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A rundown of various quantitative techniques that assist in business decision making.
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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