“Family Pharmacy”, a local drug store is trying to improve its service during the 12:00 – 2:00 lunch period. Right now the pharmacy employs 5 different single-channel queues, but management is contemplating changing over the layout to an M/M/5 (multichannel) one. In addition, management is deciding whether to change the number (currently 5) of employees at the counter as well as the number of employees preparing the prescriptions in the back. The employees cost the company $9.75/hr. (in wages and other costs). The customers’ waiting time is costly as well. This is hard to estimate and accordingly, the pharmacy uses two figures: an upper bound of $50 and a lower bound of $30 for each hour of customer wait time (before service).

During lunch, the store has an average arrival rate of 120 customers per hour. Their studies show that the average transaction currently takes 2 minutes 18 seconds (note the servers are roughly identical in speed, also, assume that each “customer” is a single person). Management already knows how the current set-up has been performing; what they want to investigate are different proposed layouts (so answer all questions with this planning in mind).

A. The first option that management wishes to explore is the M/M/5 (multichannel) one. For this system, find out

 How long do customers have to wait before service

· how much time they spend in the system

· the (average) hourly cost of the system (using both waiting cost estimates),

· What proportion of the time the system is busy?

B. The next option to consider is simply reducing the number of personnel at the counter to 4. Explain the consequences of this reduction.

C. Next, management wishes to consider moving one person from the back area to the counter. Now they would have 6 registers open but the preparation of the prescription would be slower. In this scenario, management estimates that the average time to serve customers would be 2 minutes 41 seconds.

- Investigate the same (bulleted) performance measures as in part (a.) and compare this option to that one.

D. Now, management wishes to consider systems in which the number of prescription preparers is the same (as in (a.) but the counter staff is increased.

- Find the number of counter staff that is most economical, and note the same performance measures of this set-up as above

Answer rating: 100% (QA)

A MM5 System In an MM5 system we have an arrival rate of 120 customers per hour and the number of servers is m 5 The average transaction time per customer is 2 minutes 18 seconds which can be converte... View the full answer