1. Chapter 5: Decision-making Concepts
Quantitative Decision Making with Spreadsheet Applications 7th ed.
By Lapin and Whisler
Sec 5.5 : Other Decision Criteria
Sec 5.6: Opportunity Loss and the Expected Value of Perfect Information

2. The Maximin Payoff Criterion
The maximin payoff criterion is a procedure that guarantees that the decision maker can do no worse than achieve the best of the poorest outcomes.

3. Example: Tippi-Toes Payoff Table
Event
(level of demand)
Act (choice of movement)
Gears and Levers
Spring Action
Weights and Pulleys
Light
$25,000
-$10,000
-$125,000
Moderate
$400,000
$440,000
Heavy
$650,000
$740,000
$750,000

4. Example Goal: Ensure a favorable outcome no matter what happens.
Determine the worst outcome for each act regardless of the event.
Gears and Levers
Light demand
$25,000
Spring Action
-$10,000
Weights and Pulleys
-$125,000

5. Example
Choose an act with the largest lowest payoff. This guarantees a minimum return that is the best of the poorest outcomes possible.
Gears and Levers will guarantee the toy manufacturer a payoff of at least $25,000.
Gears and Levers is the maximin payoff act.

6. Example: Tippi-Toes Payoff Table
Event
(level of demand)
Act (choice of movement)
Gears and Levers
Spring Action
Weights and Pulleys
Light
$25,000
-$10,000
-$125,000
Moderate
$400,000
$440,000
Heavy
$650,000
$740,000
$750,000
Column Minimums

7. Risk vs. Reward Event Act A1 A2 E1 $0 -$1 E2 1 10,000 Event Act B1 B2
Column Minimums
Event
Act B1 B2 E1 $1
$10,000 E2 -1
-10,000
Column Minimums
-$1
-$10,000

8. Deficiencies of Maximin Payoff Criterion
It is an extremely conservative decision criterion and may lead to some bad decisions.
It is primarily suited to decision problems with unknown probabilities that cannot be reasonably assessed.

9. The Maximum Likelihood Criterion
The maximum likelihood criterion focuses on the most likely event to the exclusion of all others.

10. Maximum Likelihood Act
Event (level of demand)
Probability
Act (Choice of Movement)
Gears & Levers
Spring Action
Weights & Pulleys
Light
.10
$25,000
-$10,000
-$125,000
Moderate
.70
400,000
440,000
Heavy
.20
650,000
740,000
750,000

11. Maximum Likelihood Criterion
Ignores most of other possible outcomes.
Prevalent decision-making behavior.

12. The Criterion of Insufficient Reason
Used when decision maker has no information about the event probabilities.
Assumes each event has a probability of 1/(number of events) of occuring.
Some knowledge of the probability of an event is almost always available.

13. The Bayes Decision Rule
The Bayes decision rule chooses the act maximizing expected payoff.
It makes the greatest use of all available information.
Its major deficiency occurs when alternatives involve different magnitudes of risk.

14. Event Probability Act C1 Act C2 Payoff Payoff x Prob E1 .5 E2
-$1,000,000
-$500,000
$250,000
$125,000 E2
2,000,000
1,000,000
750,000
375,000
Expected Payoff
$500,000

15. Opportunity Loss
Opportunity loss is the amount of payoff that is forgone by not selecting the act that has the greatest payoff for the event that actually occurs.
To calculate opportunity losses the maximum payoff for each row is determined and it’s then subtracted from its respective row maximum.

16. (in thousands of dollars)
Event
(level of demand)
Payoff
Row Maximum
Gears & Levers
Spring Action
Weights & Pulleys
Light
$25,000
-$10,000
-$125,000
Moderate
400,000
440,000
Heavy
650,000
740,000
750,000
Row maximum-Payoff = Opportunity Loss
(in thousands of dollars)
25-25=0
25-(-10)=35
25-(-125)=150
=40 =0
=100
=10 =0

17. Opportunity Loss Table
Event
(level of demand)
Act (choice of movement)
Gears & Levers
Spring Action
Weights & Pulleys
Light $0
$35,000
150,000
Moderate
40,000
Heavy
100,000
10,000

18. The Bayes Decision Rule and Opportunity Loss
The Bayes decision rule is to select the act that has the maximum expected payoff or the minimum expected opportunity loss.

19. Act (choice of movement)
Event
(level of demand)
Probability
Act (choice of movement)
Gears & Levers
Spring Action
Weights & Pulleys
Loss
Loss x Prob
Light
.10 $0
$35,000
$3,500
$150,000
$15,000
Moderate
.70
40,000
28,000
Heavy
.20
100,000
20,000
10,000
2,000
Expected Opportunity Loss
$48,000
$5,500
$43,000

20. The Expected Value of Perfect Information
When the decision maker can acquire perfect information the decision will be made under certainty. Then the decision maker can guarantee the best decision.
We want to investigate the worth of such information before it is obtained, so we will determine the expected payoff once perfect information is obtained.
This quantity is called the expected payoff under certainty.

21. Calculating Expected Payoff Under Certainty
Determine the highest payoff for each event.
Multiply the maximum payoffs with their respective event probabilities. Then sum these amounts.
Determine the worth of perfect information to the decision maker.

22. Example: Highest Payoff for each Event
Event(level of demand)
Probability
Act
Under Certainty
Gears & Levers
Spring Action
Weights & Pulleys
Maximum Payoff
Chosen Act
Payoff x Prob
Light
.10
$25,000
-$10,000
-$125,000
G&L
$2,500
Moderate
.70
400,000
440,000 SA
308,000
Heavy
.20
650,000
740,000
750,000
W&P
150,000
Expected Payoff under certainty
460,500

23. Expected Value of Perfect Information (EVPI)
EVPI = Expected payoff under certainty
- Maximum expected payoff.
Our example:
EVPI = $460,500-$455,000 = $5,500.
This is the greatest amount of money the decision maker would be willing to pay to obtain perfect information about what demand will be.