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Scenario B.2
Weary travelers arrive at Will Rogers International Airport, pick up their luggage, stumble to their cars,
and proceed to the parking lot attendant to pay for their parking. Traveler interarrival times are
exponentially distributed, as are the service times of the attendant. On average, travelers arrive every 25
seconds. The attendant can process three travelers per minute, and processing rates follow a Poisson
distribution.
23) Use the information in Scenario B.2. How many minutes per hour is the attendant not serving
customers?
A) fewer than or equal to 13
B) greater than 13 but fewer than or equal to 17
C) greater than 17 but fewer than or equal to 21
D) greater than 21
24) Use the information in Scenario B.2. What is the probability that a traveler will pull up to the
attendant's service window without having to wait for another customer?
A) less than or equal to 0.15
B) greater than 0.15 but less than or equal to 0.25
C) greater than 0.25 but less than or equal to 0.35
D) greater than 0.35
25) Use the information in Scenario B.2. What is the average number of customers in line?
A) fewer than or equal to 1.0
B) greater than 1.0 but fewer than or equal to 2.0
C) greater than 2.0 but fewer than or equal to 3.0
D) greater than 3.0
26) Use the information in Scenario B.2. What is the average number of customers in the system?
A) fewer than or equal to 3.0
B) greater than 3.0 but fewer than or equal to 5.0
C) greater than 5.0 but fewer than or equal to 7.0
D) greater than 7.0
27) Use the information in Scenario B.2. What is the average time a customer spends in line?
A) less than or equal to 1.0 minute
B) greater than 1.0 but fewer than or equal to 2.0 minutes
C) greater than 2.0 but fewer than or equal to 3.0 minutes
D) greater than 3.0 minutes
28) Use the information in Scenario B.2. What is the average amount of time a customer spends waiting in
line and being served?
A) less than or equal to 1.0 minutes
B) greater than 1.0 minutes but fewer than or equal to 1.50 minutes
C) greater than 1.5 minutes but fewer than or equal to 2.0 minutes
D) greater than 2.0 minutes
Scenario B.4
Customers arrive at an airline ticket counter at the rate of 50 customers per hour, according to a Poisson
distribution. There are three ticket agents. Customers select the first available agent from one line. Each
agent can process 20 customers per hour with exponential service times.
29) Use the information in Scenario B.4. What is the average utilization of the three-agent system?
A) less than or equal to 80 percent
B) greater than 80 percent but less than or equal to 85 percent
C) greater than 85 percent but less than or equal to 90 percent
D) greater than 90 percent
30) Use the information in Scenario B.4. What is the average number of customers waiting in line for
service?
A) fewer than or equal to 4.0
B) greater than 4.0 but fewer than or equal to 4.5
C) greater than 4.5 but fewer than or equal to 5.0
D) greater than 5.0
31) Use the information in Scenario B.4. What is the average waiting time in line?
A) fewer than or equal to 3.5 minutes
B) greater than 3.5 minutes but fewer than or equal to 4.5 minutes
C) greater than 4.5 minutes but fewer than or equal to 5.5 minutes
D) greater than 5.5 minutes
32) Use the information in Scenario B.4. What is the average time spent in the system?
A) fewer than or equal to 6.5 minutes
B) greater than 6.5 minutes but fewer than or equal to 7.5 minutes
C) greater than 7.5 minutes but fewer than or equal to 8.5 minutes
D) greater than 8.5 minutes
Scenario B.6
The Jackson Machine Company has four cutting tools that need to be refurbished after an average of 30
hours, according to an exponential distribution. The single machine that refurbishes the tools needs 15
hours for each tool on the average, with exponential service times.
33) Use the information in Scenario B.6. What is the probability that there will be no tools in the system?
A) less than or equal to 0.16
B) greater than 0.16 but less than or equal to 0.19
C) greater than 0.19 but less than or equal to 0.22
D) greater than 0.22
34) Use the information in Scenario B.6. What is the average utilization of the refurbishing machine?
A) less than or equal to 40 percent
B) greater than 40 percent but less than or equal to 50 percent
C) greater than 50 percent but less than or equal to 60 percent
D) greater than 60 percent
35) Use the information in Scenario B.6. What is the average waiting time of tools in line?
A) fewer than or equal to 15 hours
B) greater than 15 hours but fewer than or equal to 25 hours
C) greater than 25 hours but fewer than or equal to 35 hours
D) greater than 35 hours
36) The average lead time of a unit of product through a manufacturing station is 10 minutes. The
production rate has been steady at five units per hour. The average work-in-process inventory at this
station is:
A) 50 units.
B) 10 units.
C) 5 units.
D) 0.83 units.
37) The production rate has been steady at 20 units per hour. The average work-in-process inventory at
this station is 15 units. What is the average lead time through this manufacturing station?
