Chapter 10 - Introduction to Simulation Modeling
1. The primary difference between simulation models and other types of spreadsheet models is that simulation models
contain ____:
a. deterministic inputs
b. random numbers
c. output cells
d. constraints
ANSWER:
b
POINTS:
1
DIFFICULTY:
Easy |Bloom's Comprehension
QUESTION TYPE: Multiple Choice
HAS VARIABLES: False
TOPICS:
10.1 Introduction
OTHER:
BUSPROG - Communication |DISC - Intro Simulation
DATE CREATED: 5/17/2017 3:51 PM
DATE MODIFIED: 10/21/2017 9:43 PM
2. Which of the following is not one of the important distinctions of probability distributions?
a. Discrete versus continuous
b. Symmetric versus skewed
c. Bounded versus unbounded
d. Positive versus negative
ANSWER:
d
POINTS:
1
DIFFICULTY:
Moderate |Bloom's Comprehension
QUESTION TYPE: Multiple Choice
HAS VARIABLES: False
TOPICS:
10.2 Probability Distributions for Input Variables - Types of Probability Distributions
OTHER:
BUSPROG - Communication |DISC - Intro Simulation
DATE CREATED: 5/17/2017 3:51 PM
DATE MODIFIED: 10/21/2017 9:43 PM
3. Discrete distributions are sometimes used in place of continuous distributions:
a. because they are more accurate
b. because they are simpler
c. when we don't know the mean and variance of the distribution
d. when we need to generate a histogram
ANSWER:
b
POINTS:
1
DIFFICULTY:
Easy |Bloom's Comprehension
QUESTION TYPE: Multiple Choice
HAS VARIABLES: False
TOPICS:
10.2 Probability Distributions for Input Variables - Types of Probability Distributions
OTHER:
BUSPROG - Communication |DISC - Intro Simulation
DATE CREATED: 5/17/2017 3:51 PM
Copyright Cengage Learning. Powered by Cognero.
Page 1
Chapter 10 - Introduction to Simulation Modeling
DATE MODIFIED: 10/21/2017 9:43 PM
4. The RAND() function in excel models which of the following probability distributions?
a. Normal distribution with mean 0 and standard deviation 1
b. Uniform distribution with lower limit 0 and upper limit 1
c. Normal distribution with mean -1 and standard deviation 1
d. Uniform distribution with lower limit -1 and upper limit 1
ANSWER:
b
POINTS:
1
DIFFICULTY:
Easy |Bloom's Comprehension
QUESTION TYPE: Multiple Choice
HAS VARIABLES: False
TOPICS:
10.2 Probability Distributions for Input Variables - Common Probability Distributions
OTHER:
BUSPROG - Communication |DISC - Intro Simulation
DATE CREATED: 5/17/2017 3:51 PM
DATE MODIFIED: 10/21/2017 9:43 PM
5. If x is a random number between 0 and 1, then we can use x to simulate a variable that is uniformly distributed between
100 and 200 using the formula:
a. 100 + x
b. 200 − x
c. 100 + 100x
d. 200x
ANSWER:
c
POINTS:
1
DIFFICULTY:
Moderate |Bloom's Application
QUESTION TYPE: Multiple Choice
HAS VARIABLES: False
TOPICS:
10.2 Probability Distributions for Input Variables - Common Probability Distributions
OTHER:
BUSPROG - Analytic |DISC - Intro Simulation
DATE CREATED: 5/17/2017 3:51 PM
DATE MODIFIED: 10/21/2017 9:43 PM
6. A distribution for modeling the time it takes to serve a customer at a bank is probably:
a. symmetric
b. left skewed
c. right skewed
d. uniform
ANSWER:
c
POINTS:
1
DIFFICULTY:
Moderate |Bloom's Comprehension
QUESTION TYPE: Multiple Choice
HAS VARIABLES: False
TOPICS:
10.2 Probability Distributions for Input Variables - Types of Probability Distributions
Copyright Cengage Learning. Powered by Cognero.
