Unit 4
Impaler_2019
Stevenson_CH05Supp_Accessible.pptxSupplement 5
Decision Theory
© McGraw-Hill Education. All rights reserved. Authorized only for instructor use in the classroom. No reproduction or further distribution permitted without the prior written consent of McGraw-Hill Education.
1
Learning Objectives
You should be able to:
5S.1 Outline the steps in the decision process
5S.2 Name some causes of poor decisions
5S.3 Describe and use techniques that apply to decision making under uncertainty
5S.4 Describe and use the expected-value approach
5S.5 Construct a decision tree and use it to analyze a problem
5S.6 Compute the expected value of perfect information
5S.7 Conduct sensitivity analysis on a simple decision problem
5S-‹#›
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Decision Theory
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
5S-‹#›
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Characteristics of Suitable Problems
Characteristics of decisions that are suitable for using decision theory
A set of possible future conditions that will have a bearing on the results of the decision
A list of alternatives from which to choose
A known payoff for each alternative under each possible future condition
5S-‹#›
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Learning Objective 5S.1
Process for Using Decision Theory
Identify the possible future states of nature
Develop a list of possible alternatives
Estimate the payoff for each alternative for each possible future state of nature
If possible, estimate the likelihood of each possible future state of nature
Evaluate alternatives according to some decision criterion and select the best alternative
5S-‹#›
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Learning Objective 5S.1
Payoff Table (1 of 2)
A table showing the expected payoffs for each alternative in every possible state of nature
| Alternatives | Possible Future Demand: Low | Possible Future Demand: Moderate | Possible Future Demand: High |
| Small facility | $10 | $10 | $10 |
| Medium facility | 7 | 12 | 12 |
| Large facility | (4) | 2 | 16 |
5S-‹#›
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Learning Objective 5S.1
Payoff Table (2 of 2)
A decision is being made concerning which size facility should be constructed
The present value (in millions) for each alternative under each state of nature is expressed in the body of the above payoff table
5S-‹#›
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Learning Objective 5S.1
Decision Process
Steps:
Identify the problem
Specify objectives and criteria for a solution
Develop suitable alternatives
Analyze and compare alternatives
Select the best alternative
Implement the solution
Monitor to see that the desired result is achieved
5S-‹#›
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Learning Objective 5S.2
Causes of Poor Decisions
Decisions occasionally turn out poorly due to unforeseeable circumstances; however, this is not the norm
More frequently poor decisions are the result of a combination of
Mistakes in the decision process
Bounded rationality
Suboptimization
5S-‹#›
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Learning Objective 5S.2
Mistakes in the Decision Process
Errors in the Decision Process
Failure to recognize the importance of each step
Skipping a step
Failure to complete a step before jumping to the next step
Failure to admit mistakes
Inability to make a decision
5S-‹#›
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Learning Objective 5S.2
Bounded Rationality & Suboptimization
Bounded rationality
The limitations on decision making caused by costs, human abilities, time, technology, and availability of information
Suboptimization
The results of different departments each attempting to reach a solution that is optimum for that department
5S-‹#›
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Learning Objective 5S.3
Decision Environments
There are three general environment categories:
Certainty
Environment in which relevant parameters have known values
Risk
Environment in which certain future events have probabilistic outcomes
Uncertainty
Environment in which it is impossible to assess the likelihood of various possible future events
5S-‹#›
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Learning Objective 5S.3
Decision Making Under Uncertainty
Decisions are sometimes made under complete uncertainty: No information is available on how likely the various states of nature are.
