1. Welcome to MM305 Unit 4 Seminar Larry Musolino (lmusolino@kaplan
Welcome to MM305 Unit 4 Seminar Larry Musolino Decision Analysis

2. Course Reminders Each Week you are responsible for:
Posting to DISCUSSION BOARD
Must post an initial response plus at least two significant follow-up responses to fellow students
Submit the UNIT PROJECT to DROPBOX
2 to 3 problems where you show step by step solutions
Complete the UNIT QUIZ
20 multiple choice problems, one attempt, 4 hours to complete, Open book, Open notes.
Attend SEMINAR
Weds at 10pm ET
If you cannot attend seminar, complete the Seminar Option 2 assignment, place the completed assignment in the dropbox

3. More Reminders
When submitting Unit Project, show your work, partial credit awarded for correct method.
Review the SELF-TEST at the end of each Chapter (answers are in the back of the text). This is good practice for the UNIT QUIZZES.
See Chap 4 Self test on page
Review the Glossary while taking the Unit Quiz
Terminology explained, see page
When working the problems in the UNIT PROJECT, review the examples in the TEXT. Also, there are Worked-out (SOLVED) PROBLEMS in the back of each chapter.
See Chap 4 Solved Problems on page

4. Six Steps for Decision Making
Clearly define the problem
List the possible alternatives
One alternative could be “do nothing”
Identify the possible outcomes
List the payoff or profit for each combination of alternatives and outcomes
Select one of the mathematical decision theory models
Example: maximax, maximin, criterion of realism, equally likely, EMV, etc.
Apply the model and make the decision.

5. Example for Steps in Decision Making
Thompson Lumber is deciding whether to expand into backyard storage sheds
Problem Statement: Should Thompson Lumber introduce a new product line of backyard storage sheds?
Thompson Lumber decides the alternatives are:
Construct a large plant to manufacture storage sheds
Construct a small plant to manufacture storage sheds
Do not develop the new product line (do nothing alternative)

6. Example for Steps in Decision Making
3. Thompson Lumber identifies possible outcomes:
Favorable outcome – high demand for the sheds
Unfavorable outcome – low demand for the sheds
Also called State of Nature
4. List payoffs for each alternative/outcome (payoff table , decision table):
Outcome (State of Nature)
Alternative
Favorable Market
Unfavorable market
Build a large plant
$200,000
-$180,000
Build a small plant
$100,000
-$20,000
Do not expand into storage sheds

7. Example for Steps in Decision Making
Steps 5 and 6
Apply the Decision Theory Model and make a decision.

8. Types of Decision-Making Environments
Type 1: Decision making under certainty
Decision maker knows with certainty the consequences of every alternative or decision choice
Type 2: Decision making under uncertainty (Section 4.4)
The decision maker does not know the probabilities of the various outcomes
Type 3: Decision making under risk (Section 4.5)
The decision maker knows the probabilities of the various outcomes

9. 4.4 Decision Making Under Uncertainty
There are several criteria for making decisions under uncertainty (Section 4.4)
Maximax (optimistic)
Maximin (pessimistic)
Criterion of realism (Hurwicz)
Equally likely (Laplace)
Minimax regret

10. UNFAVORABLE MARKET ($)
Maximax
Used to find the alternative that maximizes the maximum payoff (optimistic outlook)
Locate the maximum payoff for each alternative
Select the alternative with the maximum number
Identifies the highest possible gain
STATE OF NATURE
ALTERNATIVE
FAVORABLE MARKET ($)
UNFAVORABLE MARKET ($)
MAXIMUM IN A ROW ($)
Construct a large plant
200,000
–180,000
Construct a small plant
100,000
–20,000
Do nothing
Maximax
MAXIMAX DECISION: Construct a large plant

11. UNFAVORABLE MARKET ($)
Maximin
Used to find the alternative that maximizes the minimum payoff (pessimistic outlook)
Locate the minimum payoff for each alternative
Select the alternative with the maximum number
Identifies the “best of the worst”
STATE OF NATURE
ALTERNATIVE
FAVORABLE MARKET ($)
UNFAVORABLE MARKET ($)
MINIMUM IN A ROW ($)
Construct a large plant
200,000
–180,000
Construct a small plant
100,000
–20,000
Do nothing
Maximin
MAXIMIN DECISION: Do nothing
Table 3.3

