# Ashford University Decision Making and Decision Analytics Worksheet

Master in Business AdministrationDecision Making and Decision Analytics (BA606)

Prof. Myriam Quispe-Agnoli

Final Sample Exam

Question (30 points)

Compare and contrast the Analytical Hierarchy Process, and Expected Monetary Value

Criterion. For your convenience, I have created this table with questions to address this

comparison.

a) How do you determine when do you use this technique? (4 points)

Analytical Hierarchy Process

Expected Monetary Value Criterion

b) How do you learn about the preferences of the decision maker regarding the choices, attributes,

characteristics in each technique? (5 points)

Analytical Hierarchy Process

Expected Monetary Value Criterion

c) What is the measurement criteria used in this technique to reach a recommendation? (i.e.

here I am asking to explain how the techniques works? (8 points)

Analytical Hierarchy Process

Expected Monetary Value Criterion

d) What are the strengths and limitations of these techniques? (5 points)

Analytical Hierarchy Process

Expected Monetary Value Criterion

e) Any other features of this technique not present in others? (4 points)

Analytical Hierarchy Process

Expected Monetary Value Criterion

f) Define sensitivity analysis and provide an example of how you can conduct a sensitivity

under ONE of these techniques. (4 points)

Question (35 points + 5 bonus points)

A producer of laptops is trying to decide about their production capacity (the size of the plant).

This decision will depend on the forecast of the demand for laptops.

The alternatives are:

i.

Expand the existing plant

ii. Build a brand new plant

iii. Do not build the plant

There are three possible scenarios:

a) Demand for laptops will grow

b) Demand for laptops stay the same

c) Demand for laptops will decline

The table below shows the payoffs or potential profits (in current million dollars) for each

alternative at each scenario

Scenarios

Demand

Demand stays

Demand

Course of Action

grows

the same

declines

Expand plant

500

400

-150

Build new plant

700

200

-300

Do not build plant

200

150

-50

a) Describe the choices of the decision maker. In a decision tree, show these choices and their

scenarios (and their payoffs). (10 points)

b) The company’s marketing manager estimates that there is:

• 60% chance that demand for laptops will grow

• 30% chance that demand for laptops will stay the same

• 10% chance that demand for laptops will decline

Assume that the producer maximizes profits.

What is the course of action that you (as business analyst) would recommend to the producer?

Explain how you reach this conclusion. (10 points). [You do not have to draw another decision

tree, but you can refer to it in your answer].

c) How would you calculate the expected value of perfect information? Explain. Calculate the

expected value of perfect information. (10 points ➔ 5 explanation + 5 calculation)

d) New forecast suggests that demand will grow. Estimates of the reliability are:

P(demand will grow when current demand is growing) = 0.3

P(demand will grow when current demand stays the same) = 0.7

P(demand will grow when current demand is declining) = 0.3

Explain how you would include this new information in your analysis. (5 points)

Would the decision recommendation change in light of the new information? 5 Bonus points.

Question (35 points)

Bakery ABC wants to improve their production of cupcakes and donuts. They are considering to

buy one additional oven or NOT, and they have currently OVEN H and they are considering

OVEN K.

The managers provide the information revenues (or sales), fixed costs (rent and utilities), and

variable cost (payroll).

a) They estimate their profits as follows:

Profit = Revenues – Fixed costs – Variable Costs

b) They also provide information about revenues, fixed and variable costs and the following

tornado diagram with OVEN H.

TABLE A

Revenues

Fixed Costs

Variable Costs

Most Likely

Value

Lowest

Highest

Possible Value Possible Value

550

250

750

175

100

300

286

176

396

Tornado Diagram

Fixed Costs

Revenues

Variable Cost

($100)

($50)

$0

$50

$100

$150

$200

$250

The probabilities of the revenues, fixed and variable costs for OVEN H are the following:

Revenues Probability Fixed Costs Probability Variable Costs Probability

250-550

0.4

100-174

0.3

176-285

0.3

551-750

0.6

175-215

0.5

286-396

0.7

216-300

0.2

1.

2.

3.

4.

After simulations this is the probability distribution of profits for OVEN H

Table B

Profit ($)

Frequency

Probability

-100

2

0

4

100

4

200

2

To answer all these questions you will need the information from the previous page.

What are the factors that will affect the profits? Explain.(5 points)

Explain and interpret the tornado diagram to your client. Table A is provided to support

your explanation (what label should go in the horizontal axis?) (10 points)

You decided to carry out a simulation in your decision analysis. Explain why. (5 points)

Using the probabilities provided in table above, how would you generate the range for

random numbers for your simulation? ONLY generate the table for random numbers for

3

FIXED COSTS. (5 points)

5. After the simulation, you are able to generate table B. Explain where do these numbers

(under profits and frequency) come from and calculate the probabilities.(5 points)

6. You make the same analysis for OVEN K and obtain this table

Profit ($)

Frequency

Probability

-200

1

-100

2

0

3

100

3

200

2

300

1

Which course of action would you (as business analyst) recommend? Explain HOW

would you reach to this decision? What other criteria would you use? (5 points)

