Question 1

What are the benefits of a Risk Solver Platform sensitivity chart?

Accepted Answer

The sensitivity chart feature allows the

Question 2

Use the information below to answer the following question(s). Below is a spreadsheet for Trance Electronics. \(\begin{array}{|c|l|c|c|c|c|c|}
\hline &\text { A } & \text { B } & \text { C } & \text { D } & \text { E } & \text { F } \
\hline 1&\text { Trance Electronics } & & & & & \\hline 2 & \
\hline 3 & \text { Data } \
\hline 4 & \\hline 5 & \text { Market size } & 20,000,000 \
\hline 6 & \text { Unit (monthly Rx) revenue } & \$ 120.00 \
\hline 7 & \text { Unit (monthly Rx) cost } & \$ 50.00 \
\hline 8 & \text { Discount rate } & 8 \% \
\hline 9 & & \\hline 10 & \text { Project costs } & \
\hline 11 & \text { R\&D } & \$ 750,000,000 \
\hline 12 & \text { Clinical Trials } & \$ 100,000,000 \
\hline 13 & \text { Total Project Costs } & \
\hline 14 & & \\hline 15 & \text { Model } & \
\hline 16 & & \
\hline 17 & \text { Year } & 1 &2&3&4&5\\hline 18&\text { Market growth factor } & & 4 \% & 4 \% & 4 \% & 4 \% \
\hline 19&\text { Market size } & & & & & \
\hline 20&\text { Market share growth rate } & & 18 \% & 18 \% & 18 \% & 18 \% \\hline 21 & \text { Market share } & 7 \% \
\hline 22 & \text { Sales } & \
\hline 23 & & \
\hline 24 & \text { Annual revenue } & \\hline 25 & \text { Annual costs } \
\hline 26 & \text { Profit } \
\hline 27 & \text { Cumulative net profit } \
\hline 28 & \
\hline 29 & \text { Net present value } \
\hline
\end{array}\) Suppose that the project manager of Trance Electronics has identified the following uncertain variables in the model and the distributions and parameters that describe them, as follows: Market size: normal with mean of 20,000,000 units and standard deviation of 4,000,000 units. R&D costs: uniform between $600,000,000 and $800,000,000.
Clinical trial costs: lognormal with mean of $150,000,000 and standard deviation $30,000,000. Annual market growth factor: triangular with minimum = 2%, maximum = 6%, and most likely = 3%.
Annual market share growth rate: triangular with minimum = 15%, maximum = 25%, and most likely = 20%.
The number of trials per simulation is equal to 10,000 at a Sim. Random Seed of 2. Run the simulation and answer the following questions using the Risk Solver Platform.
-What cumulative profit in the fifth year is likely to be realized with a probability of 0.50?

Accepted Answer

A)  $78,244,098 
B)  $101,970,955 
C)  $144,058,696 
D)  $203,676,827 
A)  $78,244,098 
B)  $101,970,955 
C)  $144,058,696 
D)  $203,676,827

Question 3

The Risk Solver Platform chart shows the minimum, first quartile, median, third quartile, and maximum values in a data set graphically.

Accepted Answer

A)  trend 
B)  sensitivity 
C)  overlay 
D)  box-whisker 
A)  trend 
B)  sensitivity 
C)  overlay 
D)  box-whisker

Question 4

Monte Carlo simulation is an inappropriate tool to analyze cash budgets because of the inherent uncertainty of the sales forecasts on which most cash budgets are based.

Accepted Answer

A) True 
 B)False

Question 5

Explain the process of running a simulation using Risk Solver Platform.

Accepted Answer

To run a simulation, first click on the

Question 6

Why is the ROUND function used in Excel?

Accepted Answer

A)  to ensure that the values generated are whole numbers 
B)  to ensure that the values generated are multiples of ten 
C)  to ensure that the values generated are always positive 
D)  to ensure that the values are even numbers 
A)  to ensure that the values generated are whole numbers 
B)  to ensure that the values generated are multiples of ten 
C)  to ensure that the values generated are always positive 
D)  to ensure that the values are even numbers

Question 7

Uniform or triangular distributions are used in the absence of data.

Accepted Answer

A) True 
 B)False

Question 8

What is Monte Carlo simulation?

