Regional Airlines is establishing a new telephone system for
handling flight reservations. During the 10:00 AM to 2:00 PM time
period, calls to the reservation agent occur randomly at an average
rate of one call every 3.75 minutes. Historical service time data
show that a reservation agent spends an average of 3 minutes with
each customer. The waiting line model assumptions of Poisson
arrivals and exponential service times appear reasonable for the
telephone reservation system.
At a planning meeting, Regional’s management team agreed that an
acceptable customer service goal is to answer at least 75% of the
incoming calls immediately. During the planning meeting, Regional’s
vice president of administration pointed out that the data show
that the average service rate for an agent is faster than the
average arrival rate of the telephone calls. The vice president’s
conclusion was that personnel costs could be minimized by using one
agent and that single agent must be able to handle the telephone
reservations and still have some idle time. The vice president of
marketing restated the importance of customer service and expressed
support for at least two reservation agents.
We already analyzed the single-agent system’s performance according
to the opinion of vice president of administration. We concluded
that operating the telephone reservation service with only one
ticket agent appears unacceptable because they won’t be able to
meet their goal. Answer to the following questions to evaluate the
opinion of vice president of marketing:
7. What is the total cost if system operates for 8 hours? The cost
of a ticket reservation agent is $20 per hour. The cost of waiting
caller in the system is $500 per hour (because we may lose the
customer due to the waiting).
What is our expected profit if, every 8 hours, 20 customers on
average purchase ticket with average value of $350?