BU.520.601
DecisionAnalysis 1
BU.520.601 Decision Models
Decision Analysis
Summer 2013
BU.520.601DecisionAnalysis 2
Let us flip a fair coin 1000 (there is a fee).If you win a toss, I give you $102. If I win, you give me $100.How much fee will you pay for the playing the entire game?
Let us flip a fair coin once (there is a fee).If you win I give you $102. If I win, you give me $100.How much fee will you pay me for playing the game: $5, $2,
$1, $0? You can select any other amount.
Suppose you are getting ready to go the office in a crowded metro. Carrying an umbrella is a hassle; you will carry it only when you feel necessary. Forecast for today is 70% chance of rain and the sky is overcast. Should you carry an umbrella - Yes or no?
My decision would be “Yes” and it is a good decision.
However, there are two possible outcomes - it will rain or not.
If it does not rain, it does not mean I have made a bad decision.
BU.520.601DecisionAnalysis 3
Decision Analysis (DA)Decision Analysis (DA)
• DA is a methodology applicable to analyze a wide variety of problems.
• Although DA was used in the 1950s (at Du Pont) and early 1960s (at Pillsbury), major DA development took place in mid sixties. One of the earliest application (at GE) was to analyze whether a super heater should be added to the current power reactor.
• DA has been considered as a technology to assist (individuals and) organizations in decision making by quantifying the considerations (even though they may be subjective) to deduce logical actions.
BU.520.601DecisionAnalysis 4
Decision Analysis (DA)Decision Analysis (DA)One can discuss many topics listed below; we will look at a few.• Problem Formulation.• Decision Making with / without Probabilities.• Risk Analysis and Sensitivity Analysis.• Decision Analysis with Sample / Perfect Information.• Multistage decision making.
Tools and terminology• Basic statistics and probability• Influence diagram / payoff table /
decision tree• EMV: Expected Monetary Value • EVSI / EVPI : Expected Value of
Sample / Perfect Information
• Bayes’ rule• Decision vs. outcome• Risk management• Minimax / maximin /• Utility theory
BU.520.601DecisionAnalysis 5
Decision analysis without probabilitiesDecision analysis without probabilities
Alternatives Economic Condition
Recession Normal Boom
Project A 4075 5000 6100Project B 0 5250 12080Project C 2500 7000 10375Project D 1500 6000 9500
Example: There are four projects; I can select only one. The payoff table shows potential “payoff” depending upon likely economic conditions.
Concepts covered: Payoff table.Different approaches: Maximax, maximin, minimax regret
Since the payoff in project C is higher than the payoff for D for every economic condition, we say that project C is dominant.
We can eliminate project D from consideration.
BU.520.601DecisionAnalysis 6
MaximaxMaximax
Alternatives Economic Condition
Recession Normal Boom
Project A 4075 5000 6100Project B 0 5250 12080Project C 2500 7000 10375
If you are an optimist, you will decide on the basis of Maximax.
Step 1: Pick the max value for each alternative.
6100
12080
10375
Step 2:Then pick the alternative with max payoff.
BU.520.601DecisionAnalysis 7
MaximinMaximin
Alternatives Economic Condition
Recession Normal Boom
Project A 4075 5000 6100Project B 0 5250 12080Project C 2500 7000 10375
1: Pick the min value for each alternative.
4075
0
2500
If you are a conservative you will use Maximin.
2: Then pick the alternative with max payoff.
BU.520.601DecisionAnalysis 8
Alternatives Regret Table
Recession Normal Boom
Project A 0 2000 5980Project B 4075 1750 0Project C 1575 0 1705
Minimax RegretMinimax Regret
Alternatives Economic Condition
Recession Normal Boom
Project A 4075 5000 6100Project B 0 5250 12080Project C 2500 7000 10375
You are neither optimist nor conservative.
Step 1: Calculate the maximum for each outcome.
4075| 7000| 12080
Stet 2: Prepare “Regret Table” by subtracting each outcome cell value from its maximum.
