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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