Decision Making

Decision Analysis

Introduction Review  Payoff

Table development  Decision Analysis under Uncertainty

Decision Criteria (Risk)  Expected 

Select alternative with highest expected payoff

 Maximum 

Monetary Value (EMV) Likelihood

Select best of payoffs that are most likely to occur

 Dominance

Models

Expected Monetary Value  Sum

of weighted payoffs associated with a specific alternative

EMV (Alt) = Σ [ CP (Alt|Statei)P(Statei)] i

Probabilities of =Demand Levels; sum = 1

Payoff Table .1

.2

.1

.4

.2

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

Demand Stock

EMV Calculations EMV (Alt) = Σ [ CP (Alt|Statei)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) =

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

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?

Value of Perfect Information  EPPI

= Expected Payoff Under Perfect Information  EPPP = Expected Payoff with Perfect Prediction  EPUC = Expected Payoff Under Certainty

If we knew demand would be 5 shirts, how much would we stock? 10? 15? 20? 25?

Payoff Table .1

.2

.1

.4

.2

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

Demand Stock

Expected Payoff Under Perfect Information

EPPI = Σi CP* (State i) P (State i) = =

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

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*

Expected Value of Perfect Information

EVPI = EPPI – EMV* EVPI = This is how much perfect information would be worth to us. It’s also the maximum amount we would be willing to pay for perfect information.

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.

Stock 5 Decision node

Stock 10 State node Stock 15

D=5 (.1) 20 D=10 (.2) 10 D=15 (.1) 0 D=20 (.4) -10 D=25 (.2) -20 D=5 (.1) 5 D=10 (.2) 40 D=15 (.1) 30 D=20 (.4) 20 D=25 (.2) 10 D=5 (.1) -10 D=10 (.2) 25 D=15 (.1) 60 D=20 (.4) 50 D=25 (.2) 40

Stock 20

Stock 25

D=5 (.1) -25 D=10 (.2) 10 D=15 (.1) 45 D=20 (.4) 80 D=25 (.2) 70 D=5 (.1) -40 D=10 (.2) -5 D=15 (.1) 30 D=20 (.4) 65 D=25 (.2) 100

Stock 5

EMV= Stock 10

EMV= Stock 15

EMV=

D=5 (.1) 20 D=10 (.2) 10 D=15 (.1) 0 D=20 (.4) -10 D=25 (.2) -20 D=5 (.1) 5 D=10 (.2) 40 D=15 (.1) 30 D=20 (.4) 20 D=25 (.2) 10 D=5 (.1) -10 D=10 (.2) 25 D=15 (.1) 60 D=20 (.4) 50 D=25 (.2) 40

Stock 20 EMV=

Stock 25 EMV=

D=5 (.1) -25 D=10 (.2) 10 D=15 (.1) 45 D=20 (.4) 80 D=25 (.2) 70 D=5 (.1) -40 D=10 (.2) -5 D=15 (.1) 30 D=20 (.4) 65 D=25 (.2) 100

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.

Decision 1 Decision 2 Decision 3

CP te 1 a t S 1 e t Sta State 2 State 2 CP State 1 State 1 CP cision 1 De State 2 Stat e2 Decision 2 CP 1 e t Sta CP ecision 1 CP D State 2 Decision 2 CP 1 Decision Decision 2

CP CP CP CP

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.

Invest in A

Invest in B

Invest in C

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.

Debt )

Invest in A

Invest in B

Invest in C

5 . ( e k o Go Br Ea rn $$ (.5 )

Embezzle Bankrupt

$50,000

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.

Debt

A

B

C

-$2K

5 9-$10K . ( ad

tr x E ) 5 . Embezzle ( e k Go Bro )Not( . 05) Ea rn $35K $$ (.5 Bankrupt Pay back(.05) ) W $50,000

ipe

do

-$4K

ut(

.95 ) $0

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.

A

B

Earn $$(.8) $25000

B fails(.2)

C

Settle $500 Earn(.1) $ 50000 Stock No option t(.9 ) $0

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.

A

B

C

Earn $$(.6) $10000

Debt(.4)

-$1000

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)

Debt

A

Go Broke(.5)

Ea

rn

Embezzle

$$(

.5)

Bankrupt

Earn $$(.8) $25000

B fails(.2) Earn $$(.6)

C

tra x E No t(.0

5)

$50000

B

5) 9 . d( -$10000

$10000

Debt(.4) -$1000

Settle Stock option

$35000

Pay ba ck

(.05)

Wi

pe d

ou

-$4000

t(.9

$500

5)

$0

Earn(.1) $50000 No t(.9 ) $0

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!!

For Next Class  Continue

reading Chapter 14 (thru page 27)  Do remaining homeworks