At least one number for each regret table outcome is zero and there
are no negative numbers. Why?
BU.520.601DecisionAnalysis 9
Alternatives Regret Table
Recession Normal Boom
Project A 0 2000 5980Project B 4075 1750 0Project C 1575 0 1705
Minimax Regret..Minimax Regret..
Alternatives Economic Condition
Recession Normal Boom
Project A 4075 5000 6100Project B 0 5250 12080Project C 2500 7000 10375
Step 3: Pick the max value for each alternative.
5980
4075
1705
Step 4: Pick the alternative with minimum regret.
4075| 7000| 12080
BU.520.601DecisionAnalysis 10
General commentsGeneral comments
The above three approaches we used involved Decision Making without Probabilities.
Table columns show outcomes (also called
state of nature).
Payoff tableAlternatives Economic Condition
Recession Normal Boom
Project A 4075 5000 6100Project B 0 5250 12080Project C 2500 7000 10375
• The maximax payoff criterion seeks the largest of the maximum payoffs among the actions.
• The maximin payoff criterion seeks the largest of the minimum
payoffs among the actions. • The minimax regret criterion seeks the smallest of the
maximum regrets among the actions.
BU.520.601DecisionAnalysis 11
Decisionpoint
Decision analysis with probabilitiesDecision analysis with probabilities
Typically, we use a tree diagram for the decision analysis.1. A decision point is shown by a rectangle
20%55%
25% Chance events must be mutually exclusive and exhaustive (total probability = 1).
4. At the end of each branch is an endpoint shown as a triangle where a payoff will be identified.
2. Alternatives available at a decision point are shown as decision branches (DB).
3. At the end of each DB, there can be two or more chance events shown by a node and chance branches (CB).
CB
DB
BU.520.601DecisionAnalysis 12
Decision analysis with probabilitiesDecision analysis with probabilities
At the chance node, we calculate the average (i.e. expected) payoff. The terminology used is Expected Monetary Value (EMV)
Decision point: Chance event : End point:DB: Decision Branch CB: Chance Branch
If there is no chance event for a particular decision branch, it’s EMV is equal to the payoff. 20%
55%
25%
DB
CB
We select the decision with the highest EMV .
What if we are dealing with costs?
BU.520.601DecisionAnalysis 13
A larger tree diagramA larger tree diagram
BU.520.601DecisionAnalysis 14
You bought 500 units of X @$10 each.
Demand: X 300 400 500 600Pr(X) 0.30 0.45 0.20 0.05
Obviously, if demand exceeds 500, you will sell all 500. On the other hand, if demand is under 500, you will have leftover units. These leftover items can disposed off for $7 each ($3 loss, the dealer will no longer buy these leftover units from you).
You can sell these yourself for $16 each ($6/unit profit) but the demand is uncertain. The demand distribution is shown in the table.
A dealer has offered to buy these from you @$14 each ( you can make $4/unit profit).
What’s your decision?
Example 1Example 1
BU.520.601DecisionAnalysis 15
Suppose you have 500 units of X in stock, purchased for $10 each. Dealer sales price:$14, self sale price:$16 with salvage value:$7.
Demand: X 300 400 500 600Pr(X) 0.30 0.45 0.20 0.05
DealerSale
Self sale
Example 1 ..Example 1 ..
Start with the tree having 2 branches (DB) at the decision point. There are no chance events in the dealer sale branch,
500, 20%
600, 5%
400, 45%300, 30%
For the self sale, there are 4 mutually exclusive possibilities.
BU.520.601DecisionAnalysis 16
Suppose you have 500 units of X in stock, purchased for $10 each. Dealer sales price:$14, self sale price:$16 with salvage value:$7.
Demand: X 300 400 500 600Pr(X) 0.30 0.45 0.20 0.05
Example 1 ...Example 1 ...
