decision theory
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CH
AP
TER 5
Decision Theory
Prepared by:Group 2 / BA 10 / G4:00PM – 5:15PM / C507
Copyright © 2009 The McGraw – Hill Companies, Inc. Publishing as McGraw – Hill / Irwin ■ Operations Management ■ Stevenson, 10e.
Supplement to
Decision Theory
Learning Objectives:Describe the different environments
under which operations decisions are made.
Describe and use techniques that apply to decision making under uncertainty.
Describe and use the expected-value approach.
Copyright © 2009 The McGraw – Hill Companies, Inc. Publishing as McGraw – Hill / Irwin ■ Operations Management ■ Stevenson, 10e.
Decision Theory
Learning Objectives:Construct a decision tree and use
it to analyze a problem.Compute the expected value of
perfect information.Conduct sensitivity analysis on a
simple decision problem.
Copyright © 2009 The McGraw – Hill Companies, Inc. Publishing as McGraw – Hill / Irwin ■ Operations Management ■ Stevenson, 10e.
Introduction : Decision Theory
Copyright © 2009 The McGraw – Hill Companies, Inc. Publishing as McGraw – Hill / Irwin ■ Operations Management ■ Stevenson, 10e.
A general approach to decision making that is suitable to a wide range of operations management decisions:
Capacity planning
Product and service
design
Equipment selection
Location planning
Decision Theory
Set of future
conditions
Known payoff
alternatives
List of alternatives
Decision Theory characterized as follows:
Copyright © 2009 The McGraw – Hill Companies, Inc. Publishing as McGraw – Hill / Irwin ■ Operations Management ■ Stevenson, 10e.
Step 1
Identify possible future
conditions or state of
nature
Identify possible future
conditions or state of
nature
Develop a list of
possible alternatives
Develop a list of
possible alternatives
Determine the payoff associated with each alternative for every possible future
condition
Determine the payoff associated with each alternative for every possible future
condition
Estimate the
likelihood of each possible future
conditions
Estimate the
likelihood of each possible future
conditions
Evaluate alternatives
based to some
decision criterion,
and select the best
alternative
Evaluate alternatives
based to some
decision criterion,
and select the best
alternative
To use this approach, a decision maker would employ this process:
Step 5Step 4Step 3Step 2
Copyright © 2009 The McGraw – Hill Companies, Inc. Publishing as McGraw – Hill / Irwin ■ Operations Management ■ Stevenson, 10e.
Copyright © 2009 The McGraw – Hill Companies, Inc. Publishing as McGraw – Hill / Irwin ■ Operations Management ■ Stevenson, 10e.
The information for a decision is often summarized in a payoff table.
Payoff TableTable showing the expected payoffs for each alternative in every possible state of nature.
Payoff Table:Payoff Table:
Copyright © 2009 The McGraw – Hill Companies, Inc. Publishing as McGraw – Hill / Irwin ■ Operations Management ■ Stevenson, 10e.
POSSIBLE FUTURE DEMAND
AlternativesLow Moderat
eHigh
Small Facility $10* $10 $10
Medium Facility 7 12 12
Large Facility (4) 2 16*Present value in $ millions.
Example 1.0
Causes for Poor DecisionsCauses for Poor Decisions
Copyright © 2009 The McGraw – Hill Companies, Inc. Publishing as McGraw – Hill / Irwin ■ Operations Management ■ Stevenson, 10e.
Suboptimization
Bounded Rationality
Mistakes in decision process
Mistakes in Decision Process It happens because of mistakes on the following decisions steps:
Mistakes in Decision Process It happens because of mistakes on the following decisions steps:
Copyright © 2009 The McGraw – Hill Companies, Inc. Publishing as McGraw – Hill / Irwin ■ Operations Management ■ Stevenson, 10e.
1
•Identify the problem.
2
•Specify the objectives and criteria for solution.
3
•Develop suitable alternatives.
4
•Analyze and compare alternatives.
5
•Select the best alternative.
6
•Implement the solution.
7
•Monitor to see that desired result is achieved.
Copyright © 2009 The McGraw – Hill Companies, Inc. Publishing as McGraw – Hill / Irwin ■ Operations Management ■ Stevenson, 10e.
Bounded Rationality
Limitations on decision making caused by costs, human abilities, time, technology, and availability of information.
Because of these limitations, managers can’t always expect to reach decisions that are optimal in the sense of providing the best possible outcome. They might instead, resort to a satisfactory solution.
Copyright © 2009 The McGraw – Hill Companies, Inc. Publishing as McGraw – Hill / Irwin ■ Operations Management ■ Stevenson, 10e.
• Organizations tend to departmentalized decisions and it sometimes falls on suboptimization.
• The result of different departments each attempting to reach a solution that is optimum for that department.