4

Master in Business Administration

Decision Making and Decision Analytics (BA606)

Prof. Myriam Quispe-Agnoli

Final Sample Exam

Question (30 points)

Compare and contrast the Analytical Hierarchy Process, and Expected Monetary Value

Criterion. For your convenience, I have created this table with questions to address this

comparison.

a) How do you determine when do you use this technique? (4 points)

Analytical Hierarchy Process

Expected Monetary Value Criterion

b) How do you learn about the preferences of the decision maker regarding the choices, attributes,

characteristics in each technique? (5 points)

Analytical Hierarchy Process

Expected Monetary Value Criterion

c) What is the measurement criteria used in this technique to reach a recommendation? (i.e.

here I am asking to explain how the techniques works? (8 points)

Analytical Hierarchy Process

Expected Monetary Value Criterion

d) What are the strengths and limitations of these techniques? (5 points)

Analytical Hierarchy Process

Expected Monetary Value Criterion

e) Any other features of this technique not present in others? (4 points)

Analytical Hierarchy Process

Expected Monetary Value Criterion

f) Define sensitivity analysis and provide an example of how you can conduct a sensitivity

under ONE of these techniques. (4 points)

Question (35 points + 5 bonus points)

A producer of laptops is trying to decide about their production capacity (the size of the plant). This decision will depend on the forecast of the demand for laptops.

The alternatives are:

i.

Expand the existing plant

ii.

Build a brand new plant

iii.

Do not build the plant

There are three possible scenarios:

a) Demand for laptops will grow

b) Demand for laptops stay the same

c) Demand for laptops will decline

The table below shows the payoffs or potential profits (in current million dollars) for each alternative at each scenario

Scenarios

Course of Action

Demand grows

Demand stays the same

Demand declines

Expand plant

500

400

-150

Build new plant

700

200

-300

Do not build plant

200

150

-50

a) Describe the choices of the decision maker. In a decision tree, show these choices and their scenarios (and their payoffs). (10 points)

Expand the

existing plant

Build new

plant

Do not build

plant

Demand

grows

500

Demand stays

the same

400

Demand

declines

-150

Demand

grows

700

Demand stays

the same

200

Demand

declines

-300

Demand

grows

200

Demand stays

the same

150

Demand

declines

-50

b) The company’s marketing manager estimates that there is:

• 60% chance that demand for laptops will grow

• 30% chance that demand for laptops will stay the same

• 10% chance that demand for laptops will decline

Assume that the producer maximizes profits.

What is the course of action that you (as business analyst) would recommend to the producer? Explain how you reach this conclusion. (10 points).

[You do not have to draw another decision tree, but you can refer to it in your answer].

Expected Value (Expand the existing plant) = 0.6*500 + 0.3*400 +0.1* (-150) = 405

Expected Value (Build plant) = 0.6*700 + 0.3*200 +0.1* (-300) = 450

Expected Value (Do not build plant) = 0.6*200 + 0.3*150 +0.1* (-50) = 160

According to these calculations, I would recommend to the decision maker to build the plant because this option is the one with the highest expected

value.

c) How would you calculate the expected value of perfect information? Explain. Calculate the expected value of perfect information. (10 points ➔ 5

explanation + 5 calculation)

The way you calculate the expected value of perfect information is that you compare expected value using the best monetary outcomes in each of the

choices (build, expand or no build a new plant) and the expected value of the imperfect information (in this case using the highest value of the

expected value). The expected value with perfect information is calculated using the

Information

Probability

What is the Best course of Value

Probability x value

action for each possible

scenario

Demand will grow

0.6

Build new plant

700

420

Demand stays the same

0.3

Expand the plant

400

120

Demand will decline

0.1

No build plant

-50

-5

Value with Perfect information

535

Best Value with imperfect information (look at the tree which the best expected value?)

450

Cost of perfect information

85

Note: What is the Best course of action for each possible scenario? Look at all the branches where Demand will grow: which course of action

has the highest value? Build new plant = 700

Look at all the branches where Demand stays the same: which course of action has the highest value? Expand the plant = 400

Look at all the branches where Demand will decline: which course of action has the highest value? No build plant = -50

Then you multiply the probability times the best action and this is the way you get the Value with Perfect information.

d) New forecast suggests that demand will grow. Estimates of the reliability are:

P(demand will grow when current demand is growing) = 0.3

P(demand will grow when current demand stays the same) = 0.7

P(demand will grow when current demand is declining) = 0.3

Explain how you would include this new information in your analysis. (5 points)

Would the decision recommendation change in light of the new information? 5 Bonus points.

3

Joint Probabilities

Demand

grows 0.6

State

Demand stays

the same 0.3

Demand

declines 0.1

Posterior Probabilities

demand will

grow 0.3

0.18

0.18/0.42 = 0.428

demand will

grow 0.7

0.21

0.21/0.42=0.5

demand will

grow 0.3

0.03

0.03/0.42= 0.072

0.42 (sum of

joint

probabilities)

Now the calculation has changed:

Expected Value (Expand the existing plant) = 0.428*500 + 0.5*400 +0.072* (-150) = 403.2

Expected Value (Build plant) = 0.428*700 + 0.5*200 +0.0.072* (-300) =378

Expected Value (Do not build plant) = 0.428*200 + 0.5*150 +0.072* (-50) = 157

The recommendation would change to expand the existing plant.