Accepted Answer

Monte Carlo simulation is the process of

Question 9

Use the information below to answer the following question(s). Below is a spreadsheet for Trance Electronics. \(\begin{array}{|c|l|c|c|c|c|c|}
\hline &\text { A } & \text { B } & \text { C } & \text { D } & \text { E } & \text { F } \
\hline 1&\text { Trance Electronics } & & & & & \\hline 2 & \
\hline 3 & \text { Data } \
\hline 4 & \\hline 5 & \text { Market size } & 20,000,000 \
\hline 6 & \text { Unit (monthly Rx) revenue } & \$ 120.00 \
\hline 7 & \text { Unit (monthly Rx) cost } & \$ 50.00 \
\hline 8 & \text { Discount rate } & 8 \% \
\hline 9 & & \\hline 10 & \text { Project costs } & \
\hline 11 & \text { R\&D } & \$ 750,000,000 \
\hline 12 & \text { Clinical Trials } & \$ 100,000,000 \
\hline 13 & \text { Total Project Costs } & \
\hline 14 & & \\hline 15 & \text { Model } & \
\hline 16 & & \
\hline 17 & \text { Year } & 1 &2&3&4&5\\hline 18&\text { Market growth factor } & & 4 \% & 4 \% & 4 \% & 4 \% \
\hline 19&\text { Market size } & & & & & \
\hline 20&\text { Market share growth rate } & & 18 \% & 18 \% & 18 \% & 18 \% \\hline 21 & \text { Market share } & 7 \% \
\hline 22 & \text { Sales } & \
\hline 23 & & \
\hline 24 & \text { Annual revenue } & \\hline 25 & \text { Annual costs } \
\hline 26 & \text { Profit } \
\hline 27 & \text { Cumulative net profit } \
\hline 28 & \
\hline 29 & \text { Net present value } \
\hline
\end{array}\) Suppose that the project manager of Trance Electronics has identified the following uncertain variables in the model and the distributions and parameters that describe them, as follows: Market size: normal with mean of 20,000,000 units and standard deviation of 4,000,000 units. R&D costs: uniform between $600,000,000 and $800,000,000.
Clinical trial costs: lognormal with mean of $150,000,000 and standard deviation $30,000,000. Annual market growth factor: triangular with minimum = 2%, maximum = 6%, and most likely = 3%.
Annual market share growth rate: triangular with minimum = 15%, maximum = 25%, and most likely = 20%.
The number of trials per simulation is equal to 10,000 at a Sim. Random Seed of 2. Run the simulation and answer the following questions using the Risk Solver Platform.
-With reference to the trend chart, which year shows the highest mean net cumulative profit?

Accepted Answer

A)  Year 1 
B)  Year 2 
C)  Year 4 
D)  Year 5 
A)  Year 1 
B)  Year 2 
C)  Year 4 
D)  Year 5

Question 10

Use the information below to answer the following question(s). Consider the following spreadsheet for an outsourcing decision model. $\begin{array}{|l|c|c|}
\hline & \text { A } & \text { B } \
\hline 1 & \text { OutsourcingDecision Model } & \
\hline 2 & & \\hline 3 & \text { Data } & \
\hline 4 & & \
\hline 5 & \text { Manufactured in-house } & \
\hline 6 & \text { Fixed cost } & \$ 60,000 \
\hline 7 & \text { Unit variable cost } & \$ 130 \\hline 8 & & \
\hline 9 & \text { Purchased from supplier } & \
\hline 10 & \text { Unit cost } & \$ 165 \
\hline 11 & & \
\hline 12 & \text { Demand volume } & 1,000 \\hline 13 & \
\hline 14 & \text { Model } \
\hline 15 & \
\hline 16 & \text { Total manufacturing cost } \
\hline 17 & \text { Total purchased cost } \
\hline 18 & \
\hline 19 & \text { Difference } \
\hline 20 & \text { Decision } \
\hline
\end{array}$ We assume that the production (demand) volume is normally distributed with a mean of 1,000 and a standard deviation of 100. For the unit cost, select the triangular distribution. It has a minimum value of $150, most likely value of $165, and a maximum value of $190. The number of trials per simulation is equal to 5,000 at a Sim. Random Seed of 1. Run the simulation and answer the following question(s) using the Risk Solver Platform.
-What is the cost difference lower cutoff in thousands of dollars if the likelihood is 60%?

