SOLVED PROBLEMS
824
Chapter Eighteen
Management of Waiting Lines
KEY POINTS
1.
Waiting line occur because there is an imbalance between supply and demand in service systems.
2.
One cause of imbalances is variability in service times and/or customer arrival times.
3.
Two important approaches to managing waiting lines are reducing variability where possible by
standardizing a process and/or altering the perceived waiting time.
channel, 797
finite-source situation, 797
infinite-source situation, 796
multiple-priority model, 812
queue discipline, 800
queuing theory, 794
KEY TERMS
Use this approach for infinite-source problems:
1. Note the number of servers. If there is only one server,
M
1. Use the basic relationship
formulas
in
Figure 18.7 and the single-server formulas in
Table 18.1. If service is constant, use Formula 18–9
for
L
q
. For
M
> 1, use the basic relationship formulas in
Figure 18.7, the multiple-server values in
Table 18.4 for
L
q
and
P
0
, and Formulas 18–12 and 18–13.
2. Determine the customer arrival rate and the service rate. If the arrival or service
time
is given
instead of a rate, convert the time to a rate. For example, a service time of 10 minutes would con-
vert to a service rate,
, of
[1/(10 minutes/customer)] (60 minutes/hour)
6 customers/hour
3. If multiple priorities are involved, use the Excel template on the Web site (preferred approach) or
the formulas in
Table 18.5.
Problem 1
Infinite source.
One of the features of a new machine shop will be a well-stocked tool crib. The
manager of the shop must decide on the number of attendants needed to staff the crib. Attendants
will receive $9 per hour in salary and fringe benefits. Mechanics’ time will be worth $30 per hour,
which includes salary and fringe benefits plus lost work time caused by waiting for parts. Based on
previous experience, the manager estimates requests for parts will average 18 per hour with a ser-
vice capacity of 20 requests per hour per attendant. How many attendants should be on duty if the
manager is willing to assume that arrival and service rates will be Poisson-distributed? (Assume the
number of mechanics is very large, so an infinite-source model is appropriate.)
Solution
The
basic relationship formulas
can be used with an infinite source model. There are formulas for
system utilization, the average number or average time waiting for service, the average number being
served, and the average number or time in the system. Refer to
Figure 18.7 on p. 802 to help you connect
with the appropriate formula. The formulas are on p. 802.
Single-channel model:
Use when there is
one
server, team, or crew. See p. 803.
Single-channel, constant service time.
See p. 804.
Multiple-channel model.
Use when there are
two or more
independent servers, teams, or crews.
See p. 805
Multiple-priority model.
Use when service order is based on priority class. See p. 813.

#### You've reached the end of your free preview.

Want to read all 8 pages?

- Fall '16
- average number, average waiting time, Jeris J. White