Deck 10: Introduction to Simulation Modeling

Question 1

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.

Answer 1

True

Question 2

Excel's standard functions, along with the RAND function, can be used to generate random numbers from many different types of probability distributions.

Answer 2

True

Question 3

The RAND() function in excel models which of the following probability distributions?

A)Normal(0,1)
B)Uniform(0,1)
C)Normal(−1,1)
D)Uniform(−1,1).

Answer 3

B

Question 4

A correlation matrix must always be symmetric, so that the correlations above the diagonal are a mirror image of those below it.

Question 5

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.

Question 6

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.

Question 7

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

Question 8

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

Question 9

Discrete distributions are sometimes used in place of continuous distributions:

A)because they are more accurate
B)because they are more simple
C)when we don't know the mean and variance of the distribution
D)when we need to generate a histogram

Question 10

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

Question 11

It is usually fairly straightforward to predict the shape of the output distribution from the shape(s) of the input distribution(s).

Question 12

When the value of a decision variable has been optimized by running several simulations, attitude toward risk should no longer be relevant.

Question 13

RISKSIMTABLE is an @RISK function for running several simulations simultaneously, one for each setting of an input or decision variable.

Question 14

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

Question 15

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

Question 16

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

Question 17

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.

Question 18

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

Question 19

The three parameters required to specify a triangular distribution are the minimum, mean and maximum.

Question 20

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

Question 21

Exhibit 10-2A large apparel company wants to determine the profitability of one of its most popular products, a particular type of 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:

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?

Question 22

Exhibit 10-2A large apparel company wants to determine the profitability of one of its most popular products, a particular type of 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:

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?

Question 23

Exhibit 10-1A 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.
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."

Question 24

Exhibit 10-2A large apparel company wants to determine the profitability of one of its most popular products, a particular type of 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:

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?

Question 25

Exhibit 10-1A 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.
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.

Question 26

Exhibit 10-1A 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.
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 .

Question 27

Exhibit 10-1A 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.
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."

Question 28

Exhibit 10-1A 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.
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.

Question 29

Exhibit 10-2A large apparel company wants to determine the profitability of one of its most popular products, a particular type of 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:

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?

Question 30

Exhibit 10-2A large apparel company wants to determine the profitability of one of its most popular products, a particular type of 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:

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)?