Suboptimization
Uncertainty
Risk
Decision Environments
Environment in which relevant
parameters have known
values.
Environment in which it is impossible to asses the likelihood of various future events.
Environment at which certain
future events have probable
outcomes.
Cer
tain
ty
Copyright © 2009 The McGraw – Hill Companies, Inc. Publishing as McGraw – Hill / Irwin ■ Operations Management ■ Stevenson, 10e.
When it is known for certain which is of the possible future conditions will happen, just choose the alternative that has the best payoff under the state of nature.
Decision Making Under Certainty
Copyright © 2009 The McGraw – Hill Companies, Inc. Publishing as McGraw – Hill / Irwin ■ Operations Management ■ Stevenson, 10e.
Decision Making Under Certainty
POSSIBLE FUTURE DEMAND
Alternatives Low Moderate High
Small Facility $10* $10 $10
Medium Facility 7 12 12
Large Facility (4) 2 16*Present value in $ millions.
If the demand will be low, just choose the small facilitywith a payoff of $10 Million.
If the demand is moderate choose to build a mediumfacility with a payoff $12 Million.
If the demand is high just build large facility with a $16Million.
What will you choose to build if the demand will be low, moderate and high?
Copyright © 2009 The McGraw – Hill Companies, Inc. Publishing as McGraw – Hill / Irwin ■ Operations Management ■ Stevenson, 10e.
Example 2.0
Decision Making Under UncertaintyDecisions are sometimes made under complete
uncertainty. No information is available on how likely the various states of nature are:
Copyright © 2009 The McGraw – Hill Companies, Inc. Publishing as McGraw – Hill / Irwin ■ Operations Management ■ Stevenson, 10e.
Maximin Choose the alternative with the best of the worst possible payoff.
Maximax Choose the alternative with the best possible payoff.Laplace Choose the alternative with the best average period of any of the alternatives.
Minimax Regret Choose the alternative that has the least of worst regrets.
Decision Making Under Uncertainty
POSSIBLE FUTURE DEMAND
Alternatives Low Moderate High
Small Facility $10* $10 $10
Medium Facility 7 12 12
Large Facility (4) 2 16*Present value in $ millions.
The worst payoffs for the alternatives are:Small Facility : $10 millionMedium Facility : 7 millionLarge Facility : (4) million
Hence, since $10 million is the best we choose to build a small facility.
Using the maximin approach what will we choose?
Copyright © 2009 The McGraw – Hill Companies, Inc. Publishing as McGraw – Hill / Irwin ■ Operations Management ■ Stevenson, 10e.
Example 3.1
Decision Making Under Uncertainty
POSSIBLE FUTURE DEMAND
Alternatives Low Moderate High
Small Facility $10* $10 $10
Medium Facility 7 12 12
Large Facility (4) 2 16*Present value in $ millions.
The best payoffs for the alternatives are:Small Facility : $10 millionMedium Facility : 12 millionLarge Facility : 16 million
The best overall payoff is the $16 million on the third row. Hence, the maximax criterion leads to building a large facility.
Using the maximax approach what will we choose?
Copyright © 2009 The McGraw – Hill Companies, Inc. Publishing as McGraw – Hill / Irwin ■ Operations Management ■ Stevenson, 10e.
Example 3.2
Decision Making Under Uncertainty
POSSIBLE FUTURE DEMAND
Alternatives Low Moderate High
Small Facility $10* $10 $10
Medium Facility 7 12 12
Large Facility (4) 2 16
*Present value in $ millions.
Because the medium facility has the highest average, it would be chosen under the Laplace criterion.
Using the laplace approach what will we choose?
Copyright © 2009 The McGraw – Hill Companies, Inc. Publishing as McGraw – Hill / Irwin ■ Operations Management ■ Stevenson, 10e.
Row in Total(in $ Million )
Row Average(in $ Million)
$30 $10.00
31 10.33
14 4.67
Example 3.3
Decision Making Under Uncertainty
POSSIBLE FUTURE DEMAND
Alternatives Low Moderate High
Small Facility $10* $10 $10
Medium Facility 7 12 12
Large Facility (4) 2 16
*Present value in $ millions.
The best of these worst regrets would be chosen using a minimax regret. The lowest regret is 4, which is for medium facility, Hence, it would be chosen.
Using the minimax regret approach what will we choose?
Copyright © 2009 The McGraw – Hill Companies, Inc. Publishing as McGraw – Hill / Irwin ■ Operations Management ■ Stevenson, 10e.
Regrets (in $ Millions)
Alternatives Low Moderate High WorstSmall Facility $0 $2 $6 $6Medium Facility 3 0 4 4Large Facility 14 10 0 14
Example 3.4
Decision Making Under Risk
Copyright © 2009 The McGraw – Hill Companies, Inc. Publishing as McGraw – Hill / Irwin ■ Operations Management ■ Stevenson, 10e.
