Operations Management: Processes and Supply Chains, 12e (Krajewski)
Supplement B Waiting Lines
1) The four elements common to all waiting-line situations are a customer population, a waiting line of
customers, the service facility, and a priority rule.
2) The calling population in a queuing problem must go to the server, that is servers do not go to the
calling population.
3) A phase represents a single step in providing a service.
4) A bank that dedicates one window for commercial account customers and one window for personal
account channel has two channels.
5) If the customer population of a service system generates customers according to a Poisson distribution,
the exponential distribution describes the probability that the next customer will arrive in the next T time
periods.
6) The mean of the Poisson distribution is equal to its standard deviation.
7) Under the assumptions of waiting line models, it is impossible for management to affect the rate of
customer arrivals.
8) The best example of a finite customer population is the:
A) car-buying public of an automotive manufacturer.
B) constituents in a precinct lining up to vote.
C) e-mail messages arriving at a major ISP mail server.
D) members of the Management department at your university waiting to speak to the Dean about their
department chairman.
9) Which statement about queue structure is best?
A) Customers are more likely to feel a sense of fairness when waiting in the multiple line system than in a
single line system.
B) When similarly skilled, multiple servers are available, a single line is best.
C) Customers that are in the same line must be colocated.
D) Machines needing repair are left in place and repair techs come to them; thus, the repair techs are
technically the customers since they must travel to the machine.
10) The distinction between an infinite customer population and a finite customer population is whether
the:
A) potential number of customers is appreciably affected by the number of customers already in the
system.
B) number of potential customers exceeds the square of the number of servers.
C) number of potential customers exceeds the number of servers raised to the power of the number of
channels.
D) number of customers exceeds infinity.
11) Ed Deadbeat races to the Bursar’s Office on the first day of class and notes that the line is four
students long. Ed figures that the wait will be at least ten minutes and, having better uses of his time, he
decides to proceed to the next item on his to-do list. Ed’s behavior is best described as:
A) reneging.
B) balking.
C) blocking.
D) queuing.
12) India Sisson wants to grab a latte before heading to her marketing class, knowing that the jolt of a
double tall mocha is the only thing that can possibly keep her eyes open during today’s presentation on
the four P’s. The server is slower than molasses in January and India notes that the pace of the line won’t
permit her to grab her favorite seat in the back row of her class. She decides to risk marketing without a
latte and leaves the line before getting served. India’s behavior is best described as:
A) balking.
B) blocking.
C) reneging.
D) queuing.
13) The single, multiple, and finite waiting line models all assume that the:
A) arrival rate exceeds the service rate.
B) number of servers exceeds the number of customers.
C) number of customers exceeds the number of servers.
D) customers are patient.
14) An automatic, one-lane, drive-through car wash is an example of a:
A) single-channel, single-phase arrangement.
B) single-channel, multiple-phase arrangement.
C) multiple-channel, single-phase arrangement.
D) multiple-channel, multiple-phase arrangement.
15) A drive-through system with one lane at a fast food restaurant where the first facility takes the order,
the second takes the money, and the third provides the food is an example of a:
A) single-channel, single-phase arrangement.
B) single-channel, multiple-phase arrangement.
C) multiple-channel, single-phase arrangement.
D) multiple-channel, multiple-phase arrangement.
16) A bank lobby with six teller windows, each with a separate line, is an example of a:
A) single-channel, single-phase arrangement.
B) single-channel, multiple-phase arrangement.
C) multiple-channel, single-phase arrangement.
D) multiple-channel, multiple-phase arrangement.
17) A Laundromat where there are washing machines and dryers is an example of a:
A) single-channel, single-phase arrangement.
B) single-channel, multiple-phase arrangement.
C) multiple-channel, single-phase arrangement.
D) multiple-channel, multiple-phase arrangement.
18) A super computer-accessory discount store often has customers who leave the checkout line before
being served because of excessive waiting times. The store has a(n):
A) infinite customer population with balking customers.
B) infinite customer population with reneging customers.
C) finite customer population with balking customers.
D) finite customer population with reneging customers.
19) A homemade-ice cream shop owner has noticed that, often, potential customers will stop outside the
store, assess the wait in line, and then pass by. The shop has a(n):
A) infinite customer population with balking customers.
B) infinite customer population with reneging customers.
C) finite customer population with balking customers.
D) finite customer population with reneging customers.
20) The owner of a desktop publishing company exclusively caters to seven loyal clients who periodically
require his services. The owner has:
A) an infinite customer population of patient customers.
B) an infinite population of impatient customers.
C) a finite customer population.
D) a finite customer population with balking customers.
21) Twelve customers arrive at the lunch counter at George’s Happy Hog per hour and select the hickory
smoked meat du jour along with a side and soda for $5. The server doubles as the cashier and can take
and fill an order in three minutes on average. What is the likelihood that there are zero customers in the
system at the George’s Happy Hog if the times can be assumed as exponentially distributed?
