Problem:

The call center of an airline company operates for 24 hours a day, 7 days a week. Calls are received more or less evenly throughout the day at an average pace of 150 calls per hour. The standard deviation of the time between when two calls are received is 72 seconds. At any moment of the day or night, the call center is staffed with 25 operators who are cross-trained and can answer all incoming calls. Calls are answered in the order in which they are received. The average duration of a conversation between operator and a caller is 8 minutes, with a standard deviation of 8 minutes. Assume that there is no limit on the number of callers who can be placed on hold at the same time and that none of the callers hang up before talking to an operator.

Answer the following questions. Please show all your work and present your answers as clearly as possible.

(a) What is the average number of callers who are on hold at any given moment in time?

(b) What is the average number of operators who are not answering calls at any given moment in time?

(c) What is the minimum number of operators which are required to avoid having the number of customers waiting on hold increase steadily over time?

(d) Instead of answering calls in the order they were received, the airline call center decides to implement the following rule: when deciding which call to answer next, they give priority to callers with the highest status in their loyalty (air miles) program (e.g., Platinum status). Among callers with the same status, priority is given to the one who has been waiting the longest. Is this new policy going to affect the average time that a random customer has to spend on hold? Explain why or why not. (Consider whether the customers with a higher status tend to spend the same amount of time as customers with a lower status on the phone with the operator)

(e) (Disregard (d)). Suppose that call center operators are paid $20 per hour. The direct cost of using a phone line (by having a customer wait on hold or talk to an operator) is 10 cents a minute. The call center manager is considering increasing the number of operators to 28 at any given moment in time. Is this a wise decision in terms of total costs?

(f) (Disregard (d) and (e)) What could the airline call center do in order to improve their customers’ waiting experience? Give two ideas that illustrate two different theories about the psychological aspects of waiting in lines. (Make sure you state the theory.)