A) 15 minutes
B) 30 minutes
C) 45 minutes
D) 1.0 hours
38) The average lead time of a unit of product through a manufacturing station is 18 minutes. The
average work-in-process inventory at this station has been 30 pieces. What is the production rate?
A) 0.33 piece per minute
B) 0.83 piece per minute
C) 1.66 pieces per minute
D) 3.0 pieces per minute
39) Customers arrive at the local grocery store at a steady rate of 40 an hour. Thirty percent of these
customers purchase 10 items or less and go to the express line where they enjoy an average checkout time
of 5 minutes. Customers that don't meet the express line criterion go to the other checkout line where
they spend an average of 10 minutes checking out. How many people are checking out in the express line
on average?
A) 1.0
B) 3.0
C) 12
D) 144
40) Customers arrive at the local grocery store at a steady rate of 40 an hour. Thirty percent of these
customers purchase 10 items or less and go to the express line where they enjoy an average checkout time
of 5 minutes. Customers that don't meet the express line criterion go to checkout line #2 where they spend
an average of 10 minutes checking out. How many people are checking out in line #2 on average?
A) less than or equal to 1.0
B) greater than 1.0 but less than or equal to 3.0
C) greater than 3.0 but less than or equal to 5.0
D) greater than 5.0
41) Customers arrive at the local grocery store at a steady rate of 40 an hour. Thirty percent of these
customers purchase 10 items or less and go to the express line where they enjoy an average checkout time
of 5 minutes. Customers that don't meet the express line criterion go to checkout line #2 where they spend
an average of 10 minutes checking out. How many people are checking out in both lines on average?
A) less than or equal to 1.0
B) greater than 1.0 but less than or equal to 3.0
C) greater than 3.0 but less than or equal to 5.0
D) greater than 5.0
42) A movie complex experiences its peak ticket sales in the early evening when several movies have
about the same start times. The ticket booth can process customers buying tickets at a maximum rate of 45
seconds each (or 80 tickets sold per hour). You arrive to buy your ticket and count 16 people in line ahead
of you. How long can you expect to wait in line before getting to the booth to buy your ticket?
A) less than or equal to 5 minutes
B) greater than 5 but less than or equal to 10 minutes
C) greater than 10 but less than or equal to 15 minutes
D) greater than 15 minutes
43) A drive thru car wash can process cars at a rate of one every five minutes. When you arrive with your
car, you see one car just leaving the washer and eight cars in line ahead of you. How long can you expect
to wait before you will reach the car wash?
A) less than or equal to 15 minutes
B) greater than 15 but less than or equal to 30 minutes
C) greater than 30 but less than or equal to 45 minutes
D) greater than 45 minutes
44) A drive thru car wash can process cars at a rate of one every five minutes. The manager notices that
during one particular day it takes cars an average of about 30 minutes in line to reach the car wash. What
was the average number of cars in line on that day?
A) 1 to 3 cars
B) 4 to 6 cars
C) 7 to 9 cars
D) 10 or more cars
45) The manager of a car wash wants to know how fast his new crew is processing cars through the wash
area. He notices that it takes cars an average of about 30 minutes in line to reach the car wash, and his
spot checks during the day indicated an average of seven cars in line waiting to be washed. What was the
processing rate for his new crew that day?
A) less than or equal to 2.0 minutes per car
B) greater than 2.0 but less than or equal to 3.0 minutes per car
C) greater than 3.0 but less than or equal to 4.0 minutes per car
D) greater than 4.0 minutes per car
46) Students arrive at a university business library during peak evening hours at a rate of 40 students
every half hour. Each student stays an average of two hours. On average, how many students are in the
library at any one time?
A) greater than 120 students
B) greater than 80 but less than or equal to 120 students
C) greater than 40 but less than or equal to 80 students
D) less than or equal to 40 students
47) Students arrive at a university business library during peak evening hours at a rate of 40 students
every half hour. A periodic count shows that there are 200 students in the library at any one time. On
average, how long is each student's stay in the library?
A) less than or equal to one hour
B) greater than 1.0 but less than or equal to 2.0 hours
C) greater than 2.0 but less than or equal to 3.0 hours
D) greater than 3.0 hours
48) ________ is a fundamental law that relates the number of customers in a waiting-line system to the
waiting time of customers.
49) Customer waiting times for a call center are extremely long. Two possible explanations for this
phenomenon are low ________ or low ________.
50) What is Little's Law? How might it be applied to determine the average length of time it takes an
MBA student to complete the program?
28
51) Customers in a small retail store arrive at the single cashier at the rate of 10 per hour. The average
service time for the cashier is five minutes. Arrivals tend to follow a Poisson distribution, and service
times follow an exponential distribution.
a. What is the average utilization of the cashier?
b. What is the average number of customers in the system?
c. What is the average number of customers in line?
d. What is the average time spent in the system?
e. What is the average time spent in line?
