Decision Theory

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.


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.


Introduction : 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

Decision Theory

Set of future

conditions

Known payoff

alternatives

List of alternatives

Decision Theory characterized as follows:


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



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:


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


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:


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.


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.


• 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


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


Decision Making Under Certainty


Alternatives Low Moderate High




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?


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:


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






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?


Example 3.1







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?


Example 3.2






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?


Row in Total(in $ Million )

Row Average(in $ Million)

$30 $10.00

31 10.33

14 4.67

Example 3.3






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?


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


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).



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







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.


Example 4.0

A schematic representation of the available alternatives and their possible consequences

Useful for analyzing sequential decisions

Composed of Nodes and Branches


Decision Trees

Decision Trees


Decision Trees


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


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)


Expected Payoff Under

Certainty

Expected Payoff Under

RiskEVPI


Expected Value of Perfect Information (EVPI)

There are two ways to determine EVPI:

orEVPI = Minimax Regret


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


End of the

Chapter 5’s

Supplement


Business

Decision Theory