DECISION ANALYSIS WITH SAMPLE INFORMATION

Vaibhav Agrawal – 06Devanshi Dhruva – 15RV Kartik – 40Aniket Sengar - 47

PROBLEM FORMULATION

First step in decision analysis is Problem Formulation.

Verbal Statement

Uncertain future events referred to as chance events

The outcome referred to as consequence

2 possible chance event outcomes are considered – strong demand and weak demand.

The possible outcome for a chance event are referred to as the states of nature.

PDC Ltd. purchased a land that will be the site of a new luxury condominium

complex. PDC plans to price the individual condominium units between

$300,000 and $1,400,000.

PDC commissioned preliminary architectural drawings for three different -

sized projects: one with 30 condominiums, one with 60 condominiums, and

one with 90 condominiums. The financial success of the project depends

upon the size of the condominium complex and the chance event concerning

the demand for the condominiums.

The statement of the PDC decision problem is to select the size of the new

luxury condominium project that will lead to the largest profit given the

uncertainty concerning the demand for the condominiums.

Decision Alternatives:

D1 – a small complex with 30 condominiumsD2 – a medium complex with 60 condominiumsD3 – a large complex with 90 condominiums

States of Nature

S1 – strong demand for the condominiumsS2 – weak demand for the condominiums

Influence Diagrams

Complex Size Profit

Demand

It is a graphical device that shows the relationship among the decisions, the chance events and the consequence.

Decision Nodes – Rectangle or SquaresChance Nodes – Circles or OvalsConsequence – DiamondsArcs – Connecting Nodes

Payoff Table

State Of Nature

Decision Alternative Strong Demand (S1) Weak Demand (S2)

Small Complex, D1 8 7

Medium Complex, D2

14 5

Large Complex, D3 20 -9

The consequence resulting from a specific combination of a decision alternative and a state of nature is referred to as Payoff.

Decision TreesA Decision Tree provides a graphical representation of the decision making process. It shows the natural or logical progression that will

occur overtime.

Strong (S1)

Weak (S2)

Strong (S1)

Weak (S2)

Strong (S1)

Weak (S2)

8

7

14

-9

5

20

1 3

2

4

Small (D1)

Medium (D2)

Large (D3)

Decision Making without Probabilities

Optimistic Approach

Mini-Max Regret Approach

Conservative Approach

Best Payoff

Opportunity Loss

Worst Payoff

Optimistic Approach Best Payoff

Decision Alternative Maximum Payoff

Small Complex (d1) 8

Medium Complex (d2) 14

Large Complex (d3) 20

Conservative Approach Worst Payoff

Decision Alternative Minimum Payoff

Small Complex (d1) 7

Medium Complex (d2) 5

Large Complex (d3) -9

Mini-Max Regret Approach Opportunity Loss

Rij = |V*j – Vij|

Decision Alternatives Strong Demand s1 Weak Demand s2

Small Complex, d1 12 (20-8) 0 (7-7)

Medium Complex, d2 6 (20-14) 2 (7-5)

Large Complex, d3 0 (20-20) 16 [7-(-9)]

Decision Alternatives Maximum Regret

Small Complex, d1 12

Medium Complex, d2 6

Large Complex, d3 16

Decision Making with Probabilities

N = Number of states of natureP(sj) = Profitability of state of nature j.

P(sj) >= 0, for all states of nature

ΣNj=1P(sj) = P(s1) + P(s2) + … + P(sN) = 1

Expected Value Approach

Expected Value of a Decision Alternative EV(di) = ΣNj=1P(sj) Vij

Expected Value of Perfect Information

To determine the potential value of the information, we begin by supposing that study could provide perfect information about states of nature, that is, we assume for a moment with certainty that, prior to the decision making

which state of nature is going to occur

EVPI=|EVwPI-EVwoPI|EVPI=expected value of perfect information

EVwPI=Expected value with perfect information about the states of natureEVPwoPI = Expected value without perfect information about the states of

nature

Expected Value of Perfect Information

If s1 would occur then, we will select d3 and receive a payoff of $20 million

If s2 would occur then, we will select d1 and receive a payoff of $7 million

Risk Analysis

• Risk analysis helps the decision maker recognize the difference b/w the expected value of a decision alternative and payoff that might actually occur.

-9 200

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Probability

Probability

Sensitivity Analysis

• It is used to determine how changes in probabilities for the states of nature or changes in payoffs affect the recommended decision.

• It helps decision maker to understand which of the inputs are critical to the choice of best alternative decision.

EV(d1) .2(8) + .8(7) =7.2

EV(d2) .2(14) + .8(5) =6.8

EV(d3) .2(20) + .8(-9) =-3.2

INFLUENCE DIAGRAM

RESERCH STUDY RESULTS

DEMAND

PROFITCOMPLEX SIZE

RESEARCH STUDY

DECISION TREE

1

2

3

4

5

6

7

8

9

10

11

12

13

14

MARKET RESEARCH

NO MARKET RESEARCH

FAVOURABLE0.23

UNFAVOURABLE .77

SMALL

MEDIUM

LARGE

SMALL

MEDIUM

LARGE

SMALL

MEDIUM

LARGE

STRONG .94

WEAK .06

STRONG .94

STRONG .94

STRONG .35

STRONG .35

STRONG .35

STRONG .8

STRONG .8

STRONG .8

WEAK .06

WEAK .06

WEAK .65

WEAK .65

WEAK .65

WEAK .2

WEAK .2

WEAK .2

• EV(node 6)=.94*8+.06*7=7.94• EV(node 7)=.94*14+.06*5=13.46• EV(node 8)=.94*20+.06*-9=18.26• EV(node 9)=.35*8+.65*7=7.35• EV(node 10)=.35*14+.65*5=8.15• EV(node 11)=.35*20+.65*-9=1.15• EV(node 12)=.80*8+.20*7=7.8• EV(node 13)=.80*14+.20*5=12.2• EV(node 14)=.80*20+.20*-9=14.2

• =>EV(node 2)=.77EV(node 3)+.23EV(node 4)=.77*18.26+.23*8.15=15.93

• Expected value of sample information

EVSI=mod[EVwSI-EVwoSI]

EVwSI-expected value with sample information

EVwoSI-expected value without sample information

=15.93-14.2=1.73• Efficiency of sample information

E=(EVSI/EVPI)*100

EVPI-expected value with perfect information

=(1.73/3)*100=54.1%

EXPECTED VALUE AND EFFICIENCY

Thank you