12. Criterion of Realism (Hurwicz)
A weighted average compromise between optimistic and pessimistic
Select a coefficient of realism 
Coefficient is between 0 and 1
A value of 1 is 100% optimistic about the future
A value of 0 is 100% pessimistic about the future
Compute the weighted averages for each alternative
Select the alternative with the highest value
Weighted average for each row = () (maximum in row) + (1 – )(minimum in row)
For our example, we will use  = 0.8

13. Criterion of Realism (Hurwicz)
For the large plant alternative using  = 0.8 (0.8)(200,000) + (1 – 0.8)(–180,000) = 124,000
For the small plant alternative using  = 0.8 (0.8)(100,000) + (1 – 0.8)(–20,000) = 76,000
Note this method only considers max and min in each row for the weighted average
STATE OF NATURE
ALTERNATIVE
FAVORABLE MARKET ($)
UNFAVORABLE MARKET ($)
CRITERION OF REALISM ( = 0.8)$
Construct a large plant
200,000
–180,000
124,000
Construct a small plant
100,000
–20,000
76,000
Do nothing
Realism
Criterion of Realism DECISION: Construct a large plant

14. Equally Likely (Laplace)
Considers all the payoffs for each alternative
Find the average payoff for each alternative
Select the alternative with the highest average
STATE OF NATURE
ALTERNATIVE
FAVORABLE MARKET ($)
UNFAVORABLE MARKET ($)
ROW AVERAGE ($)
Construct a large plant
200,000
–180,000
10,000
Construct a small plant
100,000
–20,000
40,000
Do nothing
Equally likely
Equally Likely DECISION: Construct a small plant

15. Minimax Regret
Based on opportunity loss or regret, the difference between the optimal profit and actual payoff for a decision
Create an opportunity loss table by determining the opportunity loss for not choosing the best alternative
Opportunity loss is calculated by subtracting each payoff in the column from the best payoff in the column
Find the maximum opportunity loss for each alternative and pick the alternative with the minimum number.
The opportunity lost is the amount lost by not picking the best alternative.

16. Minimax Regret STATE OF NATURE FAVORABLE MARKET ($)
Best payoff in this column is 0
Best payoff in this column is 200,000
STATE OF NATURE
FAVORABLE MARKET ($)
UNFAVORABLE MARKET ($)
200,000 – 200,000
0 – (–180,000)
200,000 – 100,000
0 – (–20,000)
200,000 – 0
0 – 0
Opportunity Loss Tables
STATE OF NATURE
ALTERNATIVE
FAVORABLE MARKET ($)
UNFAVORABLE MARKET ($)
Construct a large plant
180,000
Construct a small plant
100,000
20,000
Do nothing
200,000

17. UNFAVORABLE MARKET ($)
Find the max in each row and then pick the minimum in this column for the decision.
Minimax Regret
STATE OF NATURE
ALTERNATIVE
FAVORABLE MARKET ($)
UNFAVORABLE MARKET ($)
MAXIMUM IN A ROW ($)
Construct a large plant
180,000
Construct a small plant
100,000
20,000
Do nothing
200,000
Minimax
Minimax Regret DECISION: Construct a small plant

18. Summary of Analysis for Decision Making under Uncertainty (Section 4
Decision Criteria
Method
Decision for Thompson Lumber example
Maximax (optimistic)
Identify the maximum payoff for each alternative.
Pick the alternative with maximum payoff
Construct a large plant
Maximin (pessimistic)
1. Identify the minimum payoff for each alternative
Pick the alternative with the maximum number
Do nothing
Criterion of realism Hurwicz)
Select a value for  (coefficient of realism)
For each alternative calculate weighted average = (maximum) + (1-)(minimum)
Pick the alternative with the maximum weighted average
Equally likely (Laplace)
Identify the average payoff for each alternative
Pick the alternative with the highest average.
Construct a small plant
Minimax regret
Create opportunity table by subtracting each payoff in the column from the best payoff in that column
Then determine the maximum in each row and select the alternative with the minimum in this column as the decision

19. Using QM for Windows to assist in Decision Theory

21. We have three Alternatives : Large Plant, Small Plant, Do Nothing
We have two Nature States: Favorable Market, Unfavorable Market

