Decision Analysis

1
Chapter 14

• Decision Analysis Part 2

2
Introduction Review

• Payoff Table development
• Decision Analysis under Uncertainty

3
Decision Criteria (Risk)

• Expected Monetary Value (EMV)
• Select alternative with highest expected payoff
• Maximum Likelihood
• Select best of payoffs that are most likely to
  occur
• Dominance Models

4
Expected Monetary Value

• Sum of weighted payoffs associated with a
  specific alternative
• EMV (Alt) ? CP (AltStatei)P(Statei)

i
5
Payoff Table
Probabilities of Demand Levels sum 1
.1 .2 .1 .4
.2
Demand
5 10 15 20 25
5 20 10 0 -10 -20
10 5 40 30 20 10
15 -10 25 60 50 40
20 -25 10 45 80 70
25 -40 -5 30 65 100
Stock
6
EMV Calculations
EMV (Alt) ? CP (AltStatei)P(Statei)
i

• EMV5 .1(20) .2(10) .1(0) .4(-10)
  .2(-20)
• EMV10 .1(5) .2(40) .1(30) .4(20) .2(10)
  
• EMV15 .1(-10) .2(25) .1(60) .4(50)
  .2(40)
• EMV20 .1(-25) .2(10) .1(45) .4(80)
  .2(70)
• EMV25 .1(-40) .2(-5) .1(30) .4(65)
  .2(100)

7
Payoff Table
Demand
Best Worst Avg EMV
5 20 -20 0 -4
10 40 5 21 21.5
15 60 -10 33 38
20 80 -25 36 50
25 100 -40 30 44
Stock
8
Value of Perfect Information

• How much would it be worth to us to know the
  state of nature ahead of time (would we change
  our decision)?
• Specifically, how much additional profit could we
  make if we knew exactly what demand would be?

9
Value of Perfect Information

• EPPI Expected Payoff Under Perfect Information
• EPPP Expected Payoff with Perfect Prediction
• EPUC Expected Payoff Under Certainty

10
Payoff Table
If we knew demand would be 5 shirts, how much
would we stock? 10? 15? 20? 25?
.1 .2 .1 .4
.2
Demand
5 10 15 20 25
5 20 10 0 -10 -20
10 5 40 30 20 10
15 -10 25 60 50 40
20 -25 10 45 80 70
25 -40 -5 30 65 100
Stock
11
Expected Payoff Under Perfect Information
EPPI ? CP (State i) P (State i)
i

• This is the maximum we could expect to make if we
  always knew ahead of time what the demand was
  going to be.

12
Expected Value of Perfect Information

• EVPI is the expected value of having perfect
  information i.e. it is the amount we would
  make over and above what we could make on our own
  without perfect information
• EVPI EPPI EMV

13
Expected Value of Perfect Information

• EVPI EPPI EMV
• EVPI
• This is how much perfect information would be
  worth to us. Its also the maximum amount we
  would be willing to pay for perfect information.

14
Decision Tree

• Visual display of the decision at hand
• Allows for sequential decision making
• Steps
• For each set of state branches, find the EMV for
  the decision branch.
• Compare the EMVs across all decisions and select
  the best decision based on the highest EMV.

15
D5 (.1) 20 D10 (.2) 10 D15 (.1) 0 D20 (.4)
-10 D25 (.2) -20
Stock 5
D5 (.1) 5 D10 (.2) 40 D15 (.1) 30 D20 (.4)
20 D25 (.2) 10
Decision node
Stock 10
State node
D5 (.1) -10 D10 (.2) 25 D15 (.1) 60 D20 (.4)
50 D25 (.2) 40
Stock 15
16
D5 (.1) -25 D10 (.2) 10 D15 (.1) 45 D20
(.4) 80 D25 (.2) 70
Stock 20
D5 (.1) -40 D10 (.2) -5 D15 (.1) 30 D20 (.4)
65 D25 (.2) 100
Stock 25
17
D5 (.1) 20 D10 (.2) 10 D15 (.1) 0 D20 (.4)
-10 D25 (.2) -20
Stock 5
EMV
D5 (.1) 5 D10 (.2) 40 D15 (.1) 30 D20 (.4)
20 D25 (.2) 10
Stock 10
EMV
D5 (.1) -10 D10 (.2) 25 D15 (.1) 60 D20 (.4)
50 D25 (.2) 40
Stock 15
EMV
18
D5 (.1) -25 D10 (.2) 10 D15 (.1) 45 D20
(.4) 80 D25 (.2) 70
Stock 20
EMV
D5 (.1) -40 D10 (.2) -5 D15 (.1) 30 D20 (.4)
65 D25 (.2) 100
Stock 25
EMV
19
Sequential Decision Making

• Decision trees are very useful when there are
  multiple decisions to be made and they follow a
  sequence in time. There are also usually multiple
  sets of states.

