Decision Analysis Part 1

1
Decision AnalysisPart 1
Graduate Program in Business Information Systems
Asli Sencer Erdem
2
References

• 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.

3

• The business executive is by profession a
  decision maker.
• Uncertainty is his opponent.
• Overcoming it is his mission.
• John McDonald

4
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

5
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

6
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

7
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

8
The Decision-Making Process
9
Displaying a Decision Problem

• Decision trees
• Decision tables

10
Types of Decision Models

• Decision making under uncertainty
• Decision making under risk
• Decision making under certainty

11
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

12
Decision Table
States of Nature
State 1
State 2
Alternatives
Outcome 1
Outcome 2
Alternative 1
Outcome 3
Outcome 4
Alternative 2
13
Getz Products Decision Tree
14
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.

15
Example
16
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.

17
Decision Making under Risk

• Probabilistic decision situation
• States of nature have probabilities of occurrence
• Maximum Likelihood Criterion
• Maximize Expected Monitary Value (Bayes Decision
  Rule)

18
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.

19
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?

20
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.

21
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, i1,2,...,k
and j1,2,...,N. Pj Probability of state of
nature j
22
Example
23
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

24
Questions

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

25
Expected Value With Perfect Information (EVPI)

• EVPI Expected Payoff - Maximum expected
  payoff
• under Certainty (with no information)

Maximum expected payoffMax EMVi i1,..,k

• EVPI places an upper bound on what one would pay
  for
• additional information

26
Example Expected Value of Perfect Information
Favorable Market ()
Unfavorable Market ()
EMV
Construct a large plant
10,000
200,000
-180,000
Construct a small plant
40,000
100,000
-20,000
Do nothing
0
0
0
0.50
0.50
27
Expected Value of Perfect Information

• EVPI
• expected value - max(EMV)
• under certainty
• (200,0000.50 00.50)
• - 40,000
• 60,000
• So Getz should not be willing to pay more than
  60,000

28
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)

29
Payoff Table
30
Maximum Expected Payoff Criteria
Maximum expected payoff occurs at Spring Action!
31
Opportunity Loss

• Opportunity Loss of an act for a given event
• Best Payoff - Payoff for the
• for the event chosen act

32
Opportunity Loss Table
33
Expected Opportunity Loss
34
Similarly,
Minimum Expected Opportunity Loss occurs at
Spring Action!
35
Bayes Decision Rule

• Maximize expected payoff criteria and
• Minimize expected opportunity loss criteria
  always suggest the same decision!

36
Decision Trees

• 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.

37
Softwares for Decision Tree Analysis

• DPL
• Tree Plan
• Supertree
• Analysis with less effort.
• Full color presentations for managers

38
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

39
Decision Tree
40
Ex1Getz Products Decision Tree
Payoffs 200,000 -180,000 100,000 -20,000 0
41
A More Complex Decision Tree

• Lets say Getz Products has two sequential
  decisions to make
• Conduct a survey for 10000?
• Build a large or small plant or not build?

42
Ex1Getz Products Decision Tree
190,000 -190,000 90,000 -30,000 -10,000
49,200
190,000 -190,000 90,000 -30,000 -10,000
200,000 -180,000 100,000 -20,000 -0,000
43
Resulting Decision

• EMV of conducting the survey49,200
• EMV of not conducting the survey40,000
• So Getz should conduct the survey!
• If the survey results are favourable, build
  large plant.
• If the survey results are infavourable, build
  small plant.

44
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 45000 units nationally
• Alternative2 Market 50000 units nationally
• Outcome is a complete success (all are sold) or
  failure

45
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 cds 5,0005,000(0.250.
  75)5,00015,000
• Cost of producing 45,000 cds
• 05,000(0.250.75)45,00050,000
• Cost of producing 50,000 cds
• 5,0005,000(0.250.75)50,00060,000

46
Ex2 Ponderosa-Event Probabilities

• Without testing P(success)P(failure)0.5
• With testing
• P(successtest result is favorable)0.8
• P(failuretest result is favorable)0.2
• P(successtest result is unfavorable)0.2
• P(failuretest result is unfavorable)0.8

47
Decision Tree for Ponderosa Record Company
48
Backward Approach
49
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

50
Risk Profilefor Ponderosa Record Co.
51
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)?

52
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.