Exam 10: Introduction to Simulation Modeling

Which of the following statements is true regarding the Triangular distribution?

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

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: Estimate of Sales in Region 1 9,000 0.05 10,000 0.10 11,000 0.15 12,000 0.35 13,000 0.25 14,000 0.10 Estimate of Sales in Region 2 Smallest Value: 5000 units Most Likely Value: 7000 units Largest Value: 12000 units Estimate of Sales in Region 3 Minimum Value: $\quad 6000$ units Maximum Value: $\quad 9000$ units -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?

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.

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 . $\approx \sqrt { 202 + 502 + 302 } = 61.6$

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.

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."

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

Which of the following is not one of the important distinctions of probability distributions?

Discrete distributions are sometimes used in place of continuous distributions:

The primary difference between simulation models and other types of spreadsheet models is that simulation models contain ____:

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."

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?

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:

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: Estimate of Sales in Region 1 9,000 0.05 10,000 0.10 11,000 0.15 12,000 0.35 13,000 0.25 14,000 0.10 Estimate of Sales in Region 2 Smallest Value: 5000 units Most Likely Value: 7000 units Largest Value: 12000 units Estimate of Sales in Region 3 Minimum Value: $\quad 6000$ units Maximum Value: $\quad 9000$ units -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?

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.

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: Estimate of Sales in Region 1 9,000 0.05 10,000 0.10 11,000 0.15 12,000 0.35 13,000 0.25 14,000 0.10 Estimate of Sales in Region 2 Smallest Value: 5000 units Most Likely Value: 7000 units Largest Value: 12000 units Estimate of Sales in Region 3 Minimum Value: $\quad 6000$ units Maximum Value: $\quad 9000$ units -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?

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: Estimate of Sales in Region 1 9,000 0.05 10,000 0.10 11,000 0.15 12,000 0.35 13,000 0.25 14,000 0.10 Estimate of Sales in Region 2 Smallest Value: 5000 units Most Likely Value: 7000 units Largest Value: 12000 units Estimate of Sales in Region 3 Minimum Value: $\quad 6000$ units Maximum Value: $\quad 9000$ units -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?

A distribution for modeling the time it takes to serve a customer at a bank is probably:

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