DealerSale
Self sale500, 20%
600, 5%
400, 45%300, 30%
Payoff = 500*4 = 2000 EMV = 2000
Payoff = 300*6 – 200*3 = 1200
Payoff = 400*6 – 100*3 = 2100
Payoff = 500*6 = 3000
Payoff = 500*6 = 3000 EMV = 0.3*1200 + 0.45*2100 + 0.2* 3000 + 0.05*3000 = 2055
Your decision?
BU.520.601DecisionAnalysis 17
Risk ProfileRisk Profile
Payoff = 1200
Payoff = 2100
Payoff = 3000
Payoff = 3000
Self Sale300
400
500
600
20%
5%
45%
30%
Risk profile is the probability distribution for the payoff associated with a particular action.
The risk profile shows all the possible economic outcomes and provides the probability of each: it is a probability distribution for the principal output of the model.
BU.520.601DecisionAnalysis 18
Example 3Example 3
We have received RFP (Request For Proposal).• We may not want to bid at all (our cost: 0)• If we bid, we will have to spend $5k for proposal preparation.
Based on the information provided in the RFP, a quick decision is to bid either $115k or $120k or $125k.
We must select among 4 alternatives (including no bid).
• A quick estimate of the cost of the project (in addition to the preparation cost) is $95k.
• Looks like we may have a competitor. • If we bid the same amount as the competitor, we will get the
project because of our reputation with the client.• We have gathered some probabilities based on past experience.
BU.520.601DecisionAnalysis 19
Our bid (OB) must be 0 (no bid), 115, 120 or 125.
Competitor’s bid (CB): 0, under 115, 115 to under 120, 120 to under 125, 125 and over.
Assumption: If bids are equal, we get the contract.
Information : Preparation cost: $5 + Cost of work : $95 = $100 total
Profit for our bid
0 115 120 125
All numbers in thousand dollars
Use mini-max, maxi-max, etc?
There are probabilities involved.
Example 3..Example 3..
Competitor’s bid
1. No bid
2a. Under $115
2b. $115 to under $120
2c. $120 to under $125
2d. Over $125
00000
15-5151515
20-5-52020
25-5-5-525
BU.520.601DecisionAnalysis 20
1. There is a 30% probability that the competitor will not bid.
2. If the competitor does bid, there is
(a) 20% probability of bid under $115.
(b) 40% probability of bid $115 to under $120.
(c) 30% probability of bid under $120 to under $125.
(d) 10% probability of bid over $125.
Example 3…Example 3…
Prob.
-
20%
40%
30%
10%
Prob.
30%
70%
Profit for our bid
Competitor’s bid 0 115 120 1251. No bid 0 15 20 25
2a. Under $115 0 -5 -5 -5
2b. $115 to under $120 0 15 -5 -5
2c. $120 to under $125 0 15 20 -5
2d. Over $125 0 15 20 25
Actual Prob.
30%
14%
28%
21%
7%
BU.520.601DecisionAnalysis 21
Example 3:Example 3: Profit for our bid
Competitor 0 115 120 1251. No bid 0 15 20 25
2a. < $115 0 -5 -5 -5
2b. $115 to < $120 0 15 -5 -5
2c. $120 to < $125 0 15 20 -5
2d. > $125 0 15 20 25
Actual Prob.
30%
14%
28%
21%
7%
$0
No bid
bid
$115 Win
Lose Payoff = (-5), Probability 14%
Payoff = 15, Probability 86%
(-5)*(0.14) + 15 * (0.86) = $12.2
BU.520.601DecisionAnalysis 22
Profit for our bid
Competitor 0 115 120 1251. No bid 0 15 20 25
2a. < $115 0 -5 -5 -5
2b. $115 to < $120 0 15 -5 -5
2c. $120 to < $125 0 15 20 -5
2d. > $125 0 15 20 25
Example 3:Example 3: Actual Prob.
30%
14%
28%
21%
7%
20, 58%
-5, 42%
25, 37%
-5, 63%
15, 86%
-5, 14%
Bid $120
Bid $115
Bid= $125
L
W
L
W
L
W
No bid
$0
$9.5
$6.1
$12.2 Our decision?
