The manager of the call center of a large airline company needs to determine the optimal number of operators that she should hire. The call center serves two types of clients: Business (B) and Leisure (L) customers. She has determined that B calls arrive according to a Poisson process at a rate of 10 calls per hour. On the other hand, L calls arrive according to a Poisson process at a rate of 40 calls per hour.
Two types of operators are available on the market: High skill (H) and Average skill (A), which differ with respect to their ability and speed. H operators can serve both type of customers and the average amount of time that they need is 12 minutes per call independent of the type. On the other hand, A operators can serve only L calls and they need on average 20 minutes per call. Assume that all service times are exponentially distributed.
The cost of hiring an H operator is $30 per hour while the cost of hiring an A operator is $20 per hour. The manager has also estimated that the cost of keeping a B customer waiting is $100 per customer per hour while the cost of keeping an L customer waiting is $20 per customer per hour.
The manager is considering two possible configurations:
Configuration 1: Single queue Have a single queue for both type of calls and hire only H operators that will serve both types of calls. Calls will be served on a First-Come-First-Serve basis independent of their type.
Configuration 2: Two separate queues Have two separate queues for each type of calls. For the B calls queue she will naturally hire only H operators. For the L calls queue she can either hire H operators or A operators. However, she does not want to mix H and A operators. So she has to decide which one of the two types of operators to use.
a) (8 points) If the manager chooses configuration 1, which is the optimal number of H operators that she should hire?
b) (8 points) If she goes for configuration 2, which type of operators should she use for the L calls queue?
c) (9 points) Which one of the two alternatives do you recommend? What are the optimal staffing levels in this case?
