Business Analysis- Decision Analysis

8/3/2019 Business Analysis- Decision Analysis

1/27

Chapter 8

Decision Analysis

Slides 8a: Introduction


2/27

Decision Analysis

A set of alternative actions We may chose whichever we please

A set of possible states of nature Only one will be correct, but we dont know in

advance

A set of outcomes and a value for each Each is a combination of an alternative action and a

state of nature

Value can be monetary or otherwise


3/27

Decision Analysis Certainty

Decision Maker knows with certainty what the state of

nature will be - only one possible state of nature Ignorance

Decision Maker knows all possible states of nature,but does not know probability of occurrence

Risk Decision Maker knows all possible states of nature,

and can assign probability of occurrence for eachstate


4/27

Decision Making Under CertaintyDecision Variable

Units to build 150

Parameter Estimates

Cost to build (/unit) 6,000$Revenue (/unit) 14,000$

Demand (units) 250

Consequence Variables

Total Revenue 2,100,000$Total Cost 900,000$

Performance Measure

Net Revenue 1,200,000$


5/27

Decision Making Under Ignorance

Payoff TableKelly Construction Payoff Table (Prob. 8-17)

Low (50 units) Medium (100 units) High (150 units)

Build 50 400,000 400,000 400,000

Build 100 100,000 800,000 800,000

Build 150 (200,000) 500,000 1,200,000

State of Nature

DemandAlternative

Actions


6/27

Decision Making Under Ignorance Maximax

Select the strategy with the highest possible

return Maximin

Select the strategy with the smallest possibleloss

LaPlace-Bayes All states of nature are equally likely to occur.

Select alternative with best average payoff


7/27

Maximax:The Optimistic Point of View

Select the best of the best strategy

Evaluates each decision by the maximum possiblereturn associated with that decision (Note: if cost datais used, the minimum return is best)

The decision that yields the maximum of thesemaximum returns (maximax) is then selected

For risk takers Doesnt consider the down side risk

Ignores the possible losses from the selectedalternative


8/27

Maximax Example

Low (50 units) Medium (100 units) High (150 units) Max

Build 50 400,000 400,000 400,000 400,000

Build 100 100,000 800,000 800,000 800,000

Build 150 (200,000) 500,000 1,200,000 1,200,000

State of NatureMaximax

CriterionDemandAlternative

Actions

Kelly Construction


9/27

Maximin:The Pessimistic Point of View

Select the best of the worst strategy Evaluates each decision by the minimum

possible return associated with the decision

The decision that yields the maximum valueof the minimum returns (maximin) is selected

For risk averse decision makers A protect strategy

Worst case scenario the focus


10/27

Maximin

Low (50 units) Medium (100 units) High (150 units) Min

Build 50 400,000 400,000 400,000 400,000

Build 100 100,000 800,000 800,000 100,000

Build 150 (200,000) 500,000 1,200,000 (200,000)

State of NatureMaximin

CriterionDemandAlternative

Actions

Kelly Construction


11/27

Decision Making Under Risk Expected Return (ER)*

Select the alternative with the highest (long term)

expected return A weighted average of the possible returns for

each alternative, with the probabilities used as

weights

*Also referred to as Expected Value (EV) or ExpectedMonetary Value (EMV)

**Note that this amount will not be obtained in the shortterm, or if the decision is a one-time event!


12/27

Expected Return

Low (50 units) Medium (100 units) High (150 units) ER

Build 50 400,000 400,000 400,000 400,000

Build 100 100,000 800,000 800,000 660,000

Build 150 (200,000) 500,000 1,200,000 570,000

Probability 0.2 0.5 0.3 1.0

State of NatureExpected

ReturnDemandAlternative

Actions


13/27

Expected Value of Perfect Information

EVPI measures how much better you could do onthis decision if you could always know when eachstate of nature would occur, where:

EVUPI = Expected Value Under Perfect Information

(also called EVwPI, the EV with perfect information, or

EVC, the EV under certainty)

EVUII = Expected Value of the best action with

imperfect information (also called EVBest )

EVPI = EVUPI EVUII

EVPI tells you how much you are willing to pay forperfect information (or is the upper limit for what youwould pay for additional imperfect information!)


14/27

Expected Value of Perfect

Information

Low (50 units) Medium (100 units) High (150 units) ER

Build 50 400,000 400,000 400,000 400,000

Build 100 100,000 800,000 800,000 660,000

Build 150 (200,000) 500,000 1,200,000 570,000

Probability 0.2 0.5 0.3 1.0

Best Decision 400,000 800,000 1,200,000 840,000

EVPI 180,000

State of NatureExpected

ReturnDemandAlternative

Actions


15/27

Using Excel to Calculate EVPI:

Formulas View

A B C D E

12

3 Payoffs States of Nature Expected Return

4 Alternatives Low (50 units) Medium (100 units) High (150 units) ER

5 Build 50 400000 400000 400000 =SUMPRODUCT(B5:D5,B$8:D$8)

6 Build 100 100000 800000 800000 =SUMPRODUCT(B6:D6,B$8:D$8)

7 Build 150 -200000 500000 1200000 =SUMPRODUCT(B7:D7,B$8:D$8)

8 Probability 0.2 0.5 0.39 Best Decision =MAX(B5:B7) =MAX(C5:C7) =MAX(D5:D7)

10

11 EVwPI = =SUMPRODUCT(B9:D9,B8:D8)

12 EVBest = =MAX(E5:E7)

13 EVPI = =E11-E12

14

Kelly Construction


16/27

A newsvendor can buy the Wall Street Journalnewspapers for 40 cents each and sell them for 75cents.

