# (solution) A company has one clerk answering the telephone and taking

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A company has one clerk answering the telephone and taking special orders from customers. The
company operates this system 12 hours each day. If the clerk is occupied on one line, incoming phone
calls get a recording and the caller is asked to wait and is placed on hold. As soon as the clerk is free, the
party that has waited the longest is transferred and answered next. Calls come in at an average rate of
about 9 per hour (and this continues throughout the day). The clerk is capable of handling an order in
an average time of six minutes. Calls tend to arrive following a Poisson distribution and service times
tend to be exponentially distributed. The clerk is paid \$15 per hour, but because of lost goodwill and
sales, the company loses about \$50 per hour of customer time spent waiting for the clerk to become
available. (The arrivals are assumed to be patient).
The company wishes to evaluate four possible situations:
(1) the current situation with one employee.
(2) hiring one additional clerk who is paid the same as the original worker and works at the same
rate as the current one
(3) hiring two additional clerks who are paid the same as the original worker and who each work at
the same rate as the current one
(4) replacing the current clerk with a worker who handles the orders more quickly. This new worker
averages only 3 minutes per call, but the cost per hour for this person is \$25 per hour.
Management wants to find the total time spent on hold by all of the customers in a day, the total daily
waiting time cost, the total daily service cost, and the total daily cost of the queuing system for each of
these four configurations. Perform any calculations necessary and fill out the table. Using Excel may
help with some calculations, but these calculations can also be performed with a calculator. There are
some numbers already entered into the table to help with the more complex systems (Hint: Little?s
Equations). 1 clerk (current
rate)
Kendall notation for
queuing system # of service channels
P0
L
Lq
W
Wq
Cw
Cs
Total time on hold by
all customers in a day
Total daily waiting
time cost
Total daily service cost
Total daily cost of
queuing system 2 clerks 3 clerks 1 clerk (faster rate) 9
10 18
20 27
30 9
20 .1
9
8.1
1
.9 0.3793
1.1285 0.4035
0.9300 .5 or 1/2
.45 .333 or 1/3
.30 .091 or 1/11
.041