Week 3 discussion operation management

Decision Theory

Supplement 5

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You should be able to:

LO 5s.1 Outline the steps in the decision process

LO 5s.2 Name some causes of poor decisions

LO 5s.3 Describe and use techniques that apply to decision making under uncertainty

LO 5s.4 Describe and use the expected-value approach

LO 5s.5 Construct a decision tree and use it to analyze a problem

LO 5s.6 Compute the expected value of perfect information

LO 5s.7 Conduct sensitivity analysis on a simple decision problem

Supplement 5: Learning Objectives

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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

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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

Characteristics of Suitable Problems

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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

Process for Using Decision Theory

LO 5s.1

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Payoff Table

A table showing the expected payoffs for each alternative in every possible state of nature

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

LO 5s.1

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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

Decision Process

LO 5s.1

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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

Causes of Poor Decisions

LO 5s.2

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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

Mistakes in the Decision Process

LO 5s.2

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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

Bounded Rationality & Suboptimization

LO 5s.2

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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

Decision Environments

LO 5s.3

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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

Decision Making Under Uncertainty

LO 5s.3

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Example – Maximin Criterion

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

LO 5s.3

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Example – Maximax Criterion

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

LO 5s.3

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Example – Laplace Criterion

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

LO 5s.3

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Example – Minimax Regret

Construct a regret (or opportunity loss) table

The difference between a given payoff and the best payoff for a state of nature

LO 5s.3

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Example – Minimax Regret

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

LO 5s.3

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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

Decision Making Under Risk

LO 5s.4

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Example – EMV

EMVsmall = .30(10) +.50(10) +.20(10) = 10

EMVmedium = .30(7) + .50(12) + .20(12) = 10.5

EMVlarge = .30(-4) + .50(2) + .20(16) = $3

Build a medium facility

LO 5s.4

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Decision tree

A schematic representation of the available alternatives and their possible consequences

Useful for analyzing sequential decisions

Decision Tree

LO 5s.5

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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

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)

Decision Tree

LO 5s.5

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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.

Example – Decision Tree

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2

2

$40

$40

$50

$55

($10)

$50

$70

Build Small

Low Demand (.40)

Low Demand (.40)

High Demand (.60)

High Demand (.60)

Build Large

Do Nothing

Cut Prices

Do Nothing

Overtime

Expand

LO 5s.5

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Example – Decision Tree

1

2

2

$40

$40

$50

$55

($10)

$50

$70

Build Small

Low Demand (.40)

Low Demand (.40)

High Demand (.60)

High Demand (.60)

Build Large

Do Nothing

Cut Prices

Do Nothing

Overtime

Expand

EVSmall = .40(40) + .60(55) = $49

EVLarge = .40(50) + .60(70) = $62

Build the large facility

LO 5s.5

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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

Expected Value of Perfect Information

LO 5s.6

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Example – EVPI

EVwith perfect information = .30(10) + .50(12) + .20(16) = $12.2

EMV = $10.5

EVPI = EVwith perfect information – EMV

= $12.2 – 10.5

= $1.7

You would be willing to spend up to $1.7 million to obtain perfect information

LO 5s.6

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Example – EVPI

Expected Opportunity Loss

EOLSmall = .30(0) + .50(2) + .20(6) = $2.2

EOLMedium = .30(3) + .50(0) + .20(4) = $1.7

EOLLarge = .30(14) + .50(10) + .20(0) = $9.2

The minimum EOL is associated with the building the medium size facility. This is equal to the EVPI, $1.7 million

LO 5s.6

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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.

Sensitivity Analysis

LO 5s.7

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Sensitivity Analysis

LO 5s.7