Page 2
Chapter 10 - Introduction to Simulation Modeling
OTHER:
BUSPROG - Analytic |DISC - Intro Simulation
DATE CREATED: 5/17/2017 3:51 PM
DATE MODIFIED: 10/21/2017 9:43 PM
7. Which of the following statements is true regarding the Normal distribution?
a. It is always the appropriate distribution in simulation modeling
b. It does not permit negative values
c. There is a 95% chance that values will be within ± 2 standard deviations of the mean
d. All of these options
ANSWER:
c
POINTS:
1
DIFFICULTY:
Moderate |Bloom's Comprehension
QUESTION TYPE: Multiple Choice
HAS VARIABLES: False
TOPICS:
10.2 Probability Distributions for Input Variables - Using @RISK to Explore Probability
Distributions
OTHER:
BUSPROG - Analytic |DISC - Intro Simulation
DATE CREATED: 5/17/2017 3:51 PM
DATE MODIFIED: 10/21/2017 9:43 PM
8. Which of the following statements is true regarding the Triangular distribution?
a. It is a discrete distribution with a minimum, maximum and most likely value
b. It is more flexible and intuitive than the normal distribution
c. It is a symmetric distribution
d. All of these options
ANSWER:
b
POINTS:
1
DIFFICULTY:
Moderate |Bloom's Comprehension
QUESTION TYPE: Multiple Choice
HAS VARIABLES: False
TOPICS:
10.2 Probability Distributions for Input Variables - Using @RISK to Explore Probability
Distributions
OTHER:
BUSPROG - Analytic |DISC - Intro Simulation
DATE CREATED: 5/17/2017 3:51 PM
DATE MODIFIED: 10/21/2017 9:43 PM
9. When n is reasonably large and p isn't too close to 0 or 1, the binomial distribution can be well approximated by which
of the following distributions?
a. Uniform distribution
b. Normal distribution
c. Triangular distribution
d. None of these options
ANSWER:
b
POINTS:
1
Copyright Cengage Learning. Powered by Cognero.
Page 3
Chapter 10 - Introduction to Simulation Modeling
DIFFICULTY:
QUESTION TYPE:
HAS VARIABLES:
TOPICS:
Challenging |Bloom's Comprehension
Multiple Choice
False
10.2 Probability Distributions for Input Variables - Using @RISK to Explore Probability
Distributions
OTHER:
BUSPROG - Analytic |DISC - Intro Simulation
DATE CREATED: 5/17/2017 3:51 PM
DATE MODIFIED: 10/21/2017 9:43 PM
10. If a model contains uncertain outputs, it can be very misleading to build a deterministic model by using the means of
the inputs to predict an output. This is called the:
a. Law of Large Numbers.
b. Flaw of Averages
c. Law of Inevitable Disappointment
d. Central Limit Theorem
ANSWER:
b
POINTS:
1
DIFFICULTY:
Easy |Bloom's Comprehension
QUESTION TYPE: Multiple Choice
HAS VARIABLES: False
TOPICS:
10.3 Simulation and the Flaw of Averages
OTHER:
BUSPROG - Analytic |DISC - Intro Simulation
DATE CREATED: 5/17/2017 3:51 PM
DATE MODIFIED: 10/21/2017 9:43 PM
11. One of the primary advantages of simulation models that they enable managers to answer what-if questions about
changes in systems without actually changing the systems themselves.
a. True
b. False
ANSWER:
True
POINTS:
1
DIFFICULTY:
Easy |Bloom's Comprehension
QUESTION TYPE: True / False
HAS VARIABLES: False
TOPICS:
10.1 Introduction
OTHER:
BUSPROG - Communication |DISC - Intro Simulation
DATE CREATED: 5/17/2017 3:51 PM
DATE MODIFIED: 10/21/2017 9:43 PM
12. Excel's standard functions, along with the RAND function, can be used to generate random numbers from many
different types of probability distributions.
a. True
b. False
ANSWER:
True
POINTS:
1
Copyright Cengage Learning. Powered by Cognero.