A) 0.40
B) 0.25
C) 0.19
D) 0.81
22) Twelve customers arrive at the lunch counter at George’s Happy Hog per hour and select the hickory
smoked meat du jour along with a side and soda for $5. The server doubles as the cashier and can take
and fill an order in three minutes on average. What is the likelihood that there is one customer in the
system at the George’s Happy Hog if the times can be assumed as exponentially distributed?
A) 0.24
B) 0.19
C) 0.81
D) 0.75
23) Twelve customers arrive at the lunch counter at George’s Happy Hog per hour and select the hickory
smoked meat du jour along with a side and soda for $5. The server doubles as the cashier and can take
and fill an order in three minutes on average. What is the likelihood that there are two customers in the
system at the George’s Happy Hog if the times can be assumed as exponentially distributed?
A) .33
B) .25
C) .144
D) .05
24) Twelve customers arrive at the lunch counter at George’s Happy Hog per hour and select the hickory
smoked meat du jour along with a side and soda for $5. The server doubles as the cashier and can take
and fill an order in three minutes on average. What is the lowest number n such that the likelihood of n or
more customers in line and receiving service is 0? Assume that the arrival and service times can be
assumed as exponentially distributed.
A) one
B) two
C) three
D) four
25) Customers arrive according to a Poisson distribution. The average number of customer arrivals per
hour is four. The probability that three customers will arrive in the next two hours is:
A) less than or equal to 0.015.
B) greater than 0.015 but less than or equal to 0.020.
C) greater than 0.020 but less than or equal to 0.025.
D) greater than 0.025.
26) Customers arrive according to a Poisson distribution. The average number of customer arrivals per
hour is six. The probability that four customers will arrive in the next three hours is:
A) less than or equal to 0.01.
B) greater than 0.01 but less than or equal to 0.02.
C) greater than 0.02 but less than or equal to 0.03.
D) greater than 0.03.
27) Customers are serviced at a rate of four customers per hour according to an exponential distribution.
What is the probability that customer service will require fewer than 30 minutes?
A) less than or equal to 0.50
B) greater than 0.50 but less than or equal to 0.60
C) greater than 0.60 but less than or equal to 0.70
D) greater than 0.70
28) Customers are serviced at a rate of six customers per hour according to an exponential distribution.
What is the probability that customer service will require fewer than 20 minutes?
A) less than or equal to 0.70
B) greater than 0.70 but less than or equal to 0.80
C) greater than 0.80 but less than or equal to 0.90
D) greater than 0.90
29) Customers are serviced at a rate of five customers per hour according to an exponential distribution.
What is the probability that customer service will require fewer than 20 minutes?
A) less than or equal to 0.75
B) greater than 0.75 but less than or equal to 0.80
C) greater than 0.80 but less than or equal to 0.85
D) greater than 0.85
30) A ________ is a single step in the service process.
31) A ________ is one or more facilities required to perform a given service.
32) Customers arrive and wait in one line single file as their documents are checked. Then they load their
carry-on items on the conveyor belt for inspection. Finally, they walk through a metal detector before
retrieving their carry-on items and proceeding to their departure gate. This facility is ________ channel,
________ phase.
33) A(n) ________ selects the next customer to be served at the service facility.
34) You drive your car into the parking lot of your favorite fast food establishment and get in the line for
drive through service. After placing your order into the speaker, you proceed to the first window to pay,
and then to the second window to pick up your meal. Since you just studied waiting lines that day in
your Operations Management class, you quickly realize as you drive away that this was an example of a
________ channel ________ phase queuing system.
35) A(n) ________ is a single step in providing a service.
36) A(n) ________ is a rule that allows a customer of higher priority to interrupt the service of another
customer.
37) The ________ distribution specifies the probability that n customers will arrive in T time periods.
38) The exponential distribution is based on the assumption that each service time is ________ of those
that preceded it.
39) Explain how waiting lines can develop even when the service time is a constant.
40) What are the assumptions of the exponential distribution applied to the single server queuing
situation? Provide examples of when these assumptions might be violated.
41) Comment on the tension between cost management and customer satisfaction management in a call
center situation.
Answer: Cost control in a call center situation is typically achieved by setting staffing levels and use of an
42) What are priority rules? Provide examples and indicate why a manager would choose to adopt one
over another.
Answer: A priority rule determines which customer to serve next. Most service systems that do not use
appointments use a first-come, first-served (FCFS) rule. The customer who arrives first and is at the head
43) Your employer is considering a choice between a single-line and a multiple-line arrangement. The
operation involves multiple servers and a single-phase service. When would each arrangement be ideal?
44) What is a finite-source model? Give an example of its appropriate use.
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B.2 Using Waiting-Line Models to Analyze Operations
1) The number of customers in line and being served also relates to service efficiency and capacity.
2) The best method for analyzing a waiting-line problem is to relate the five operating characteristics and
their alternatives to dollars.
3) The standard assumption in the single-server model is that there is an infinite number of customers
and that customers will wait in line as long as it takes to get served.
4) The standard assumption in the single-server model is that customers are served according to the
earliest due date, i.e., which customer needs to be finished first.
