Catherine Blake, the office manager for the College of Business Administration, has received numerous complaints lately from several department chairpersons. In the past few months, the chairpersons have insisted that something be done about the amount of time their administrative assistants waste waiting in line to make copies. Currently, the college has two photocopy centers dedicated to small copying jobs: copy center A on the third floor and copy center B on the fourth floor. Both centers are self-serve and have identical processing capabilities. The copying machines are not visible to the administrative assistants from their offices. When copying is required, the administrative assistant goes to the copy room and waits in line to make the necessary copies. Catherine’s assistant, Brian, was assigned to investigate the problem. Brian reported that, on average, administrative assistants arrive at copy center A at the rate of 10 per hour and at copy center B at the rate of 14 per hour. Each of the copy centers can service 15 jobs per hour. The administrative assistants’ arrivals essentially follow a Poisson distribution, and the service times are approximated by a negative exponential distribution. Brian has proposed that the two copy centers be combined into a single copy center with either two or three identical copy machines. He estimates that the arrival rate would be 24 per hour. Each machine would still service 15 jobs per hour. Currently, administrative assistants earn an average of $15 per hour (a) Determine the utilization of each of the copy centers. (b) Determine the average waiting time at each of the copy centers. (c) What is the annual cost of the administrative assistants’ average waiting time using the current system?
Catherine Blake, the office manager for the College of Business Administration, has received numerous complaints lately
from several department chairpersons. In the past few months,
the chairpersons have insisted that something be done about the
amount of time their administrative assistants waste waiting in line
to make copies. Currently, the college has two photocopy centers
dedicated to small copying jobs: copy center A on the third floor
and copy center B on the fourth floor. Both centers are self-serve
and have identical processing capabilities. The copying machines
are not visible to the administrative assistants from their offices.
When copying is required, the administrative assistant goes to the
copy room and waits in line to make the necessary copies. Catherine’s assistant, Brian, was assigned to investigate the problem.
Brian reported that, on average, administrative assistants arrive
at copy center A at the rate of 10 per hour and at copy center B at the
rate of 14 per hour. Each of the copy centers can service 15 jobs per
hour. The administrative assistants’ arrivals essentially follow a Poisson distribution, and the service times are approximated by a negative exponential distribution. Brian has proposed that the two copy
centers be combined into a single copy center with either two or three
identical copy machines. He estimates that the arrival rate would be
24 per hour. Each machine would still service 15 jobs per hour. Currently, administrative assistants earn an average of $15 per hour
(a) Determine the utilization of each of the copy centers.
(b) Determine the average waiting time at each of the copy
centers.
(c) What is the annual cost of the administrative assistants’
average waiting time using the current system?
(d) Determine the utilization of the combined copy center
with two copiers.
(e) Determine the average waiting time at the combined
copy center.
(f) What would be the annual cost of the administrative
assistants’ average waiting time using the combined twocopier setup?
(g) What would be the utilization of the combined copy
center with three copiers?
(h) What would be the annual cost of the administrative
assistants’ average waiting time using the combined
three-copier setup?
(i) What would you recommend to Catherine?
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