1. Decision Analysis Steps in Decision making
Decision analysis with decision tables
Types of decision (decision modelling environments)
Decision trees

2. Steps in Decision making
Clearly define the problem
List all possible alternatives
Identify all possible outcomes for each alternative
Identify the payoff for each alternative & outcome combination
Use a decision modeling technique to choose an alternative

3. Decision analysis with decision table
The quantitative data of many decision situations can be arranged in a standardized tabular form known as decision table.
Also known as payoff table
Decision table typically contains four elements. They are:
The alternative courses of action
The state of nature
The probabilities of state of nature
The payoffs

4. The alternative course of action
DM involves two or more options
One, and only one of these alternatives must be selected
Alternative courses of actions are designated by a1,a2,a3…… an
Number of alternative may be either finite or infinite. As for example…….

5. The States of Nature
Also known as Events or possible futures that a decion maker can not control
A state of nature can be
A state of economy (e.g. inflation)
A weather condition
A political development
Or other situations

6. One goal: maximize the yield after one year
Investment example
One goal: maximize the yield after one year
Yield depends on the status of the economy
(the state of nature)
Solid growth
Stagnation
Inflation

7. Possible Situations
1. If solid growth in the economy, bonds yield 12%; stocks 15%; time deposits 6.5%
2. If stagnation, bonds yield 6%; stocks 3%; time deposits 6.5%
3. If inflation, bonds yield 3%; stocks lose 2%; time deposits yield 6.5%

8. Decision Table .5 .3 .2 Solid G Stagnation Inflation A1 Bonds 12 6 3
Alternatives .5 .3 .2
Solid G
Stagnation
Inflation
A1 Bonds 12 6 3
A2 Stocks 15 -2
A3 Time deposits
6.5
State of nature

9. The probabilities of States of Nature & Payoffs
Likelihood of these states of nature
Payoff also known as outcome
Payoff can be measured in terms of money, market share or other measures.

10. Types of decision modelling environment
Type 1: Decision making under certainty
Type 2: Decision making under uncertainty
Type 3: Decision making under risk

11. Decision making under certainty
The consequence of every alternative is known
Usually there is only one outcome for each alternative
This seldom occurs in reality

12. Decision making under uncertainty
Probabilities of the possible outcomes are not known. Choice here is made by organizational policy the attitude of the decision maker toward risk or both.
Decision making methods:
Laplace
Maximin
Maximax
Coefficient of Optimism(Hurwicz Criterion)
The criterion of Regret(Savage’s Criterion

13. Example
The palm tree Hotel is considering the construction of an additional wing. Mgt is evaluating the possibility of adding 30,40,50 rooms. The success of the addition depends on a combination of local government legislation and competition in the field, four states of nature are being considered. They are shown together with the anticipated payoff. Mgt cannot agree on the probabilities of the state of nature. The problem is : how many rooms to build in order to maximize the return on investment.

14. Laplace (The criterion of equal probabilities
Alternative/State of Nature s1 s2 s3 s4
A1=30 10 5 4 -2
A2=40 17 1
-10
A3=50 24 15 -3
-20
E(a1)
=.25*10+.25*5+.25*4+.25* =4.25
E(a2)
=.25*17+.25* *1+25* =4.5 Largest Expected Yield
E(a3)
.25*24+.25*15+.25*-3+.25* =4

15. Criterion of Pessimism (Maximin)
Alternative/State of Nature s1 s2 s3 s4
Worst
Best of Worst
A1=30 10 5 4 -2
-2*
A2=40 17 1
-10
A3=50 24 15 -3
-20

16. Criterion of Optimism(Maximax)
Alternative/State of Nature s1 s2 s3 s4
Best
Best of Bests
A1=30 10 5 4 -2
A2=40 17 1
-10
A3=50 24 15 -3
-20
24*

17. Coefficient of Optimism(Hurwicz)
Alternative/State of Nature s1 s2 s3 s4
A1=30 10 5 4 -2
A2=40 17 1
-10
A3=50 24 15 -3
-20
Hurwicz suggested that the best alternative is the one with the highest (in maximization) weighted value (WV).
WV(a1)
.7*10+(1-.7)*(-2)=6.4
WV(a2)
.7*17+(1-.7)*(-10)=8.9
WV(a3)
.7*24+(1-.7)*(-20)=10.8 (Maximum)*

18. The criterion of regret (savage’s Criterion)
Alternative/State of Nature s1 s2 s3 s4
A1=30 10 5 4 -2
A2=40 17 1
-10
A3=50 24 15 -3
-20
Alternative/State of Nature s1 s2 s3 s4
Largest regret(Worst)
A1=30
24-10=14
15-5=10
4-4=0
-2- (-2)=0 14
A2=40
24-17=7
15-10=5
4-1=3
-2 (-10)=8
8* Minimum
A3=50
24-24=0
15-15=0
4-(-3)=7
-2-(-20)=18 18

19. Example2
The manager of an advertising agency has to make decisions between three available programs (a1,a2,a3)There are three possible futures that can be expected ie market rises, market falls, no change in the market. The manager can estimate the yields in each case but can not estimate the possibilities of the various future occurring.
Programs s1 s2 s3 a1 3 6 -1 a2 8 5 4 a3 -4 7 12
Which program will the manager select if he uses the following decision approaches
Laplace
Pessimistic
Otimistic
Hurwicz criterion
Minimax regret (Savage)

20. Decision making under Risk
Where probabilities of outcomes are available
Expected payoff criterion: Here the Decision maker selects the alternative with the best expected(average) payoff
EMV (for alternative i) =
∑(probability of outcome) x (payoff of outcome)
EOL criterion:

21. Investment Problem Decision Table Model
States of Nature
Solid Stagnation Inflation
Alternatives Growth
Bonds 12% 6% 3%
Stocks 15% 3% -2%
CDs 6.5% 6.5% %

22. Table 5.3: Decision Under Risk and Its Solution
Solid Stagnation Inflation Expected
Growth Value
Alternatives
Bonds 12% 6% 3% 8.4% *
Stocks 15% 3% -2% 8.0%
CDs 6.5% 6.5% % 6.5%

23. How to find the Expected payoff
E(a1)=12*.5+6*.3+3*.2=8.4
E(a2)=15*.5+3*.3+-2*.2=8.0
E(a3)=6.5*.5+6.5*.3+6.5*2=6.5

24. Expected Opportunity Loss
Also called regret criterion
Opportunity loss is defined as the relative loss resulting from selecting an alternative.
Minimizing expected regret. Regret is always bad and is to be avoided or minimized

25. EOL/Regret Criterion Solid Stagnation Inflation Expected Growth Value
Alternatives
Bonds 12% 6% 3% * Smallest
Stocks 15% 3% -2%
CDs 6.5% 6.5% %

26. EOL/Regret Criterion Solid Stagnation Inflation Expected Value Growth
Alternatives
Bonds = = =3 =3*.5+.5*.5*.3+3*.2=2.35*
Stocks = = ( -2) =2.75
CDs = = =4.25

27. Example2
Find the best alternative in the following decisions table: Use both an expected value and an EOL
State of nature
Alternative .6 s1 .1 s2 .2 s3 s4 a1 3 5 8 -1 a2 6 2 a3 4

28. Example3
A survey conducted over last 20 yrs in Hamburg Germany indicated that in 8 of them the winter was mild, in 7 of them it was cold and in remaining 5 it was very cold. A company sells 1000 heavy coats in mild year,1300 in cold year and 2000 in very cold year. Find the yearly expected profit of the company if a coat cost 85 euro & sold to 123 euro.

29. Decision Trees