A fast-food franchise is considering offering a drive-through service. Arriving customers will place orders at an intercom station at the back of the parking lot and then drive up to the service window to pay for and receive their order. Customer arrivals are expected to have an average arrival rate of 24 cars per hour, with customer inter-arrival times having a standard deviation of 2.5 minutes. Four different service alternatives are being considered, and the goal of the exercise is to assist the franchisee with choosing among them. We will focus on service quality (not cost).
a. [One window – one employee] The first mode of operation involves one employee who both fills the order and takes payment from the customer. The average service time for this alternative is 2 minutes with a standard deviation of 2 minutes. What will be the average waiting time for consumers under this mode of operation? What will be the average length of the queue? [Hint: To get the length of the queue, apply Little’s law to the queue. What is the flow rate of the queue? What is the flow time of the queue (the average time a customer spends there)?]
b. [One window – two employees] The second mode of operation involves two employees who work as a team (not in parallel) to serve each customer. One fills the order and one handles the payment. The average service time for this alternative is 1.25 minutes, with a standard deviation of 1.25 minutes. What will be the average waiting time for consumers under this mode of operation? What will be the average length of the queue?
c. [Two windows – two employees – one queue] The fourth mode of operation involves two service windows and two employees. Newly arriving customers join a queue which feeds both service windows. The employee stationed at each window fills the order and takes payment for customers arriving at that window (this time the two employees work in parallel). The average service time for this alternative is 2 minutes, with a standard deviation of 2 minutes. What will be the average waiting time for consumers under this mode of operation? What will be the average length of the queue?
d. [Two windows – two employees – two queues] The third mode of operation involves two service windows and two employees. There is a separate queue for each of the service windows. Newly arriving customers randomly choose one of two queues (that is, the two windows equally split the incoming demand). The employee stationed at each window fills the order and receives payment for customers arriving at that window. The average service time for this alternative is 2 minutes with a standard deviation of 2 minutes. What will be the average waiting time for consumers under this mode of operation? What will be the average length of each of the queues?
e. How do you evaluate the four alternatives? [Hint: When discussing the pros and cons of each, keep in mind that there is a psychological effect to facing a long queue]