Accepted Answer

A)  approximately 13.56 
B)  approximately 22.45 
C)  approximately 29.67 
D)  approximately 38.97 
A)  approximately 13.56 
B)  approximately 22.45 
C)  approximately 29.67 
D)  approximately 38.97

Question 11

Use the information below to answer the following question(s). Consider the following spreadsheet for an outsourcing decision model. $\begin{array}{|l|c|c|}
\hline & \text { A } & \text { B } \
\hline 1 & \text { OutsourcingDecision Model } & \
\hline 2 & & \\hline 3 & \text { Data } & \
\hline 4 & & \
\hline 5 & \text { Manufactured in-house } & \
\hline 6 & \text { Fixed cost } & \$ 60,000 \
\hline 7 & \text { Unit variable cost } & \$ 130 \\hline 8 & & \
\hline 9 & \text { Purchased from supplier } & \
\hline 10 & \text { Unit cost } & \$ 165 \
\hline 11 & & \
\hline 12 & \text { Demand volume } & 1,000 \\hline 13 & \
\hline 14 & \text { Model } \
\hline 15 & \
\hline 16 & \text { Total manufacturing cost } \
\hline 17 & \text { Total purchased cost } \
\hline 18 & \
\hline 19 & \text { Difference } \
\hline 20 & \text { Decision } \
\hline
\end{array}$ We assume that the production (demand) volume is normally distributed with a mean of 1,000 and a standard deviation of 100. For the unit cost, select the triangular distribution. It has a minimum value of $150, most likely value of $165, and a maximum value of $190. The number of trials per simulation is equal to 5,000 at a Sim. Random Seed of 1. Run the simulation and answer the following question(s) using the Risk Solver Platform.
-What is the value of mean obtained from the simulation results? [Hint: Choose the nearest answer]

Accepted Answer

A)  $18,385 
B)  $21,608 
C)  $14,894 
D)  $23,946 
A)  $18,385 
B)  $21,608 
C)  $14,894 
D)  $23,946

Question 12

The Risk Solver Platform feature allows you to determine the influence that each uncertain model input has individually on an output variable based on its correlation with the output variable.

Accepted Answer

A)  trend chart 
B)  sensitivity chart 
C)  overlay chart 
D)  box-whisker chart 
A)  trend chart 
B)  sensitivity chart 
C)  overlay chart 
D)  box-whisker chart

Question 13

A normal distribution has a limited range and can be skewed in either direction.

Accepted Answer

A) True 
 B)False

Question 14

Use the information below to answer the following question(s). Below is a spreadsheet for Trance Electronics. \(\begin{array}{|c|l|c|c|c|c|c|}
\hline &\text { A } & \text { B } & \text { C } & \text { D } & \text { E } & \text { F } \
\hline 1&\text { Trance Electronics } & & & & & \\hline 2 & \
\hline 3 & \text { Data } \
\hline 4 & \\hline 5 & \text { Market size } & 20,000,000 \
\hline 6 & \text { Unit (monthly Rx) revenue } & \$ 120.00 \
\hline 7 & \text { Unit (monthly Rx) cost } & \$ 50.00 \
\hline 8 & \text { Discount rate } & 8 \% \
\hline 9 & & \\hline 10 & \text { Project costs } & \
\hline 11 & \text { R\&D } & \$ 750,000,000 \
\hline 12 & \text { Clinical Trials } & \$ 100,000,000 \
\hline 13 & \text { Total Project Costs } & \
\hline 14 & & \\hline 15 & \text { Model } & \
\hline 16 & & \
\hline 17 & \text { Year } & 1 &2&3&4&5\\hline 18&\text { Market growth factor } & & 4 \% & 4 \% & 4 \% & 4 \% \
\hline 19&\text { Market size } & & & & & \
\hline 20&\text { Market share growth rate } & & 18 \% & 18 \% & 18 \% & 18 \% \\hline 21 & \text { Market share } & 7 \% \
\hline 22 & \text { Sales } & \
\hline 23 & & \
\hline 24 & \text { Annual revenue } & \\hline 25 & \text { Annual costs } \
\hline 26 & \text { Profit } \
\hline 27 & \text { Cumulative net profit } \
\hline 28 & \
\hline 29 & \text { Net present value } \
\hline
\end{array}\) Suppose that the project manager of Trance Electronics has identified the following uncertain variables in the model and the distributions and parameters that describe them, as follows: Market size: normal with mean of 20,000,000 units and standard deviation of 4,000,000 units. R&D costs: uniform between $600,000,000 and $800,000,000.
Clinical trial costs: lognormal with mean of $150,000,000 and standard deviation $30,000,000. Annual market growth factor: triangular with minimum = 2%, maximum = 6%, and most likely = 3%.
Annual market share growth rate: triangular with minimum = 15%, maximum = 25%, and most likely = 20%.
The number of trials per simulation is equal to 10,000 at a Sim. Random Seed of 2. Run the simulation and answer the following questions using the Risk Solver Platform.
-With reference to the trend chart, which year shows the highest uncertainty in forecasting the future?