22. We used an Alpha = 0.8 in our example
Once all data is entered Click on SOLVE
Enter the decision table data for our example

23. Hurwicz Decision: Large Plant
Maximin Decision: Do Nothing
Maximax Decision: Large Plant

24. Equally Likely: Small Plant
Minimax Regret: Small Plant

25. Cal and Becky – Word Processing Business
Another Example for Decision Making under Uncertainty – Solved Problem 4.2 page 146
Cal and Becky – Word Processing Business
Three Alternatives Identified:
Alternative #1 – invest in expensive computer system
Alternative #2 – invest in less expensive computer system
Alternative #3 – do nothing
Cal is a risk taker, Becky avoids risk
What decisions should be made?
Decision Table shown on next slide

26. Another Example for Decision Making under Uncertainty – Solved Problem 4.2 page 146
Decision Table
State of Nature
Alternative
Favorable
Unfavorable
Expensive Computer System
10,000
-8000
Inexpensive Computer System
8000
-4000
Do Nothing

27. Setup in QM for Windows

28. Results from QM for Windows
Since Becky is risk averse, she would use maximin decision criteria which is to do nothing, (the pessimistic approach)
Since Cal is a risk taker, he would probably use the Maximax decision criteria, which is to select the Expensive Computer alternative (as the optimistic approach)

29. Results from QM for Windows
For Equally Likely Outcomes:
Find the average payoff for each alternative, then select the alternative with the highest average.
If Cal and Becky were indifferent to risk, they could use equally likely outcomes, in this case, they would select Alternative #2, Inexpensive computer

30. 4.5 - Decision Making Under Risk
Decision making when there are several possible states of nature and we know the probabilities associated with each possible state
Most popular method is to choose the alternative with the highest expected monetary value (EMV)
EMV (alternative i) = (payoff of first state of nature)
x (probability of first state of nature)
+ (payoff of second state of nature)
x (probability of second state of nature)
+ … + (payoff of last state of nature)
x (probability of last state of nature)

31. EMV for Thompson Lumber
EMV (large plant)= (0.50)($200,000) + (0.50)(–$180,000) = $10,000
EMV (small plant) = (0.50)($100,000) + (0.50)(–$20,000)= $40,000
EMV (do nothing) = (0.50)($0) + (0.50)($0) = $0
STATE OF NATURE
ALTERNATIVE
FAVORABLE MARKET ($)
UNFAVORABLE MARKET ($)
EMV ($)
Construct a large plant
200,000
–180,000
10,000
Construct a small plant
100,000
–20,000
40,000
Do nothing
Probabilities
0.50
Largest EMV
Decision based on EMV : Build small plant

32. Worked out Example – Prob 4.1 page 145
Maria wants to decide whether to open a dress shop
Alternatives:
Open small shop
Open medium sized shop
Do nothing
Probabilities for outcomes:
0.2 probability for good market
0.5 probability for average market
0.3 probability for good market
Let’s use EMV criterion to come to a decision
EMV = expected monetary value

33. Worked out Example – Prob 4.1 page 145
State of Nature
Alternative
Good Market
Average Market
Bad Market
EMV
Small Shop
75,000
25,000
-40,000
15,500
Medium Shop
100,000
35,000
-60,000
19,500
Do Nothing
Probabilities
0.20
0.50
0.30
EMV Calculations:
EMV (Small Shop) = (0.2)(75000) + (0.50)(25000) + (0.30)(-40000) = 15,500
EMV (Medium Shop) = (0.2)(100000) + (0.50)(35000) + (0.30)(-60000) = 19,500
EMV (Do Nothing) = (0.2)(0) + (0.50)(0) + (0.30)(0) = 0
EMV Decision: Build the Medium Shop

34. Using QM for Windows
Setup:

35. Using QM for Windows
Results

36. Comments on Unit 4 Project
Problem #1

37. Comments on Unit 4 Project
Problem #2

38. Expected Value of Perfect Information (EVPI)
EVPI places an upper bound on what you should pay for additional information
EVPI = EVwPI – Maximum EMV
EVwPI is the long run average return if we have perfect information before a decision is made