CP
Decision 1
State 1
CP
State 1
Decision 2
Decision 1
State 2
State 2
CP
CP
State 1
State 1
CP
CP
Decision 1
Decision 2
State 2
State 2
Decision 2
CP
State 1
CP
CP
Decision 1
CP
Decision 3
State 2
Decision 2
CP
20
Sequential Decision Example

• Suppose that you are trying to decide which of
  three companies to invest in Company A, B, or C.
  If you choose A, there is a 50/50 chance of
  going broke or earning 50,000. If you go broke
  with A, you then have three choices accept a
  debt of 2,000 embezzle 35,000 of company
  money (not that we would EVER do this) and leave
  the country or file for personal bankruptcy at
  the hands of a court-appointed trustee.

21
Invest in A
Invest in B
Invest in C
22
Sequential Decision Example

• Suppose that you are trying to decide which of
  three companies to invest in Company A, B, or C.
  If you choose A, there is a 50/50 chance of
  going broke or earning 50,000. If you go broke
  with A, you then have three choices accept a
  debt of 2,000 embezzle 35,000 of company
  money (not that we would EVER do this) and leave
  the country or file for personal bankruptcy at
  the hands of a court-appointed trustee.

23
Debt
Embezzle
Go Broke(.5)
Invest in A
Bankrupt
Earn (.5)
50,000
Invest in B
Invest in C
24
Sequential Decision Example

• If you embezzle money and leave the country,
  there is a 95 chance of being extradited and
  fined 10,000. If you file for personal
  bankruptcy, there is a 95 chance that your debts
  will be wiped out and a 5 chance that you will
  have to pay back 4,000.

25
Debt
-2K
Extrad(.95)
-10K
Go Broke(.5)
Embezzle
A
Not(.05)
35K
Earn (.5)
Bankrupt
Pay back(.05)
-4K
B
50,000
Wiped out(.95)
0
C
26
Sequential Decision Example

• If you choose Company B, there is an 80 percent
  chance of earning 25,000. If Business B fails,
  you still have the option of either settling for
  500 or taking a stock option in the company that
  will be worth 50,000 with probability 0.1 or
  zero with probability 0.9.

27
A
Earn (.8)
B
25000
Settle
B fails(.2)
500
Earn(.1)
Stock option
50000
C
Not(.9)
0
28
Sequential Decision Example

• Finally if you choose Company C, you will either
  earn 10,000 with probability 0.6, or be in debt
  for 1,000 with probability 0.4.

29
A
B
Earn (.6)
10000
C
Debt(.4)
-1000
30
Sequential Decision Example

• Solve by folding back the tree
• Trees are drawn from left to right they are
  folded back from right to left.
• For each set of state branches, find the EMV for
  the connected decision.
• For each set of decisions, select the one with
  the highest EMV and carry the EMV forward (to
  the left)

31
Debt
Extrad(.95)
-10000
Go Broke(.5)
Embezzle
A
Not(.05)
35000
Earn (.5)
Bankrupt
Pay back(.05)
50000
-4000
Earn (.8)
B
25000
Wiped out(.95)
Settle
B fails(.2)
500
0
Earn(.1)
Stock option
Earn (.6)
50000
10000
C
Not(.9)
Debt(.4)
-1000
0
32
Sequential Decision Example

• After you fold back the tree and determine the
  best initial decision, then state the complete
  optimal sequence of decisions
• Invest in Company A. If you go broke, then file
  for bankruptcy. Otherwise enjoy the 50,000!!

33
For Next Class

• Continue reading Chapter 14 (thru page 27)
• Do remaining homeworks