Page 4
Chapter 10 - Introduction to Simulation Modeling
DIFFICULTY:
QUESTION TYPE:
HAS VARIABLES:
TOPICS:
OTHER:
DATE CREATED:
DATE MODIFIED:
Easy |Bloom's Comprehension
True / False
False
10.2 Probability Distributions for Input Variables - Common Probability Distributions
BUSPROG - Communication |DISC - Intro Simulation
5/17/2017 3:51 PM
10/21/2017 9:43 PM
13. The three parameters required to specify a triangular distribution are the minimum, mean and maximum.
a. True
b. False
ANSWER:
False
POINTS:
1
DIFFICULTY:
Moderate |Bloom's Comprehension
QUESTION TYPE: True / False
HAS VARIABLES: False
TOPICS:
10.2 Probability Distributions for Input Variables - Using @RISK to Explore Probability
Distributions
OTHER:
BUSPROG - Communication |DISC - Intro Simulation
DATE CREATED: 5/17/2017 3:51 PM
DATE MODIFIED: 10/21/2017 9:43 PM
14. A common guideline for constructing a 95% confidence interval is to place upper and lower bounds one standard error
on either side of the mean.
a. True
b. False
ANSWER:
False
POINTS:
1
DIFFICULTY:
Moderate |Bloom's Application
QUESTION TYPE: True / False
HAS VARIABLES: False
TOPICS:
10.4 Simulation with Built-in Excel Tools - Notes about Confidence Intervals
OTHER:
BUSPROG - Analytic |DISC - Intro Simulation
DATE CREATED: 5/17/2017 3:51 PM
DATE MODIFIED: 10/21/2017 9:43 PM
15. RISKSIMTABLE is an @RISK function for running several simulations simultaneously, one for each setting of an
input or decision variable.
a. True
b. False
ANSWER:
True
POINTS:
1
DIFFICULTY:
Easy |Bloom's Comprehension
QUESTION TYPE: True / False
Copyright Cengage Learning. Powered by Cognero.
Page 5
Chapter 10 - Introduction to Simulation Modeling
HAS VARIABLES:
TOPICS:
OTHER:
DATE CREATED:
DATE MODIFIED:
False
10.5 Introduction to @RISK
BUSPROG - Analytic |DISC - Intro Simulation
5/17/2017 3:51 PM
10/21/2017 9:43 PM
16. When the value of a decision variable has been optimized by running several simulations, attitude toward risk should
no longer be relevant.
a. True
b. False
ANSWER:
False
POINTS:
1
DIFFICULTY:
Moderate |Bloom's Comprehension
QUESTION TYPE: True / False
HAS VARIABLES: False
TOPICS:
10.5 Introduction to @RISK - Using Risksimtable
OTHER:
BUSPROG - Analytic |DISC - Intro Simulation
DATE CREATED: 5/17/2017 3:51 PM
DATE MODIFIED: 10/21/2017 9:43 PM
17. It is usually fairly straightforward to predict the shape of the output distribution from the shape(s) of the input
distribution(s).
a. True
b. False
ANSWER:
False
POINTS:
1
DIFFICULTY:
Moderate |Bloom's Comprehension
QUESTION TYPE: True / False
HAS VARIABLES: False
TOPICS:
10.6 The Effects of the Input Distribution on Results
OTHER:
BUSPROG - Analytic |DISC - Intro Simulation
DATE CREATED: 5/17/2017 3:51 PM
DATE MODIFIED: 10/21/2017 9:43 PM
18. A correlation matrix must always have 1's along its diagonal (because a variable is always perfectly correlated with
itself) and numbers between −1 and +1 elsewhere.
a. True
b. False
ANSWER:
True
POINTS:
1
DIFFICULTY:
Easy |Bloom's Comprehension
QUESTION TYPE: True / False
HAS VARIABLES: False
TOPICS:
10.6 The Effects of the Input Distribution on Results - Effect of Correlated Input Variables
Copyright Cengage Learning. Powered by Cognero.