Answer:
29
52) A professor sits in his office and answers questions from his students the afternoon before the final
exam. His class is a mass lecture of 350 students, so he concentrates on providing explanations as quickly
as possible. On average, he can answer 60 questions an hour and students arrive at his office every five
minutes. Student arrivals are Poisson distributed, each student has only one question and answer times
are exponentially distributed.
a. What fraction of his time does the professor spend answering questions?
b. What is the average number of students waiting outside his office?
c. What is the average time a student spends in line outside the professor's office?
Answer:
a.
30
53) A harvesting firm has six combines, each requiring service at an average rate of once every 40 hours,
according to an exponential distribution. The firm has a mechanic who needs four hours to complete the
average repair with exponential service times.
a. What is the average utilization of the mechanic?
b. What is the average number of combines in the system?
c. What is the average number of combines in line?
d. What is the average time spent being repaired and waiting?
e. What is the average time spent in line waiting for repair?
Answer:
31
54) A professor's teaching assistants sit in their communal office and answer questions from students the
afternoon before the final exam. The class is a mass lecture of 350 students, and the teaching assistants
have final exams of their own, so they concentrate on providing explanations as quickly as possible. On
average, the three teaching assistants can answer 30 questions an hour and students arrive at their office
every five minutes. Student arrivals are Poisson distributed, each student has only one question and
answer times are exponentially distributed.
a. What fraction of their time do the teaching assistants spend answering questions?
b. What is the average number of students waiting outside their office?
c. What is the average time a student spends in line outside the teaching assistants' office and having their
question answered?
Answer:
32
55) The delivery wagon that the hominy man had used for the last three decades was beyond repair, so
he decided to open a hominy stand at a busy intersection in downtown Luther. Customers arrive at the
rate of 8 per hour and it takes 5 minutes on average to fill their buckets with hominy.
a. What is the likelihood that the line is longer than three people?
b. What is the average waiting time in line?
c. What is the average number of customers in line?
Answer:
a. The likelihood the line is longer than three people is the complement that the line contains three or
fewer customers:
B.3 Waiting Lines and Simulation
1) Customer arrival rates vary throughout the day and the priority rules change depending on the
customer mix and influence each has over the finances of the firm. Such a situation is best analyzed using
simulation rather than one of the queuing formulas.
2) SimQuick is a process simulation software tool that can provide statistics on cycle time for simple
processes such as waiting lines, inventory control, and projects.
3) If you were using SimQuick to determine how opening an additional airport security inspection station
would affect passenger wait times, each inspection station would be modeled in SimQuick with a:
A) workstation.
B) buffer.
C) decision point.
D) entrance.
4) If you were using SimQuick to determine how opening an additional airport security inspection station
would affect passenger wait times, a ________ would be used to model each of the waiting lines.
A) workstation
B) buffer
C) decision point
D) entrance
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Copyright © 2019 Pearson Education, Inc.
B.4 Decision Areas for Management
1) In a waiting-line problem, increasing advertising expenditures, increasing the number of promotions,
or changing the price of a service is most likely to affect:
A) customer arrival rates.
B) service rates.
C) the priority rule.
D) the line arrangement.
2) In a waiting-line problem, assigning additional employees to a service facility will have a direct effect
on:
A) the line arrangement.
B) service rates.
C) the size of the customer population.
D) the number of service phases.
3) An operations manager decides that customers should be processed based on the anticipated duration
of their request instead of their arrival time. The system has been changed in what fashion?
A) number of phases
B) server efficiency
C) priority rule
D) line arrangement
4) An operations manager organizes a process improvement team and the resulting process has a lower
mean (µ). Which statement is the best description of this change?
A) Arrival rate has fallen.
B) There are fewer phases in the new system.
C) Interarrival time has fallen.
D) Server efficiency has declined.
5) Instead of having one worker perform all eight steps to process a customer, an operations manager
assigns each step to a different worker. In doing so, the operations manager has increased the:
A) number of phases.
B) number of channels.
C) arrival rate.
D) interarrival rate.
6) If the nature of the customer population, constraints on the line, the priority rule, and the service time
distribution renders waiting line theory no longer useful, then an operations manager should rely on:
A) decision tree analysis.
B) linear programming.
C) simulation.
D) Little's Law.
36
7) A customer support call center grades their employees on how quickly they resolve customer problems
(average call time) and how many times the customer request escalates to the point that a supervisor
must be summoned to resolve the dispute. What might an employee do to perform well on these metrics
without actually providing good customer service? What could management do to prevent such
behaviors?
8) Create a table that lists any three performance measures for a service system in the left column. In the
center column, indicate what steps management can take to improve system performance on those
metrics. In the rightmost column indicate what steps management can take to improve customers'
perceptions of performance on those metrics.
Answer: Answers will vary. The text indicates that management might be concerned about the length of
the queue, the total number of customers in the system, the waiting time in line, the total time in the