Decision criteria:
Maximin
Choose the alternative with the best of the worst possible payoffs
Maximax
Choose the alternative with the best possible payoff
Laplace
Choose the alternative with the best average payoff
Minimax regret
Choose the alternative that has the least of the worst regrets
5S-‹#›
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Learning Objective 5S.3
Example – Maximin Criterion
| Alternatives | Possible Future Demand: Low | Possible Future Demand: Moderate | Possible Future Demand: High |
| Small Facility | $10 | $10 | $10 |
| Medium Facility | 7 | 12 | 12 |
| Large Facility | (4) | 2 | 16 |
The worst payoff for each alternative is
Small facility: $10 million
Medium facility: $7 million
Large facility: -$4 million
Choose to construct a small facility
5S-‹#›
© McGraw-Hill Education.
Learning Objective 5S.3
Example – Maximax Criterion
| Alternatives | Possible Future Demand: Low | Possible Future Demand: Moderate | Possible Future Demand: High |
| Small Facility | $10 | $10 | $10 |
| Medium Facility | 7 | 12 | 12 |
| Large Facility | (4) | 2 | 16 |
The best payoff for each alternative is
Small facility: $10 million
Medium facility: $12 million
Large facility: $16 million
Choose to construct a large facility
5S-‹#›
© McGraw-Hill Education.
Learning Objective 5S.3
Example – Laplace Criterion
| Alternatives | Possible Future Demand: Low | Possible Future Demand: Moderate | Possible Future Demand: High |
| Small Facility | $10 | $10 | $10 |
| Medium Facility | 7 | 12 | 12 |
| Large Facility | (4) | 2 | 16 |
The average payoff for each alternative is
Small facility: (10+10+10)/3 = $10 million
Medium facility: (7+12+12)/3 = $10.33 million
Large facility: (-4+2+16)/3 = $4.67 million
Choose to construct a medium facility
5S-‹#›
© McGraw-Hill Education.
Learning Objective 5S.3
Example – Minimax Regret (1 of 2)
| Alternatives | Possible Future Demand: Low | Possible Future Demand: Moderate | Possible Future Demand: High |
| Small Facility | $10 | $10 | $10 |
| Medium Facility | 7 | 12 | 12 |
| Large Facility | (4) | 2 | 16 |
Construct a regret (or opportunity loss) table
The difference between a given payoff and the best payoff for a state of nature
5S-‹#›
© McGraw-Hill Education.
Learning Objective 5S.3
Example – Minimax Regret (2 of 2)
| Alternatives | Regrets: Low | Regrets: Moderate | Regrets: High |
| Small Facility | $0 | $2 | $6 |
| Medium Facility | 3 | 0 | 4 |
| Large Facility | 14 | 10 | 0 |
Identify the worst regret for each alternative
Small facility: $6 million
Medium facility: $4 million
Large facility: $14 million
Select the alternative with the minimum of the maximum regrets
Build a medium facility
5S-‹#›
© McGraw-Hill Education.
Learning Objective 5S.4
Decision Making Under Risk
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)
EMV
Determine 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
5S-‹#›
© McGraw-Hill Education.
Learning Objective 5S.4
Example – EMV
| Alternatives | Possible Future Demand: Low (.30) | Possible Future Demand: Moderate (.50) | Possible Future Demand: Moderate (.20) |
| Small Facility | $10 | $10 | $10 |
| Medium Facility | 7 | 12 | 12 |
| Large Facility | (4) | 2 | 16 |
Build a medium facility
5S-‹#›
© McGraw-Hill Education.
Learning Objective 5S.5
Decision Tree (1 of 2)
Decision tree
A schematic representation of the available alternatives and their possible consequences
Useful for analyzing sequential decisions
Composed of
Nodes
Decisions – represented by square nodes
Chance events – represented by circular nodes
Branches
Alternatives – branches leaving a square node
Chance events – branches leaving a circular node
5S-‹#›
© McGraw-Hill Education.
Learning Objective 5S.5
Decision Tree (2 of 2)
Analyze from right to left
For each decision, choose the alternative that will yield the greatest return
If chance events follow a decision, choose the alternative that has the highest expected monetary value (or lowest expected cost)
5S-‹#›
© McGraw-Hill Education.
