1. Decision Analysis Part 1
Graduate Program in Business Information Systems
Decision Analysis Part 1
Aslı Sencer

2. Analytical Decision Making
Can Help Managers to:
Gain deeper insight into the nature of business relationships
Find better ways to assess values in such relationships; and
See a way of reducing, or at least understanding, uncertainty that surrounds business plans and actions

3. Steps to Analytical DM Define problem and influencing factors
Establish decision criteria
Select decision-making tool (model)
Identify and evaluate alternatives using decision-making tool (model)
Select best alternative
Implement decision
Evaluate the outcome

4. Models
Are less expensive and disruptive than experimenting with the real world system
Allow operations managers to ask “What if” types of questions
Are built for management problems and encourage management input
Force a consistent and systematic approach to the analysis of problems
Require managers to be specific about constraints and goals relating to a problem
Help reduce the time needed in decision making

5. Limitations of the Models
They may be expensive and time-consuming to develop and test
Often misused and misunderstood (and feared) because of their mathematical and logical complexity
Tend to downplay the role and value of nonquantifiable information
Often have assumptions that oversimplify the variables of the real world

6. The Decision-Making Process
Problem
Decision
Quantitative Analysis
Logic
Historical Data
Marketing Research
Scientific Analysis
Modeling
Qualitative Analysis
Emotions
Intuition
Personal Experience
and Motivation
Rumors

7. Decision trees Decision tables Displaying a Decision Problem Outcomes
Alternatives
States of Nature
Outcomes
Decision trees
Decision tables

8. Types of Decision Models
Decision making under uncertainty
Decision making under risk
Decision making under certainty

9. Fundamentals of Decision Theory
Terms:
Alternative: course of action or choice
State of nature: an occurrence over which the decision maker has no control
Symbols used in a decision tree:
A decision node from which one of several alternatives may be selected
A state of nature node out of which one state of nature will occur

10. Decision Table States of Nature State 1 State 2 Alternatives
Outcome 1
Outcome 2
Alternative 2
Outcome 3
Outcome 4

11. Getz Products Decision Tree1 2
Unfavorable market
Favorable market
Construct small plant
Construct large plant
Do nothing
A decision node
A state of nature node

12. Decision Making under Uncertainty
Maximax - Choose the alternative that maximizes the maximum outcome for every alternative (Optimistic criterion)
Maximin - Choose the alternative that maximizes the minimum outcome for every alternative (Pessimistic criterion)
Equally likely - chose the alternative with the highest average outcome.

13. Example: States of Nature Maximax Maximin Equally likely Favorable
Alternatives
Favorable
Market
Unfavorable
Maximum
in Row
Minimum
Row
Average
Construct
large plant
$200,000 -
$180,000
$10,000
small plant
$100,000
$20,000
$40,000 $0 $
Maximax
Maximin
Equally likely
Do nothing

14. Decision criteria
The maximax choice is to construct a large plant. This is the maximum of the maximum number within each row or alternative.
The maximin choice is to do nothing. This is the maximum of the minimum number within each row or alternative.
The equally likely choice is to construct a small plant. This is the maximum of the average outcomes of each alternative. This approach assumes that all outcomes for any alternative are equally likely.

15. Decision Making under Risk
Probabilistic decision situation
States of nature have probabilities of occurrence
Maximum Likelihood Criterion
Maximize Expected Monitary Value (Bayes Decision Rule)

16. Maximum Likelihood Criteria
Maximum Likelihood: Identify most likely event, ignore others, and pick act with greatest payoff.
Personal decisions are often made that way.
Collectively, other events may be more likely.
Ignores lots of information.