Decisions made under the condition that the probability of occurrence for each state of nature can be estimated
A widely applied criterion is expected monetary value (EMV).
Decision Making Under Risk
Copyright © 2009 The McGraw – Hill Companies, Inc. Publishing as McGraw – Hill / Irwin ■ Operations Management ■ Stevenson, 10e.
EMVDetermine the expected payoff of each alternative, and choose the alternative that has the best expected payoff
This approach is most appropriate when the decision maker is neither risk averse nor risk seeking
Decision Making Under Risk
POSSIBLE FUTURE DEMAND
Alternatives Low Moderate High
Small Facility $10* $10 $10
Medium Facility 7 12 12
Large Facility (4) 2 16*Present value in $ millions.
EVSmall = .30($10)+.50($10)+.20($10) =$10EVMedium = .30($7) +.50($12)+.20($12) =$10.5EVLarge = .30($-4) +.50($2) +.20($16) = $3
Hence, choose the medium facility because it has the highest expected value.
Using the EMV criterion, identify the best alternative for theseprobabilities: low=.30,moderate=.50 and high=.20.
Copyright © 2009 The McGraw – Hill Companies, Inc. Publishing as McGraw – Hill / Irwin ■ Operations Management ■ Stevenson, 10e.
Example 4.0
A schematic representation of the available alternatives and their possible consequences
Useful for analyzing sequential decisions
Composed of Nodes and Branches
Copyright © 2009 The McGraw – Hill Companies, Inc. Publishing as McGraw – Hill / Irwin ■ Operations Management ■ Stevenson, 10e.
Decision Trees
Decision Trees
Copyright © 2009 The McGraw – Hill Companies, Inc. Publishing as McGraw – Hill / Irwin ■ Operations Management ■ Stevenson, 10e.
Decision Trees
Copyright © 2009 The McGraw – Hill Companies, Inc. Publishing as McGraw – Hill / Irwin ■ Operations Management ■ Stevenson, 10e.
Determine the product of the chance probabilities and their respective payoffs of the branches and the expected value of each initiative:
Example 5.0
Decision Trees
Copyright © 2009 The McGraw – Hill Companies, Inc. Publishing as McGraw – Hill / Irwin ■ Operations Management ■ Stevenson, 10e.
Build SmallLow Demand .4($40) = $16High Demand .6($55) = $33
Build LargeLow Demand .4($50) = $20High Demand .6($70) = $42
______________________________________________________________________
Build Small$16 + $33 = $49
Build Large$20 + $42 = $62
Hence, the choice should be to build the large facilitybecause it has a larger expected value than the small facility.
The difference between the expected payoff with perfect information and the expected payoff under risk.
Expected Value of Perfect Information (EVPI)
Copyright © 2009 The McGraw – Hill Companies, Inc. Publishing as McGraw – Hill / Irwin ■ Operations Management ■ Stevenson, 10e.
Expected Payoff Under
Certainty
Expected Payoff Under
RiskEVPI
Copyright © 2009 The McGraw – Hill Companies, Inc. Publishing as McGraw – Hill / Irwin ■ Operations Management ■ Stevenson, 10e.
Expected Value of Perfect Information (EVPI)
There are two ways to determine EVPI:
orEVPI = Minimax Regret
Copyright © 2009 The McGraw – Hill Companies, Inc. Publishing as McGraw – Hill / Irwin ■ Operations Management ■ Stevenson, 10e.
Expected Value of Perfect Information (EVPI)Example 6.1 (Using the first method)
.30($10) + .50($12) + .20($16) = $12.2
The expected payoff risk based on Example 4.0 is $10.5.
EVPI = $12.2 - $10.5 = $1.7
Expected Value of Perfect Information (EVPI)Example 6.2 (Using the second method)
Using the table of regrets in Example 3.4, we can compute the expected regret for each alternative. Thus:
Small Facility .30(0) + .50(2) + .20(6) = 2.2
Medium Facility .30(3) + .50(0) + .20(4) = 1.7
Large Facility.30(14)+.50(10)+.20(0) = 9.2
The lowest expected regret is 1.7. Therefore, EVPI = 1.7.
Determining the range of probability for which an alternative has the best expected payoff.
Sensitivity Analysis
Copyright © 2009 The McGraw – Hill Companies, Inc. Publishing as McGraw – Hill / Irwin ■ Operations Management ■ Stevenson, 10e.
End of the
Chapter 5’s
Supplement
Copyright © 2009 The McGraw – Hill Companies, Inc. Publishing as McGraw – Hill / Irwin ■ Operations Management ■ Stevenson, 10e.
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