We will now use Excel to solve the problem.
BU.520.601DecisionAnalysis 23
Ex. 3: ExcelEx. 3: Excel =SUMPRODUCT(Profit_bid_115,Probabilities)
=MAX(D9:G9)INDEX+MATCH
HLOOKUP ?
Value we are looking (12.2) is not in the ascending order in the table.
BU.520.601DecisionAnalysis 24
Example 3: Sensitivity analysisExample 3: Sensitivity analysis
What if 30% probability of no bid from competitor is incorrect?
We can build a one variable data table. Variable: Competitor’s no bid probability.
We select two outputs: bid and (corresponding maximum) profit.
BU.520.601DecisionAnalysis 25
Profit for our bid
Competitor’s bid 0 115 120 1251. No bid 0 15 20 25
2a. Under $115 0 -5 -5 -5
2b. $115 to under $120 0 15 -5 -5
2c. $120 to under $125 0 15 20 -5
2d. Over $125 0 15 20 25
Ex. 3: DA and value of informationEx. 3: DA and value of information
Our decision was to bid $115 and EMV was $12.2. Suppose we get competitor’s bid information. Can we improve our profit?
What is the probability?
Earned Value of Perfect Information (EVPI) = $17.65 – $12.2 = $5.45
EMV = 0.3*25+0.14*0+0.28*15+0.21*20+0.07*25 = 17.65
0.300.7 * 0.2 = 0.140.7 * 0.4 = 0.280.7 * 0.3 = 0.210.7 * 0.1 = 0.07
Sometimes we may have partial information.
BU.520.601DecisionAnalysis 26
$0
No bid
OB= $115
$15-$5
$15 $15 $15
OB= $120
OB= $125
CB=0
CB
30%
70%
15(.3)+11(.7) = $12.2
30%
70%
$20
$5$9.5
30%
70%
$25
-$2$6.1
<115115 to <120
120 to < 125>125
30%10%
40%20%
EMV Payoff
-5(.2)+15(.4+.3+.1) = $11
bid$12.2Our
decision
Example 3: Alternate methodExample 3: Alternate method
BU.520.601DecisionAnalysis 27
Values 12.2, 9.5 and 6.1 represent Expected Monetary Values (EMV).
This line indicates the decision made.
This is called folding back the decision tree.
$0OB= $115
OB= $125
$12.2
$9.5
$6.1
bid$12.2
OB= $120
No bid
Example 3…..Example 3…..
BU.520.601DecisionAnalysis 28
Utility theoryUtility theoryConsider the gambling
problems again.– Let us flip a fair coin once.– If you win I give you $102– If I win, you give me $100– How much will you pay me
to play this game: $5, $2, $1, $0 ?
Consider another gamble– Let us flip the same coin
(500 times) with the same payoffs
– How much will you pay me to play this game?
• Different people will pay different amounts to play the first game
Expected payoff in the first game is $1 but most people do not want to play the game at all.
Why? Losing $100 is a bigger event than winning $102
• Most people will play the second game.
Still differ in how much they will pay.
• For most people a gain that is twice as big is not twice as good.
• A loss of twice as much is more than twice as bad.
• People’s attitude towards risk can be categorized as: risk averse, risk seeker and risk neutral.
• A common way to express it is through the decision-maker’s utility function.
BU.520.601DecisionAnalysis 29
0 100 0 100 0 100
U(100)
U(0)
U(100)
U(0)
U(100)
U(0)
0 100 0 100 0 100
U(100)
U(0)
U(100)
U(0)
U(100)
U(0)
Risk seeker Risk averse Risk neutral
Utility is a measure of relative satisfaction. We can plot a graph of amount of money spent vs. “utility” on a 0 to 100 scale. Typical shapes for different types of risk takers generally follow the patterns shown below.
Graphs above show that to achieve 50% utility, risk seekers will pay maximum, risk averse will pay minimum and risk neutral will pay an average amount.
Top Related