17. Bayes Decision Rule
It is not a perfect criterion because it can lead to the less preferred choice.
Consider the Far-Fetched Lottery decision:
Would you gamble?
EVENTS
Probability
ACTS
Gamble
Don’t Gamble
Head .5
+$10,000 $0
Tail
-5,000

18. The Far-Fetched Lottery Decision
Most people prefer not to gamble!
That violates the Bayes decision rule.
But the rule often indicates preferred choices even though it is not perfect.
EVENTS
Proba-bility
ACTS
Gamble
Don’t Gamble
Payoff × Prob.
Payoff × Prob
Head .5
+$5,000 $0
Tail
-2,500
Expected Payoff:
$2,500

19. Expected Monetary Value
N: Number of states of nature
k: Number of alternative decisions
Xij: Value of Payoff for alternative i in state of nature j, i=1,2,...,k and j=1,2,...,N.
Pj: Probability of state of nature j

20. Example: States of Nature Best choice Favorable Market P(0.5)
Alternatives
Favorable
Market
P(0.5)
Unfavorable
Market P(0.5)
Expected
value
Construct
$200,000
-$180,000
$10,000
small plant
$100,000
-$20,000
$40,000
Do nothing $0
Best choice
large plant

21. Decision Making under Certainty
What if Getz knows the state of the nature with certainty?
Then there is no risk for the state of the nature!
A marketing research company requests $65000 for this information

22. Questions: Should Getz hire the firm to make this study?
How much does this information worth?
What is the value of perfect information?

23. Expected Value With Perfect Information (EVPI)
EVPI = Expected Payoff - Maximum expected payoff
under Certainty with no information
Let N: Number of states of nature and k: Number of actions,
Expected Payoff under Ceratinty=
Maximum expected payoff with no information=Max {EMVi; i=1,..,k}
EVPI places an upper bound on what one would pay for additional information

24. Example: Expected Value of Perfect Information
Favorable Market ($)
Unfavorable Market ($)
EMV
Construct a
large plant
200,000
-$180,000
$10,000
Construct a small plant
$100,000
-$20,000
$40,000
Do nothing $0 $0 $0
0.50
0.50

25. Expected Value of Perfect Information
Expected Value Under Certainty
=($200,000* *0.50)= $100,000
Max(EMV)= Max{10,000, 40,000, 0}=$40,000
EVPI = Expected Value Under Certainty - Max(EMV)
= $100,000 - $40,000
= $60,000
So Getz should not be willing to pay more than $60,000

26. Ex: Toy Manufacturer How to choose among 4 types of tippi-toes?
Demand for tippi-toes is uncertain:
Light demand: 25,000 units (10%)
Moderate demand: 100,000 units (70%)
Heavy demand: 150,000 units (20%)

27. Payoff Table Event ACT (choice) Light 0.10 $25,000 -$10,000 -$125,000
(State of nature)
Probability
ACT (choice)
Gears and levers
Spring Action
Weights and pulleys
Light
0.10
$25,000
-$10,000
-$125,000
Moderate
0.70
400,000
440,000
Heavy
0.20
650,000
740,000
750,000

28. Maximum Expected Payoff Criteria
ACT (choice)
Gears and levers
Spring Action
Weights and pulleys
Expected Payoff
$412,500
$455,500
$417,000
Maximum expected payoff occurs at Spring Action!

29. Decision Trees with one set of alternatives and states of nature.
Graphical display of decision process, i.e., alternatives, states of nature, probabilities, payoffs.
Decision tables are convenient for problems
with one set of alternatives and states of nature.
With several sets of alternatives and states of nature (sequential decisions), decision trees are used!
EMV criterion is the most commonly used criterion in decision tree analysis.