39. EVwPI
Expected Value with Perfect Information = (Best payoff for 1st state of nature )
* (probability for 1st state of nature)
+ (Best payoff for 2nd state of nature )
* (probability for 2nd state of nature)
+ …
+ (Best payoff for last state of nature )
* (probability for last state of nature)

40. Thompson Lumber Example
STATE OF NATURE
ALTERNATIVE
FAVORABLE MARKET ($)
UNFAVORABLE MARKET ($)
EMV ($)
Construct a large plant
200,000
–180,000
10,000
Construct a small plant
100,000
–20,000
40,000
Do nothing
Probabilities
0.50
Maximum EMV

41. Thompson Lumber Example
EVPI = EVwPI – Maximum EMV
First we calculate EVwPI
For the 1st state of nature (favorable market) the best alternative is “build a large plant” with payoff of $200,000.
For the 2nd state of nature (unfavorable market), the best alternative is “do nothing” with payoff of $0.
Thus, EVwPI = (200000)(0.5) + 0(0.5) = 100,000
We know Maximum EMV = 40,000
Thus,
EVPI = 100,000 – 40,000 = $60,000

42. Using QM for Windows

43. EVPI from QM for Windows

44. Summary for EMV and EVPI
EMV – Expected Monetary Value:
For each row in the decision table, the EMV for that row is calculated by multiplying the payoff for each outcome by the corresponding probability for each outcome and sum up the results for that row.
Then select the alternative (row) with the maximum EMV.
See Page 123

45. Summary for EMV and EVPI (cont’d)
EVPI – Expected Value of Perfect Information
EVPI = EVwPI – Maximum EMV
First we calculate EVwPI
EVwPI = Expected Value with Perfect Information
For each state of nature (column), pick the best payoff and then multiply by the probability for that column.
Add up these values for all the columns
This will be the EVwPI
We will know the Maximum EMV based on procedure from previous slide.
Then calculate EVPI = EVwPI – Maximum EMV

46. Expected Opportunity Loss
Expected opportunity loss (EOL) is the cost of not picking the best solution
First construct an opportunity loss table
For each alternative, multiply the opportunity loss by the probability of that loss for each possible outcome and add these together
Minimum EOL will always result in the same decision as maximum EMV
Minimum EOL will always equal EVPI

47. Expected Opportunity Loss
STATE OF NATURE
ALTERNATIVE
FAVORABLE MARKET ($)
UNFAVORABLE MARKET ($)
EOL
Construct a large plant
180,000
90,000
Construct a small plant
100,000
20,000
60,000
Do nothing
200,000
Probabilities
0.50
Minimum EOL
EOL (large plant) = (0.50)($0) + (0.50)($180,000)
= $90,000
EOL (small plant) = (0.50)($100,000) + (0.50)($20,000)
= $60,000
EOL (do nothing) = (0.50)($200,000) + (0.50)($0)
= $100,000

48. Sensitivity Analysis
Sensitivity analysis examines how our decision might change with different input data
For the Thompson Lumber example
P = probability of a favorable market
(1 – P) = probability of an unfavorable market

49. Sensitivity Analysis EMV(Large Plant) = $200,000P – $180,000)(1 – P)
EMV(Small Plant) = $100,000P – $20,000)(1 – P)
= $100,000P – $20,000 + $20,000P
= $120,000P – $20,000
EMV(Do Nothing) = $0P + 0(1 – P)
= $0

50. Sensitivity Analysis $300,000 $200,000 $100,000 –$100,000 –$200,000
–$100,000
–$200,000
EMV Values
EMV (large plant)
Point 1
Point 2
EMV (small plant)
EMV (do nothing)
.167
.615 1
Values of P

51. Sensitivity Analysis BEST ALTERNATIVE RANGE OF P VALUES Do nothing
Less than 0.167
Construct a small plant
0.167 – 0.615
Construct a large plant
Greater than 0.615
$300,000
$200,000
$100,000
–$100,000
–$200,000
EMV Values
EMV (large plant)
Point 1
Point 2
EMV (small plant)
EMV (do nothing)
.167
.615 1
Values of P

52. Sensitivity Analysis Point 1: EMV(do nothing) = EMV(small plant)
EMV(small plant) = EMV(large plant)

53. Using Excel QM to Solve Decision Theory Problems
Program 4.1B