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Decision Analysis
• Steps in Decision making
• Decision analysis with decision tables
• Types of decision (decision modelling
environments)
• Decision trees
Steps in Decision making
1. Clearly define the problem2. List all possible alternatives3. Identify all possible outcomes for each
alternative4. Identify the payoff for each alternative &
outcome combination5. Use a decision modeling technique to choose
an alternative
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
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…….
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
• 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
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%
Decision Table
Alternatives
.5 .3 .2
Solid G Stagnation Inflation
A1 Bonds 12 6 3
A2 Stocks 15 3 -2
A3 Time deposits
6.5 6.5 6.5
State of nature
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.
Types of decision modelling environment
Type 1: Decision making under certainty
Type 2: Decision making under uncertainty
Type 3: Decision making under risk
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
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:1. Laplace2. Maximin3. Maximax4. Coefficient of Optimism(Hurwicz Criterion)5. The criterion of Regret(Savage’s Criterion
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.
Laplace (The criterion of equal probabilities
Alternative/State of Nature
s1 s2 s3 s4
A1=30 10 5 4 -2
A2=40 17 10 1 -10
A3=50 24 15 -3 -20
E(a1) =.25*10+.25*5+.25*4+.25*-2 =4.25
E(a2) =.25*17+.25*10+..25*1+25*-10 =4.5 Largest Expected Yield
E(a3) .25*24+.25*15+.25*-3+.25*-20 =4
Criterion of Pessimism (Maximin)
Alternative/State of Nature
s1 s2 s3 s4 Worst Best of Worst
A1=30 10 5 4 -2 -2 -2*
A2=40 17 10 1 -10 -10
A3=50 24 15 -3 -20 -20
Criterion of Optimism(Maximax)Alternative/State of Nature
s1 s2 s3 s4 Best Best of Bests
A1=30 10 5 4 -2 10
A2=40 17 10 1 -10 17
A3=50 24 15 -3 -20 24 24*
Coefficient of Optimism(Hurwicz)
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)*
Alternative/State of Nature
s1 s2 s3 s4
A1=30 10 5 4 -2
A2=40 17 10 1 -10
A3=50 24 15 -3 -20
The criterion of regret (savage’s Criterion)Alternative/State of Nature
s1 s2 s3 s4
A1=30 10 5 4 -2
A2=40 17 10 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
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 approachesi. Laplaceii. Pessimisticiii. Otimisticiv. Hurwicz criterionv. Minimax regret (Savage)
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:
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% 6.5%
Table 5.3: Decision Under Risk and Its Solution
Solid Stagnation InflationExpected
Growth Value
Alternatives .5 .3 .2
Bonds 12% 6% 3% 8.4% *
Stocks 15% 3% -2% 8.0%
CDs 6.5% 6.5% 6.5% 6.5%
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
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
EOL/Regret Criterion
Solid Stagnation InflationExpected
Growth Value
Alternatives .5 .3 .2
Bonds 12% 6% 3% 2.35* Smallest
Stocks 15% 3% -2%
CDs 6.5% 6.5% 6.5%
EOL/Regret Criterion
Solid Stagnation Inflation Expected Value
Growth
Alternatives .5 .3 .2
Bonds 15-12=3 6.5-6=.5 6.5- 3=3 =3*.5+.5*.5*.3+3*.2=2.35*
Stocks 15-15=0 6.5- 3=3. 6.5-( -2) =2.75
CDs 15-6.5=8.5 6.5 -6.5=0 6.5-6.5 =4.25
Example2
• Find the best alternative in the following decisions table: Use both an expected value and an EOL
State of natureAlternative
.6
s1
.1
s2
.2
s3
.1
s4
a1 3 5 8 -1
a2 6 5 2 0
a3 0 5 6 4
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.
Decision Trees