Consider a fast-food restaurant that is trying to improve its service during the 12:00 - 2:00 lunch period.  Right now the restaurant employs 5 different single-channel queues, but management is contemplating changing over the layout to a 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 food in the back.

The employees cost the company $9.25/hr. (in wages and other costs).  The customers' waiting time is costly as well.  This is hard to estimate but currently, the restaurant uses a figure of $45 for each hour of customer wait time (before service). 

During lunch the restaurant has an average arrival rate of 98 customers per hour.  Their studies show that the average transaction currently takes 2 minutes 40 seconds (note that 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 multichannel one.  For this system, find out

• how long customers have to wait before service
• the (average) hourly cost of the system, and
• what proportion of the time the entire line exceeds 8 persons.

(Note: write down all input values you have used for POM-QM as well for the entire problem!)

(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 food preparation would be slower.  In this scenario management estimates that the average time to serve a customer would be 3 minutes 8 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 food preparers is the same (as in (c.)) but the counter staff is increased.

• Find the number of counter staff that is most economical.

(e.) Finally, management is informed that some customers "balk" (show up at the restaurant but immediately exit) when the lines get too long.   "Too long" in this context is more than 10 persons.  Management wishes to hire enough counter personnel to reduce the proportion of time that lines exceed 10 persons to be no more than 5%.  As compared to your answer in (d.), how many extra people (if any) do you need to meet this additional requirement, and by how much (if at all) does the average hourly cost increase?