Question: A fast food franchise is considering operating a drive up window food service operation. Assume that customer arrivals follow a poisson probability distribution, with an arrival rate of 24 cars per hours, and that service times follow an exponential probability distribution. Arriving customers place orders at an intercom station at the back o the parking lot and then drive to the service window to pay for and receive their orders. The following three service alternative are being considered.

 A single channel operation in which one employee fills the order and takes the money from the customer. The average service time for this alternative is 2 minutes

 a single channel operation in which one employee fills the order while a second employee takes the money from the customer,. The average service time for this alternative is 1.25 minutes

 A two channel operation with two service windows and two employees, The employee stationed at each window fills the order and takes the money for customers arriving at the window. The average service time for this alternative is 2 minutes or each channel.

Answer the following questions and recommend an alternative design for the fast food franchise.

1. What is the probability that no cars are in the system?
2. What is the average number of cars waiting for service?
3. What is the average number of cars in the systems?
4. What is the average time a car waits for service?
5. What is the average time in the system?
6. What is the probability than an arriving car will have to wait for service?

The following cost information is available for the fast food franchise above.

 Customer waiting time is valued at $25 per hour to reflect the fact that waiting time is costly to the fast food business.

 The cost of each employee is $6.50 an hour

 To account for equipment an space, an additional cost of $20 per hour is attributable to each channel.

What is the lowest cost design for the fast food business?

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