Accepted Answer

A)  Year 1 
B)  Year 3 
C)  Year 4 
D)  Year 5 
A)  Year 1 
B)  Year 3 
C)  Year 4 
D)  Year 5

Question 15

Answer the following question(s) using the Risk Solver Platform (5000 trials per simulation; use the Latin Hypercube sampling method).
Consider the spreadsheet for a Newsvendor Model. \(\begin{array}{|l|l|c|c|l|c|}
\hline &{\text { A }} & \text { B } & \text { C } & \text { D } & \text { E } \
\hline 1 & \text { Newsvendor Model } & & & \begin{array}{l}
\text { Historical } \
\text { Candy Sales }
\end{array} &\$ 264.00 \\hline 2 & & && 50 & \$ 264.00 \
\hline 3 && \text { Data } & & 45 & \$ 264.00 \
\hline 4 && & & 40 & \$ 228.00 \
\hline 5 & \text { Sellingprice } & \$ 18.00 && 46 & \$ 264.00 \
\hline 6 & \text { Cost } & \$ 12.00 && 43 & \$ 255.00 \
\hline 7 & \text { Discount price } & \$ 9.00 && 43 & \$ 255.00 \
\hline 8 & & && 46 & \$ 264.00 \
\hline 9 & \text { Model } & && 42 & \$ 246.00 \
\hline 10 & & && 44 & \$ 264.00 \
\hline 11 & \text { Demand } & 44 && 43 & \$ 255.00 \
\hline 12 & \text { Purchase Quantity } & 44 && 47 & \$ 264.00 \
\hline 13 & & && 41 & \$ 237.00 \
\hline 14 & \text { Quantity Sold } & && 41 & \$ 237.00 \
\hline 15 & \text { Surplus Quantity } & && 45 & \$ 264.00 \
\hline 16 & & && 51 & \$ 264.00 \
\hline 17 & \text { Profit } & && 43 & \$ 255.00 \
\hline 18 & & & & 45 & \$ 264.00 \
\hline 19 & & & & 42 & \$ 246.00 \
\hline 20 & & & & 44 & \$ 264.00 \
\hline 21 & & & & 48 & \$ 264.00 \
\hline 22 & & & \text { Average Profit } & & \
\hline
\end{array}\)
-What is the value of mean profit?

Accepted Answer

A)  $255.90 
B)  $251.45 
C)  $245.98 
D)  $264.00 
A)  $255.90 
B)  $251.45 
C)  $245.98 
D)  $264.00

Question 16

Which of the following is a parameter in the Normal Distribution Dialog of the Risk Solver Platform?

Accepted Answer

A)  maximum value 
B)  minimum value 
C)  most likely value 
D)  mean 
A)  maximum value 
B)  minimum value 
C)  most likely value 
D)  mean

