# Unit 4

Impaler_2019Supplement 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-‹#›

© McGraw-Hill Education.

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-‹#›

© McGraw-Hill Education.

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-‹#›

© McGraw-Hill Education.

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-‹#›

© McGraw-Hill Education.

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-‹#›

© McGraw-Hill Education.

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-‹#›

© McGraw-Hill Education.

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-‹#›

© McGraw-Hill Education.

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-‹#›

© McGraw-Hill Education.

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-‹#›

© McGraw-Hill Education.

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-‹#›

© McGraw-Hill Education.

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-‹#›

© McGraw-Hill Education.

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-‹#›

© McGraw-Hill Education.

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-‹#›

© McGraw-Hill Education.

Learning Objective 5S.5

Example – Decision Tree (3 of 3)

Build the large facility

5S-‹#›

© McGraw-Hill Education.

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

=

+

+

=

=

+

+

=

=

+

+

=

$62

.60(70)

.40(50)

Large

EV

$49

.60(55)

.40(40)

Small

EV

=

+

=

=

+

=

$1.7

10.5

–

$12.2

EMV

–

n

informatio

perfect

with

EV

EVPI

$10.5

EMV

$12.2

.20(16)

.50(12)

.30(10)

n

informatio

perfect

with

EV

=

=

=

=

=

+

+

=

$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

EOL

Loss

y

Opportunit

Expected

=

+

+

=

=

+

+

=

=

+

+

=