5) Customers are serviced at a rate of 10 customers per hour according to an exponential distribution.
What is the probability that customer service will require fewer than two minutes?
A) less than or equal to 0.25
B) greater than 0.25 but less than or equal to 0.30
C) greater than 0.30 but less than or equal to 0.35
D) greater than 0.35
6) With a single-server model, increasing the service rate while holding all other factors constant will:
A) increase the utilization of the server.
B) increase the time spent per customer.
C) decrease the probability that there are two customers in the system at any time.
D) decrease the arrival rate of customers.
7) With a single-server model, increasing the promotions for a service through advertising will most
likely:
A) increase the utilization of the server.
B) decrease the average number of customers in the service system.
C) decrease the average time a customer spends in the system.
D) increase the probability that the server will be idle.
8) With a single-server model, increasing the capital-to–labor ratio will most likely:
A) increase the utilization of the server.
B) have no effect on the operating characteristics because they are affected only by work-methods
changes.
C) decrease the probability that there are zero customers in the system at any time.
D) decrease the average number of customers in the waiting line.
9) With a single-server model, increasing the arrival rate by 10 percent and also increasing the service rate
by 10 percent will result in a(n):
A) increase in the utilization of the server.
B) increase in the average number of customers in the system.
C) decrease in the average time spent in the system, including service.
D) increase in the waiting-line time.
10) With a single-server model, increasing the arrival rate by 10 percent and also increasing the service
rate by 10 percent will result in:
A) a decrease in the utilization of the server.
B) no change in the average number of customers in the service system.
C) an increase in the average number of customers in the waiting line.
D) an increase in the waiting time in line.
11) With a single-server model, increasing the arrival rate by 10 percent and also increasing the service
rate by 10 percent will result in:
A) no change in the probability that there are n customers in the system.
B) a decrease in the average waiting time in line.
C) an increase in the average time spent in the system, including service.
D) an increase in the average number of customers in the system.
12) In the single-server model, the:
A) customers are assumed to arrive at constant intervals of time.
B) variability of customer arrivals is most often described by a Poisson distribution.
C) mean of the distribution of customer arrivals must be greater than the variance of customer arrivals to
get meaningful results.
D) probability of n arrivals in T time periods comes from a normal distribution.
13) In the single-server model, the:
A) service time of a customer is most often described by an exponential distribution.
B) service time depends on the number of customers in the system as long as there is at least one
customer in the waiting line.
C) mean of the service-time distribution must be as great as the target service time for a feasible solution.
D) service times are always constant to avoid large waiting lines.
14) With a multiple-server model, increasing the arrival rate by 10 percent and also increasing the service
rate of each server by 10 percent will result in:
A) a decrease in the utilization of the system.
B) no change in the average number of customers in the waiting line.
C) a decrease in the average number of customers in the waiting line.
D) an increase in the waiting time in line.
15) With a finite-source model, increasing the arrival rate by 10 percent and also increasing the service
rate by 10 percent will result in a(n):
A) increase in the utilization of the server.
B) increase in the average number of customers in the service system.
C) decrease in the average time spent in the system, including service.
D) increase in the waiting time in line.
16) With a finite-source model, increasing the arrival rate by 10 percent and also increasing the service
rate by 10 percent will result in:
A) a decrease in the utilization of the server.
B) no change in the average number of customers in the system.
C) an increase in the average number of customers in the waiting line.
D) an increase in the waiting time in line.
Scenario B.1
A single volunteer octogenarian usher can scan tickets with a handheld device and direct theater patrons
to their seats at a rate of 30 per hour with an accuracy rate approaching 23%. On average, about twenty–
five customers arrive every hour for assistance and always wait, regardless of how long the line gets.
Arrivals are governed by the Poisson distribution and service is governed by the exponential distribution.
17) When not directing patrons to their seats, the octogenarian usher in Scenario B.1 sneaks in a little
knitting. If she can knit one stitch every two seconds, how many stitches can she knit in an average hour
of seating patrons?
A) 200
B) 300
C) 400
D) 500
18) How many theater patrons are waiting for their favorite octogenarian usher in Scenario B.1?
A) two
B) three
C) four
D) five
19) What is the likelihood that two patrons are in the system?
A) .12
B) .17
C) .83
D) .50
20) The curtain goes up at 8 pm for the play “The Life and Times of A.K. Erlang.” If the parameters in
Scenario B.1 are at work, what’s the latest a patron of the theater would want to arrive in order to be
seated before the light dims, the curtain rises, and the actor playing A.K. Erlang takes his rightful place at
center stage?
A) 7:58 pm
B) 7:54 pm
C) 7:50 pm
D) 7:48 pm
21) How many theater patrons from Scenario B.1 are either waiting in line to be seated or being seated by
the volunteer octogenarian usher?
A) four
B) five
C) six
D) seven
22) How busy is the octogenarian usher described in Scenario B.1?
A) 74% busy
B) 83% busy
C) 91% busy
D) 100% busy