Question 17

Conduct Monte Carlo simulation using historical data and resampling techniques. Use the information below to answer the following question(s).
Below is a spreadsheet for a hotel overbooking model. $\begin{array}{|c|c|c|c|l|l|}
\hline & \text { A } & \text { B } & \text { C } &{\text { D }} & \text { E } \
\hline 1 & \text { Hotel Overbooking Model } & & & \text { Demand } & \text { Probability } \
\hline 2 & & & & 290 & 0.03 \\hline 3 & \text { Data } & & & 295 & 0.05 \
\hline 4 & & && 300 & 0.08 \
\hline 5 & \text { Rooms av ailable } & 350 && 305 & 0.12 \\hline 6 & \text { Price } & \$ 120 & & 310 & 0.15 \
\hline 7 & \text { Overbooking cost } & \$ 100 && 315 & 0.20 \
\hline 8 && & & 320 & 0.15 \\hline 9 & \text { Model } & & & 325 & 0.10 \
\hline 10 & & & & 330 & 0.05 \\hline 11 & \text { Reserv ation limit } & 350 && 335 & 0.04 \
\hline 12 & \text { Customer demand } & 320 && 340 & 0.02 \
\hline 13 & \text { Reservations made } & & &345 & 0.01 \\hline 14 & \text { Cancellations } & 15 \
\hline 15 & \text { Customer arrivals } & \
\hline 16 & & \
\hline 17 & \text { Overbooked customers } & \
\hline 18 & \text { Net revenue } & \
\hline
\end{array}$ Assume that each reservation has a constant probability p = 0.04 of being cancelled. Answer the question(s) using the Risk Solver Platform.
-Which of the following cells is defined as an output cell?

Accepted Answer

A)  B13 
B)  B14 
C)  B15 
D)  B17 
A)  B13 
B)  B14 
C)  B15 
D)  B17

Question 18

Use the information below to answer the following question(s). Consider the following spreadsheet for an outsourcing decision model. $\begin{array}{|l|c|c|}
\hline & \text { A } & \text { B } \
\hline 1 & \text { OutsourcingDecision Model } & \
\hline 2 & & \\hline 3 & \text { Data } & \
\hline 4 & & \
\hline 5 & \text { Manufactured in-house } & \
\hline 6 & \text { Fixed cost } & \$ 60,000 \
\hline 7 & \text { Unit variable cost } & \$ 130 \\hline 8 & & \
\hline 9 & \text { Purchased from supplier } & \
\hline 10 & \text { Unit cost } & \$ 165 \
\hline 11 & & \
\hline 12 & \text { Demand volume } & 1,000 \\hline 13 & \
\hline 14 & \text { Model } \
\hline 15 & \
\hline 16 & \text { Total manufacturing cost } \
\hline 17 & \text { Total purchased cost } \
\hline 18 & \
\hline 19 & \text { Difference } \
\hline 20 & \text { Decision } \
\hline
\end{array}$ We assume that the production (demand) volume is normally distributed with a mean of 1,000 and a standard deviation of 100. For the unit cost, select the triangular distribution. It has a minimum value of $150, most likely value of $165, and a maximum value of $190. The number of trials per simulation is equal to 5,000 at a Sim. Random Seed of 1. Run the simulation and answer the following question(s) using the Risk Solver Platform.
-What is the expected loss determined from the simulation results?

Accepted Answer

A)  $(78) 
B)  $(120) 
C)  $(60) 
D)  $(47) 
A)  $(78) 
B)  $(120) 
C)  $(60) 
D)  $(47)

Question 19

Use the information below to answer the following question(s). Below is a spreadsheet for Trance Electronics. \(\begin{array}{|c|l|c|c|c|c|c|}
\hline &\text { A } & \text { B } & \text { C } & \text { D } & \text { E } & \text { F } \
\hline 1&\text { Trance Electronics } & & & & & \\hline 2 & \
\hline 3 & \text { Data } \
\hline 4 & \\hline 5 & \text { Market size } & 20,000,000 \
\hline 6 & \text { Unit (monthly Rx) revenue } & \$ 120.00 \
\hline 7 & \text { Unit (monthly Rx) cost } & \$ 50.00 \
\hline 8 & \text { Discount rate } & 8 \% \
\hline 9 & & \\hline 10 & \text { Project costs } & \
\hline 11 & \text { R\&D } & \$ 750,000,000 \
\hline 12 & \text { Clinical Trials } & \$ 100,000,000 \
\hline 13 & \text { Total Project Costs } & \
\hline 14 & & \\hline 15 & \text { Model } & \
\hline 16 & & \
\hline 17 & \text { Year } & 1 &2&3&4&5\\hline 18&\text { Market growth factor } & & 4 \% & 4 \% & 4 \% & 4 \% \
\hline 19&\text { Market size } & & & & & \
\hline 20&\text { Market share growth rate } & & 18 \% & 18 \% & 18 \% & 18 \% \\hline 21 & \text { Market share } & 7 \% \
\hline 22 & \text { Sales } & \
\hline 23 & & \
\hline 24 & \text { Annual revenue } & \\hline 25 & \text { Annual costs } \
\hline 26 & \text { Profit } \
\hline 27 & \text { Cumulative net profit } \
\hline 28 & \
\hline 29 & \text { Net present value } \
\hline
\end{array}\) Suppose that the project manager of Trance Electronics has identified the following uncertain variables in the model and the distributions and parameters that describe them, as follows: Market size: normal with mean of 20,000,000 units and standard deviation of 4,000,000 units. R&D costs: uniform between $600,000,000 and $800,000,000.
Clinical trial costs: lognormal with mean of $150,000,000 and standard deviation $30,000,000. Annual market growth factor: triangular with minimum = 2%, maximum = 6%, and most likely = 3%.
Annual market share growth rate: triangular with minimum = 15%, maximum = 25%, and most likely = 20%.
The number of trials per simulation is equal to 10,000 at a Sim. Random Seed of 2. Run the simulation and answer the following questions using the Risk Solver Platform.
-What is the expected value margin obtained from the simulation results of the net present value?