However, he must buy the papers before he knowshow many he can actually sell. If he buys morepapers than he can sell, he disposes of the excess atno additional cost. If he does not buy enoughpapers, he loses potential sales now and possibly inthe future.

Suppose that the loss of future sales is captured by aloss of goodwill cost of 50 cents per unsatisfiedcustomer.

The Newsvendor ModelThe Newsvendor Model


17/27

The demand distribution is as follows:

P0 = Prob{demand = 0} = 0.1




Each of these four values represent the states ofnature. The number of papers ordered is the decision.The returns or payoffs are as follows:


18/27

State of Nature (Demand)

0 1 2 3Decision

0 0 -50 -100 -150

1 -40 35 -15 -65

2 -80 -5 70 20

3 -120 -45 30 105

Payoff = 75(# papers sold) 40(# papers ordered) 50(unmet demand)

Where 75 = selling price40 = cost of buying a paper

50 = cost of loss of goodwill


19/27

Now, the ER is calculated for each decision:

State of Nature (Demand)

0 1 2 3Decision

0 0 -50 -100 -150 -85

1 -40 35 -15 -65 -12.5

2 -80 -5 70 20 22.5

3 -120 -45 30 105 7.5

ER

Prob. 0.1 0.3 0.4 0.2

ER1 = -40(0.1) + 35(0.3) 15(0.4) 65(0.2) = -12.5

ER2 = -80(0.1) 5(0.3) + 70(0.4) + 20(0.2) = 22.5

ER3 = -120(0.1) 45(0.3) + 30(0.4) 105(0.2) = 7.5

ER0

= 0(0.1) 50(0.3) 100(0.4) 150(0.2) = -85

Of these four ERs,

choose the maximum,

and order 2 papers


20/27

ER(new) = 0(0.1) + 35(0.3) + 70(0.4) + 105(0.2)

State of Nature

0 1 2 3Decision

0 0 -50 -100 -1501 -40 35 -15 -65

2 -80 -5 70 20

3 -120 -45 30 105Prob. 0.1 0.3 0.4 0.2

= 59.5

ER(current) = 22.5

EVPI = 59.5 22.5 = 37.0 cents


21/27

The decision that yields the maxmaximum of these maxmaximum

returns (maximax) is then selected.

This method evaluates each decision by the maximummaximum

possible return associated with that decision.

Maximax Criterion:Maximax Criterion: The Maximax criterion is anoptimistic decision making criterion.


22/27

Then, the decision that yields the maxmaximum value of theminminimum returns (maximin) is selected.

Maximin Criterion:Maximin Criterion: The Maximin criterion is anextremely conservative, or pessimistic, approach to

making decisions.

Maximin evaluates each decision by the minimumminimum possible

return associated with the decision.


23/27

So, using the 3 criteria, we made the followingdecisions regarding the newsvendor data:

CriteriaCriteria DecisionDecision

Maximin Cash Flow Order 1 paper

Expected Return Order 2 papers

Maximax Cash Flow Order 3 papers


24/27

Most people are riskrisk--averseaverse, which means theywould feel that the loss of a certain amount of

money would be more painful than the gain ofthe same amount of money.

Utility functionsUtility functions in decision analysis measure theattractiveness of money.

Utility can be thought of as a measure ofsatisfaction.

THE RATIONALE FOR UTILITYTHE RATIONALE FOR UTILITY


25/27

Utility

1.00.9100.8500.775

0.680

0.524

100 200 300 400 500 600 Dollars

Typical risk-averse utility function:

Go from $400 to

$500 results in

A gainin

utilityof 0.06


26/27

To illustrate, first suppose you have $100 and someonegives you an additional $100. Note that your utility

increases by

U(200) U(100) = 0.680 0.524 = 0.156

Now suppose you start with $400 and someone gives youan additional $100. Now your utility increases by

U(500) U(400) = 0.910 0.850 = 0.060

This illustrates that an additional $100 is less attractive ifyou have $400 on hand than it is if you start with $100.


27/27

Utilities and Decisions under RiskUtilities and Decisions under Risk

Summary:Summary:

UtilityUtility is a way to incorporate risk aversion into theexpected return calculation.

Calculating a utility function is out of the scope ofthis course, but it can be calculated by a series oflottery questions (e.g., Would you prefer one milliondollars or a 50% chance of earning five million?).

Business Analysis- Decision Analysis

Documents