decision analysis decision trees n.
Download
Skip this Video
Loading SlideShow in 5 Seconds..
Decision Analysis (Decision Trees ) PowerPoint Presentation
Download Presentation
Decision Analysis (Decision Trees )

Loading in 2 Seconds...

play fullscreen
1 / 21

Decision Analysis (Decision Trees ) - PowerPoint PPT Presentation


  • 131 Views
  • Uploaded on

Decision Analysis (Decision Trees ). Y. İlker TOPCU , Ph .D. www.ilkertopcu. net www. ilkertopcu .org www. ilkertopcu . info www. facebook .com/ yitopcu twitter .com/ yitopcu. Decision Trees. A decision tree is a diagram consisting of decision nodes (squares)

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about 'Decision Analysis (Decision Trees )' - mireya


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
decision analysis decision trees

Decision Analysis(Decision Trees)

Y. İlker TOPCU, Ph.D.

www.ilkertopcu.net www.ilkertopcu.org www.ilkertopcu.info

www.facebook.com/yitopcu

twitter.com/yitopcu

decision trees
Decision Trees
  • A decision tree is a diagram consisting of
    • decision nodes (squares)
    • chance nodes (circles)
    • decision branches (alternatives)
    • chance branches (state of natures)
    • terminal nodes (payoffsorutilities)
decision tree method
Decision Tree Method
  • Define the problem
  • Structure / draw the decision tree
  • Assign probabilities to the states of nature
  • Calculate expected payoff (or utility) for the corresponding chance node – backward, computation
  • Assign expected payoff (or utility) for the corresponding decision node – backward, comparison
  • Represent the recommendation
example 1
Example 1

A chancenode

Favorable market(0.6)

$200,000

1

Unfav. market(0.4)

Constructlargeplant

-$180,000

A decisonnode

Favorable market(0.6)

$100,000

Constructsmallplant

2

Unfav. market

(0.4)

-$20,000

Do nothing

$0

slide6

A chancenode

Favorable market(0.6)

$200,000

1

Unfav. market(0.4)

EV =

$48,000

Constructlargeplant

-$180,000

A decisonnode

Favorable market(0.6)

$100,000

Constructsmallplant

2

Unfav. market

(0.4)

EV =

$52,000

-$20,000

Do nothing

$0

example 2
Example 2

184

220

130

%60

%60

%60

186

210

%40

%40

%40

150

170

162

150

sequential decision tree
Sequential Decision Tree
  • A sequential decision tree is used to illustrate a situation requiring a series of decisions (multi-stage decision making) and it is used where a payoff matrix (limited to a single-stage decision) cannot be used
example 3
Example 3
  • Let’s say that DM has two decisions to make, with the second decision dependent on the outcome of the first.
  • Before deciding about building a new plant, DM has the option of conducting his own marketing research survey, at a cost of $10,000.
  • The information from his survey could help him decide whether to construct a large plant, a small plant, or not to build at all.
slide10
Before survey, DM believes that the probability of a favorable market is exactly the same as the probability of an unfavorable market: each state of nature has a 50% probability
  • There is a 45% chance that the survey results will indicate a favorable market
  • Such a market survey will not provide DM with perfect information, but it may help quite a bit nevertheless by conditional (posterior) probabilities:
    • 78% is the probability of a favorable market given a favorable result from the market survey
    • 27% is the probability of a favorable market given a negative result from the market survey
example 4
Example 4
  • A manager has to decide whether to market a new product nationally and whether to test market the product prior to the national campaign.
  • The costs of test marketing and national campaign are respectively $20,000 and $100,000.
  • Their payoffs are respectively $40,000 and $400,000.
  • A priori, the probability of the new product's success is 50%.
  • If the test market succeeds, the probability of the national campaign's success is improved to 80%.
  • If the test marketing fails, the success probability of the national campaign decreases to 10%.
slide14

[240]

S(.8)

320

C

[240]

F(.2)

~C

S(.5)

-80

20

[110]

S(.1)

[-80]

280

F(.5)

T

[-20]

F(.9)

C

[110]

-120

~C

~T

-20

[100]

[100]

C

S(.5)

300

~C

F(.5)

-100

0

expected value of sample information
Expected Value of Sample Information

EVSI

= EV of best decision withsample information, assuming no cost to gather it

– EV of best decision without sample information

= EV with sample info. + cost – EV without sample info.

DM could pay up to EVSI for a survey.

If the cost of the survey is less than EVSI, it is indeed worthwhile.

In the example:

EVSI = $49,200 + $10,000 – $40,000 = $19,200

estimating probability values by bayesian analysis
Estimating Probability Values by Bayesian Analysis

Bayes Theorem

Posterior

probabilities

Prior

probabilities

New data

  • Management experience or intuition
  • History
  • Existing data
  • Need to be able to reviseprobabilities based upon new data
bayesian analysis
Bayesian Analysis

Example:

  • Market research specialists have told DM that, statistically, of all new products with a favorable market, market surveys were positive and predicted success correctly 70% of the time.
  • 30% of the time the surveys falsely predicted negative result
  • On the other hand, when there was actually an unfavorable market for a new product, 80% of the surveys correctly predicted the negative results.
  • The surveys incorrectly predicted positive results the remaining 20% of the time.
market survey reliability
Market Survey Reliability

Actual States of Nature

Result of Survey

Favorable

Unfavorable

Market (FM)

Market (UM)

(survey positive|FM)

(survey positive|UM)

Positive (predicts

P

P

= 0.70

=

0.20

favorable market

for product)

(survey

(survey negative|UM)

Negative (predicts

P

P

negative|FM) = 0.30

= 0.80

unfavorable

market for

product)

calculating posterior probabilities
Calculating Posterior Probabilities

P(BA) P(A)

P(AB) =

P(BA) P(A) + P(BA’) P(A’)

where A and B are any two events, A’ is the complement of A

P(FMsurvey positive) =

[P(survey positiveFM)P(FM)] /

[P(survey positiveFM)P(FM) + P(survey positiveUM)P(UM)]

P(UMsurvey positive) =

[P(survey positiveUM)P(UM)] /

[P(survey positiveFM)P(FM) + P(survey positiveUM)P(UM)]

slide20

Probability Revisions Given a Positive Survey

Conditional

Probability

State

P(Survey positive|State of Nature

Prior Probability

Joint Probability

Posterior Probability

of

Nature

0.35

= 0.78

FM

0.70

* 0.50

0.35

0.45

0.10

= 0.22

0.20

0.10

* 0.50

UM

0.45

1.00

0.45

slide21

Probability Revisions Given a Negative Survey

Conditional

Probability

State

P(Survey

Prior Probability

Joint Probability

Posterior Probability

of

negative|State

Nature

of Nature)

0.15

= 0.27

0.15

0.30

* 0.50

FM

0.55

0.40

= 0.73

0.40

UM

0.80

* 0.50

0.55

0.55

1.00