Page 6
Chapter 10 - Introduction to Simulation Modeling
OTHER:
BUSPROG - Analytic |DISC - Intro Simulation
DATE CREATED: 5/17/2017 3:51 PM
DATE MODIFIED: 10/21/2017 9:43 PM
19. A correlation matrix must always be symmetric, so that the correlations above the diagonal are a mirror image of those
below it.
a. True
b. False
ANSWER:
True
POINTS:
1
DIFFICULTY:
Easy |Bloom's Comprehension
QUESTION TYPE: True / False
HAS VARIABLES: False
TOPICS:
10.6 The Effects of the Input Distribution on Results - Effect of Correlated Input Variables
OTHER:
BUSPROG - Analytic |DISC - Intro Simulation
DATE CREATED: 5/17/2017 3:51 PM
DATE MODIFIED: 10/21/2017 9:43 PM
20. Correlation between two random input variables may change the mean of an output, but it will not affect the
variability and shape of an output distribution.
a. True
b. False
ANSWER:
False
POINTS:
1
DIFFICULTY:
Challenging |Bloom's Analysis
QUESTION TYPE: True / False
HAS VARIABLES: False
TOPICS:
10.6 The Effects of the Input Distribution on Results - Effect of Correlated Input Variables
OTHER:
BUSPROG - Analytic |DISC - Intro Simulation
DATE CREATED: 5/17/2017 3:51 PM
DATE MODIFIED: 10/21/2017 9:43 PM
Exhibit 10-1
A company is in the planning phase of constructing a new production facility. It wants to build a simulation model for the
economics of the facility, and one key uncertain input is the construction cost. For each of the scenarios in the questions
below, choose an "appropriate" distribution, together with its parameters, and explain your choice.
21. Refer to Exhibit 10-1. Company management currently has no idea what the distribution of the construction cost is.
All they can state is that "we think it will be somewhere between $5,000,000 and $8,000,000."
ANSWER:
The "no idea" suggests the uniform distribution, with a lower bound of $5M and an upper bound of
$8M.
POINTS:
1
DIFFICULTY:
Moderate |Bloom's Analysis
QUESTION TYPE: Subjective Short Answer
HAS VARIABLES: False
Copyright Cengage Learning. Powered by Cognero.
Page 7
Chapter 10 - Introduction to Simulation Modeling
PREFACE NAME:
TOPICS:
OTHER:
DATE CREATED:
DATE MODIFIED:
Exhibit 10-1
10.2 Probability Distributions for Input Variables - Common Probability Distributions
BUSPROG - Analytic |DISC - Intro Simulation
5/17/2017 3:51 PM
10/21/2017 9:43 PM
22. Refer to Exhibit 10-1. A little later on, management still believes the upper and lower bounds for the costs are $5M
and $8M, but now they can also state that "we believe the most likely value is about $6.5M."
ANSWER:
This suggests a triangular distribution, with a min of $5M, most likely value of $6.5M, and max of
$8M.
POINTS:
1
DIFFICULTY:
Moderate |Bloom's Analysis
QUESTION TYPE: Subjective Short Answer
HAS VARIABLES: False
PREFACE NAME: Exhibit 10-1
TOPICS:
10.2 Probability Distributions for Input Variables - Common Probability Distributions
OTHER:
BUSPROG - Analytic |DISC - Intro Simulation
DATE CREATED: 5/17/2017 3:51 PM
DATE MODIFIED: 10/21/2017 9:43 PM
23. Refer to Exhibit 10-1. Management believes the facility construction time will be somewhere from 5 to 9 months.
They believe the probabilities of the extremes (5 and 9 months) are both 10%, and the probabilities will vary linearly from
those endpoints to a most likely value at 7 months.
ANSWER:
This is a general discrete distribution. We just have to choose the probabilities of the values 5 to 9 so
that they increase and then decrease linearly, and add up to 1: P(5)=0.1, P(6)=0.225, P(7)=0.35,
P(8)=0.225, P(9)=0.1.