30. Softwares for Decision Tree Analysis
DPL
Tree Plan
Supertree
Analysis with less effort.
Full color presentations for managers

31. Steps of Decision Tree Analysis
Define the problem
Structure or draw the decision tree
Assign probabilities to the states of nature
Estimate payoffs for each possible combination of alternatives and states of nature
Solve the problem by computing expected monetary values for each state-of-nature node

32. Decision Tree 1 2 State 1 State 2 Outcome 1 Outcome 2 Outcome 3
Alternative 1
Alternative 2
Decision Node
Outcome 1
Outcome 2
Outcome 3
Outcome 4
State of Nature Node

33. Ex1:Getz Products Decision Tree
Payoffs
$200,000
-$180,000
$100,000
-20,000 1 2
Unfavorable market (0.5)
Favorable market (0.5)
Construct small plant
Construct large plant
Do nothing
EMV for node 2 = $40,000
EMV for node 1 = $10,000

34. A More Complex Decision Tree
Let’s say Getz Products has two sequential decisions to make:
Conduct a survey for $10000?
Build a large or small plant or not build?

35. Ex1:Getz Products Decision Tree4 7
$49,200
$106,400
$40,000
$2,400 2 3 5 6
$190,000
-$190,000
$90,000
-$30,000
-$10,000
$200,000
-$180,000
$100,000
-$20,000 $0
Survey
No survey
Large plant
Small plant
No plant
Fav. Mkt (0.78)
Fav. Mkt (0.27)
Fav. Mkt (0.5)
Unfav. Mkt (0.22)
Unfav. Mkt (0.73)
Unfav. Mkt (0.5)
$63,600
-$87,400
$10,000
Sur. Res. Neg. (.55)
Sur. Res. Pos. (.45)
1st decision point
2nd decision point
$49,200

36. Resulting Decision EMV of conducting the survey=$49,200
EMV of not conducting the survey=$40,000
So Getz should conduct the survey!
If the survey results are favourable, build large plant.
If the survey results are infavourable, build small plant.

37. Ex2: Ponderosa Record Company
Decide whether or not to market the recordings of a rock group.
Alternative1: test market 5000 units and if favorable, market units nationally
Alternative2: Market units nationally
Outcome is a complete success (all are sold) or failure

38. Ex2: Ponderosa-costs, prices
Fixed payment to group: $5000
Production cost: $5000 and $0.75/cd
Handling, distribution: $0.25/cd
Price of a cd: $2/cd
Cost of producing 5,000 cd’s =5,000+5,000+( )5,000=$15,000
Cost of producing 45,000 cd’s
=0+5,000+( )45,000=$50,000
Cost of producing 50,000 cd’s
=5,000+5,000+( )50,000=$60,000

39. Ex2: Ponderosa-Event Probabilities
Without testing P(success)=P(failure)=0.5
With testing
P(success|test result is favorable)=0.8
P(failure|test result is favorable)=0.2
P(success|test result is unfavorable)=0.2
P(failure|test result is unfavorable)=0.8

40. Decision Tree for Ponderosa Record Company

41. Backward Approach

42. Optimal Decision Policy
Precision Tree provides excell add-ins.
Optimal decision is:
Test market
If the market is favorable, market nationally
Else, abort
Risk Profile
Possible outcomes for the opt. soln.
$35,000 with probability 0.4
-$55,000 with probability 0.1
-$15,000 with probability 0.5

43. Risk Profile for Ponderosa Record Co.

44. Sensitivity Analysis
The optimal solution depends on many factors. Is the optimal policy robust?
Question:
-How does $1000 payoff change with respect to a change in
success probability (0.8 currently)?
earnings of success ($90,000 currently)?
test marketing cost ($15,000 currently)?

45. Application Areas of Decision Theory
Investments in
research and development
plant and equipment
new buildings and structures
Production and Inventory control
Aggregate Planning
Maintenance
Scheduling, etc.

46. References
Lapin L.L., Whisler W.D., Quantitative Decision Making, 7e, 2002.
Heizer J., Render, B., Operations Management, 7e, 2004.
Render, B., Stair R. M., Quantitative Analysis for Management, 8e, 2003.
Anderson, D.R., Sweeney D.J, Williams T.A., Statistics for Business and Economics, 8e, 2002.
Taha, H., Operations Research, 1997.