, what benefits does this arrangement have?