POINTS:
1
DIFFICULTY:
Moderate |Bloom's Analysis
QUESTION TYPE: Subjective Short Answer
HAS VARIABLES: False
PREFACE NAME: Exhibit 10-1
TOPICS:
10.2 Probability Distributions for Input Variables - Common Probability Distributions
OTHER:
BUSPROG - Analytic |DISC - Intro Simulation
DATE CREATED: 5/17/2017 3:51 PM
DATE MODIFIED: 10/21/2017 9:43 PM
24. Refer to Exhibit 10-1. Engineering also believes the construction time will be from 5 to 9 months. However, they
believe that 7 months is twice as likely as either 6 months or 8 months and that either of these latter possibilities is three
times as likely as either 5 months or 9 months.
ANSWER:
This is another general discrete distribution, where we have to choose the probabilities so that they
have the specified ratios, and add up to 1: P(5)=0.071, P(6)=0.214, P(7)=0.429, P(8)=0.214,
P(9)=0.071.
POINTS:
1
DIFFICULTY:
Moderate |Bloom's Analysis
QUESTION TYPE: Subjective Short Answer
HAS VARIABLES: False
Copyright Cengage Learning. Powered by Cognero.
Page 8
Chapter 10 - Introduction to Simulation Modeling
PREFACE NAME:
TOPICS:
OTHER:
DATE CREATED:
DATE MODIFIED:
Exhibit 10-1
10.2 Probability Distributions for Input Variables - Common Probability Distributions
BUSPROG - Analytic |DISC - Intro Simulation
5/17/2017 3:51 PM
10/21/2017 9:43 PM
25. If you add n lognormally distributed random numbers, the mean of the distribution for the sum is the sum of the
individual means, and the variance of the distribution of the sum is the individual variances. This result is difficult to
prove mathematically, but it is easy to demonstrate with simulation. To do so, run a simulation where you add three
lognormally distributed random numbers, with means of 300, 700 and 100, and standard deviations of 20, 50, and 30,
respectively. Your single output variable should be the sum of these three numbers. Verify with @RISK that the
distribution of this output has a mean of 1,000 and standard deviation
.
ANSWER:
The output distribution from @RISK yields just about what is expected. This is based on 10,000
iterations.
POINTS:
1
DIFFICULTY:
Challenging |Bloom's Application
QUESTION TYPE Subjective Short Answer
:
HAS VARIABLES: False
TOPICS:
10.6 The Effects of the Input Distribution on Results
OTHER:
BUSPROG - Analytic |DISC - Intro Simulation
DATE CREATED: 5/17/2017 3:51 PM
DATE MODIFIE 10/21/2017 9:43 PM
D:
Exhibit 10-2
A large apparel company wants to determine the profitability of one of its most popular products, a particular type of
Copyright Cengage Learning. Powered by Cognero.
Page 9
Chapter 10 - Introduction to Simulation Modeling
jacket. Demand is uncertain, due to economic conditions, competition, weather and other factors, and the following
probability distributions have been estimated for each of the company's three regions:
Estimate of Sales in Region 1
Units
9,000
10,000
11,000
12,000
13,000
14,000
Probability
0.05
0.10
0.15
0.35
0.25
0.10
Estimate of Sales in Region 2
Smallest Value:
Most Likely Value:
Largest Value:
5000 units
7000 units
12000 units
Estimate of Sales in Region 3
Minimum Value:
Maximum Value:
6000 units
9000 units
26. Refer to Exhibit 10-2. Use @RISK distributions to generate the three random variables for regional sales and derive a
distribution for the total sales. What is the expected total sales?
ANSWER:
The above output histogram shows mean expected sales is approximately 27,405 units.
POINTS:
1
DIFFICULTY:
Challenging |Bloom's Application
QUESTION TYPE: Subjective Short Answer
HAS VARIABLES: False
PREFACE NAME: Exhibit 10-2
TOPICS:
10.6 The Effects of the Input Distribution on Results
Copyright Cengage Learning. Powered by Cognero.