Learning Objective 5S.5
Example – Decision Tree (1 of 3)
A manager must decide on the size of a video arcade to construct. The manager has narrowed the choices to two: large or small. Information has been collected on payoffs, and a decision tree has been constructed. Analyze the decision tree and determine which initial alternative (build small or build large) should be chosen in order to maximize expected monetary value.
5S-‹#›
© McGraw-Hill Education.
Learning Objective 5S.5
Example – Decision Tree (2 of 3)
5S-‹#›
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Learning Objective 5S.5
Example – Decision Tree (3 of 3)
Build the large facility
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Learning Objective 5S.6
Expected Value of Perfect Information
Expected value of perfect information (EVPI)
The difference between the expected payoff with perfect information and the expected payoff under risk
Two methods for calculating EVPI
EVPI = expected payoff under certainty – expected payoff under risk
EVPI = minimum expected regret
5S-‹#›
© McGraw-Hill Education.
Learning Objective 5S.6
Example – EVPI (1 of 4)
| Alternatives | Possible Future Demand: Low (.30) | Possible Future Demand: Moderate (.50) | Possible Future Demand: Moderate (.20) |
| Small Facility | $10 | $10 | $10 |
| Medium Facility | 7 | 12 | 12 |
| Large Facility | (4) | 2 | 16 |
5S-‹#›
© McGraw-Hill Education.
Learning Objective 5S.6
Example – EVPI (2 of 4)
You would be willing to spend up to $1.7 million to obtain perfect information
5S-‹#›
© McGraw-Hill Education.
Learning Objective 5S.6
Example – EVPI (3 of 4)
| Alternatives | Possible Future Demand: Low (.30) | Possible Future Demand: Moderate (.50) | Possible Future Demand: Moderate (.20) |
| Small Facility | $0 | $2 | $6 |
| Medium Facility | 3 | 0 | 4 |
| Large Facility | 14 | 10 | 0 |
5S-‹#›
© McGraw-Hill Education.
Learning Objective 5S.6
Example – EVPI (4 of 4)
The minimum EOL is associated with the building the medium size facility. This is equal to the EVPI, $1.7 million.
5S-‹#›
© McGraw-Hill Education.
Learning Objective 5S.7
Sensitivity Analysis (1 of 2)
Sensitivity analysis
Determining the range of probability for which an alternative has the best expected payoff
The approach illustrated is useful when there are two states of nature
It involves constructing a graph and then using algebra to determine a range of probabilities over which a given solution is best
5S-‹#›
© McGraw-Hill Education.
Learning Objective 5S.7
Sensitivity Analysis (2 of 2)
| Alternative | State of Nature: #1 | State of Nature: #2 | Slope | Equation |
| A | 4 | 12 | 12 – 4 = +8 | 4 + 8P(2) |
| B | 16 | 2 | 2 – 16 = -14 | 16 – 14P(2) |
| C | 12 | 8 | 8 - 12 = -4 | 12 – 4P(2) |
5S-‹#›
© McGraw-Hill Education.
End of Presentation
© McGraw-Hill Education. All rights reserved. Authorized only for instructor use in the classroom. No reproduction or further distribution permitted without the prior written consent of McGraw-Hill Education.
5S-‹#›
$3
.20(16)
.50(2)
.30(-4)
large
EMV
10.5
.20(12)
.50(12)
.30(7)
medium
EMV
10
.20(10)
.50(10)
.30(10)
small
EMV
=
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$62
.60(70)
.40(50)
Large
EV
$49
.60(55)
.40(40)
Small
EV
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$1.7
10.5
–
$12.2
EMV
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EV
EVPI
$10.5
EMV
$12.2
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.50(12)
.30(10)
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perfect
with
EV
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=
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$9.2
.20(0)
.50(10)
.30(14)
Large
EOL
$1.7
.20(4)
.50(0)
.30(3)
Medium
EOL
$2.2
.20(6)
.50(2)
.30(0)
Small
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Loss
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Opportunit
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