4

Question (35 points)

Bakery ABC wants to improve their production of cupcakes and donuts. They are considering to buy one additional oven or NOT, and they have

currently OVEN H and they are considering OVEN K.

The managers provide the information revenues (or sales), fixed costs (rent and utilities), and variable cost (payroll).

a) They estimate their profits as follows:

Profit = Revenues – Fixed costs – Variable Costs

b) They also provide information about revenues, fixed and variable costs and the following tornado diagram with OVEN H.

TABLE A

Revenues

Fixed Costs

Variable Costs

Most Likely

Value

Lowest

Highest

Possible Value Possible Value

550

250

750

175

100

300

286

176

396

Tornado Diagram

Fixed Costs

Revenues

Variable Cost

($100)

($50)

$0

$50

$100

$150

$200

$250

The probabilities of the revenues, fixed and variable costs for OVEN H are the following:

Revenues Probability Fixed Costs Probability Variable Costs Probability

250-550

0.4

100-174

0.3

176-285

0.3

551-750

0.6

175-215

0.5

286-396

0.7

216-300

0.2

After simulations this is the probability distribution of profits for OVEN H

5

Table B

Profit ($)

Frequency

Probability

-100

2

0

4

100

4

200

2

To answer all these questions you will need the information from the previous page.

1. What are the factors that will affect the profits? Explain.(5 points)

The factors that affect the profit are Revenues (price times the number of units sold), Fixed costs (costs that you have to pay no matter the

level of production) and Variable Costs (these costs depend on the level or the amount of units that you produce).

The model that shows how profits are affected by these factors is given by

Profits = Revenues – Fixed costs – Variable Costs

2. Explain and interpret the tornado diagram to your client. Table A is provided to support your explanation (what label should go in the

horizontal axis?) (10 points)

The tornado diagram shows how the highest and lowest levels of each factor, keeping all other factors at their most likely levels) affect

profits.

For example revenues’ at their lowest values, can affect profits the most. On the other hand, variable costs have a lower range in profit

variation.

In the horizontal axis, we have profits and how they vary at the highest and lowest values of its factors.

3. You decided to carry out a simulation in your decision analysis. Explain why. (5 points)

Simulation help us to combine all probability and outcome of all factors to come with a calculation of the probability at different levels of

profits. Without this technique, the process would be very cumbersome. Instead we can run several experiments, and by doing a large number

of experiments we could approximate the distribution probability of our main variable in this case profits to the theoretical distribution. In this

case we could come out with the different ranges of profits and their probabilities.

4. Using the probabilities provided in table above, how would you generate the range for random numbers for your simulation? ONLY generate

the table for random numbers for FIXED COSTS. (5 points)

Revenues Probability Random

Numbers

250-550

0.4

00-39

551-750

0.6

40-99

Fixed Costs

Probability

100-174

0.3

175-215

0.5

216-300

0.2

I generated the ranges for the random numbers for all variables here

Random

Numbers

00-29

30-79

80-99

Variable Costs

176-285

286-396

Probability Random

Numbers

0.3

00-29

0.7

30-99

6

5. After the simulation, you are able to generate table B. Explain where do these numbers (under profits and frequency) come from and calculate

the probabilities.(5 points)

Table B

Profit ($)

Frequency

Probability

-100

2

2/12

0

4

4/12

100

4

4/12

200

2

2/12

Total of Frequency = 12

After we calculated the range of random numbers, we generated random numbers for each factor: revenue, fixed costs, and variable costs.

With the random numbers we could assign randomly the values for these factors and calculated profits for each round.

Given the outcomes of these profits, we can generate the frequency table (the number for each event) and the probability of each profit range

(frequency divided by the total number of events). Now we have the probability distribution for profits.

6. You make the same analysis for OVEN K and obtain this table

Profit ($)

Frequency

Probability

-200

1

-100

2

0

3

100

3

200

2

300

1

Which course of action would you (as business analyst) recommend? Explain HOW would you reach to this decision? What other criteria

would you use? (5 points)

Profit ($)

Frequency

Probability oven K

Cumulative Probability oven H Cumulative

-200

1

1/12 = 0.083

0.083

-100

2

2/12 = 0.166

0.249

0.166

0.166

0

3

3/12 = 0.25

0.499

0.333

0.499

100

3

3/12 = 0.25

0.749

0.333

0.832

200

2

2/12=0.166

0.915

0.166

1

300

1

1/12=0.083

1

T Total of Frequency = 12

We have to look at the first order or second order dominance and see if it is conclusive or not. In this case because the cumulative intersect,

we need to look at the second order dominance and see if one are is bigger than the other, looking at their averages and differences.

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