Page 10
Chapter 10 - Introduction to Simulation Modeling
OTHER:
BUSPROG - Analytic |DISC - Intro Simulation
DATE CREATED: 5/17/2017 3:51 PM
DATE MODIFIED: 10/21/2017 9:43 PM
27. Refer to Exhibit 10-2. Total sales is a product of three different types of input distributions. What does the output
distribution look like? What is the standard deviation of the total sales? What are the 5th and 95th percentiles of this
distribution?
ANSWER:
Although the input distributions are different, the combination of the three looks symmetric and
fairly normal. The standard deviation is about 2,100 units, and the 5th and 95th percentiles are about
24,000 units and 31,000 units, respectively.
POINTS:
1
DIFFICULTY:
Moderate |Bloom's Analysis
QUESTION TYPE: Subjective Short Answer
HAS VARIABLES: False
PREFACE NAME: Exhibit 10-2
TOPICS:
10.6 The Effects of the Input Distribution on Results
OTHER:
BUSPROG - Analytic |DISC - Intro Simulation
DATE CREATED: 5/17/2017 3:51 PM
DATE MODIFIED: 10/21/2017 9:43 PM
28. Refer to Exhibit 10-2. Suppose the jacket sales price also varies, depending on the individual retailers and their pricing
strategies. Assume that sales price is normally distributed with a mean of $65 per unit and a standard deviation of $10.
How much revenue will the jacket line produce (ignore discounting)?
ANSWER:
Extending the total units sold by the unit price (and making that quantity a simulation output) yields
the following output graph. The mean revenue is ˜$1.8M.
POINTS:
DIFFICULTY:
1
Moderate |Bloom's Application
Copyright Cengage Learning. Powered by Cognero.
Page 11
Chapter 10 - Introduction to Simulation Modeling
QUESTION TYPE:
HAS VARIABLES:
PREFACE NAME:
TOPICS:
OTHER:
DATE CREATED:
DATE MODIFIED:
Subjective Short Answer
False
Exhibit 10-2
10.5 Introduction to @RISK - @RISK Models with Several Random Input Variables
BUSPROG - Analytic |DISC - Intro Simulation
5/17/2017 3:51 PM
10/21/2017 9:43 PM
29. Refer to Exhibit 10-2. Finally, suppose the apparel company receives an uncertain fraction of the total retail revenue
from its retailers, modeled as a Triangular(0.70,0.75,0.80) distribution, and then must subtract production and operations
costs, which are modeled as a Lognormal distribution with mean of $1,000,000 and standard deviation of $300,000. In
that case, what is the expected net profit from the jacket line?
ANSWER:
Applying the fractional multiplier and subtracting the costs from the revenues (and making that
quantity a simulation output) yields the following output graph. The mean net profit is just under
$370,000.
POINTS:
DIFFICULTY:
QUESTION TYPE:
HAS VARIABLES:
PREFACE NAME:
TOPICS:
OTHER:
DATE CREATED:
DATE MODIFIED:
1
Challenging |Bloom's Application
Subjective Short Answer
False
Exhibit 10-2
10.5 Introduction to @RISK - @RISK Models with Several Random Input Variables
BUSPROG - Analytic |DISC - Intro Simulation
5/17/2017 3:51 PM
10/21/2017 9:43 PM
30. Refer to Exhibit 10-2. What is the probability that the apparel company will exceed a profit at least $0.5M from the
jacket line?
ANSWER:
From the histogram, there is approximately a 38% chance of exceeding $0.5M profit.
Copyright Cengage Learning. Powered by Cognero.
Page 12
Chapter 10 - Introduction to Simulation Modeling
POINTS:
DIFFICULTY:
QUESTION TYPE:
HAS VARIABLES:
PREFACE NAME:
TOPICS:
OTHER:
DATE CREATED:
DATE MODIFIED:
1
Moderate |Bloom's Application
Subjective Short Answer
False
Exhibit 10-2
10.5 Introduction to @RISK - @RISK Models with Several Random Input Variables
BUSPROG - Analytic |DISC - Intro Simulation
5/17/2017 3:51 PM
10/21/2017 9:43 PM
Copyright Cengage Learning. Powered by Cognero.
Page 13