Accepted Answer

A)  0.864 
B)  -0.726 
C)  0.343 
D)  -0.467 
A)  0.864 
B)  -0.726 
C)  0.343 
D)  -0.467

Question 20

If a simulation has multiple output variables that are related to one another, the distributions of all output variables can be viewed on a single Risk Solver Platform chart called a(n) .

Accepted Answer

A)  trend chart 
B)  sensitivity chart 
C)  overlay chart 
D)  box-whisker chart 
A)  trend chart 
B)  sensitivity chart 
C)  overlay chart 
D)  box-whisker chart

What are the benefits of a Risk Solver Platform sensitivity chart?

The Risk Solver Platform chart shows the minimum, first quartile, median, third quartile, and maximum values in a data set graphically.

Monte Carlo simulation is an inappropriate tool to analyze cash budgets because of the inherent uncertainty of the sales forecasts on which most cash budgets are based.

Explain the process of running a simulation using Risk Solver Platform.

Why is the ROUND function used in Excel?

Uniform or triangular distributions are used in the absence of data.

What is Monte Carlo simulation?

The Risk Solver Platform feature allows you to determine the influence that each uncertain model input has individually on an output variable based on its correlation with the output variable.

A normal distribution has a limited range and can be skewed in either direction.

Which of the following is a parameter in the Normal Distribution Dialog of the Risk Solver Platform?

If a simulation has multiple output variables that are related to one another, the distributions of all output variables can be viewed on a single Risk Solver Platform chart called a(n) .

Business Analytics

Analytics on Spreadsheets

Visualizing and Exploring Data

Descriptive Statistical Measures

Probability Distributions and Data Modeling

Sampling and Estimation

Statistical Inference

Trendlines and Regression Analysis

Forecasting Techniques

Introduction to Data Mining

Spreadsheet Modeling and Analysis

Linear Optimization

Applications of Linear Optimization

Integer Optimization

Decision Analysis

Filters

Exam 12: Monte Carlo Simulation and Risk Analysis

What are the benefits of a Risk Solver Platform sensitivity chart?

The Risk Solver Platform chart shows the minimum, first quartile, median, third quartile, and maximum values in a data set graphically.

Monte Carlo simulation is an inappropriate tool to analyze cash budgets because of the inherent uncertainty of the sales forecasts on which most cash budgets are based.

Explain the process of running a simulation using Risk Solver Platform.

Why is the ROUND function used in Excel?

Uniform or triangular distributions are used in the absence of data.

What is Monte Carlo simulation?

The Risk Solver Platform feature allows you to determine the influence that each uncertain model input has individually on an output variable based on its correlation with the output variable.

A normal distribution has a limited range and can be skewed in either direction.

Which of the following is a parameter in the Normal Distribution Dialog of the Risk Solver Platform?

If a simulation has multiple output variables that are related to one another, the distributions of all output variables can be viewed on a single Risk Solver Platform chart called a(n) .

Business Analytics

Analytics on Spreadsheets

Visualizing and Exploring Data

Descriptive Statistical Measures

Probability Distributions and Data Modeling

Sampling and Estimation

Statistical Inference

Trendlines and Regression Analysis

Forecasting Techniques

Introduction to Data Mining

Spreadsheet Modeling and Analysis

Linear Optimization

Applications of Linear Optimization

Integer Optimization

Decision Analysis

Filters