Operations Management. Source of reference Operations Management by Stevenson, 10e.

1. CHAPTER
Supplement to
5
Decision Theory
Prepared by:
Group 2 / BA 10 / G
4:00PM – 5:15PM / C507
Copyright © 2009 The McGraw – Hill Companies, Inc. Publishing as McGraw – Hill / Irwin ￭ Operations Management ￭ Stevenson, 10e.

2. 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 expectedvalue approach.
Copyright © 2009 The McGraw – Hill Companies, Inc. Publishing as McGraw – Hill / Irwin ￭ Operations Management ￭ Stevenson, 10e.

3. 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.

4. 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
Copyright © 2009 The McGraw – Hill Companies, Inc. Publishing as McGraw – Hill / Irwin ￭ Operations Management ￭ Stevenson, 10e.

5. Decision Theory characterized as follows:
Set of
future
conditions
Decision
Theory
Known
payoff
alternatives
List of
alternatives
Copyright © 2009 The McGraw – Hill Companies, Inc. Publishing as McGraw – Hill / Irwin ￭ Operations Management ￭ Stevenson, 10e.

6. To use this approach, a decision maker
would employ this process:
Step 1
Identify
possible
future
conditions
or state of
nature
Step 2
Develop a
list of
possible
alternatives
Step 3
Determine
the payoff
associated
with each
alternative
for every
possible
future
condition
Step 4
Estimate
the
likelihood of
each
possible
future
conditions
Step 5
Evaluate
alternatives
based to
some
decision
criterion,
and select
the best
alternative
Copyright © 2009 The McGraw – Hill Companies, Inc. Publishing as McGraw – Hill / Irwin ￭ Operations Management ￭ Stevenson, 10e.

7. The information for a decision is often
summarized in a payoff table.
Payoff Table
Table showing the expected payoffs for each
alternative in every possible state of nature.
Copyright © 2009 The McGraw – Hill Companies, Inc. Publishing as McGraw – Hill / Irwin ￭ Operations Management ￭ Stevenson, 10e.

8. Payoff Table:
Example 1.0
POSSIBLE FUTURE
DEMAND
Alternatives
Small Facility
Medium Facility
Large Facility
Low
Moderate
$10*
$10
7
(4)
12
2
High
$10
12
16
*Present value in $ millions.
Copyright © 2009 The McGraw – Hill Companies, Inc. Publishing as McGraw – Hill / Irwin ