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 25 cars per hour, and that service times follow an exponential probability distribution. Arriving customers place orders at an intercom station at the back of the parking lot and then drive to the service window to pay for and receive their orders. The following service alternative is being considered:

System C: A two-server 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 2.5 minutes for each server.

The following cost information is available.

Customer waiting time is valued at $26 per hour to reflect the fact that waiting time is costly to the fast-food business.

The cost of each employee is $5.5 per hour.

To account for equipment and space, an additional cost of $22 per hour is attributable to each server.

System C

$

Answer 1

System C: this is an M/M/s queue system with s = 2 servers and following parameters

Arrival rate = 25 cars per hour

Service rate = 60/2.5 = 24 cars per hour

Waiting cost, Cw = $ 26 per hour

Server cost, Cs = 22+5.5 = $ 27.5 per hour

System C cost per hour = $ 65.08  (this includes the server cost and waiting cost)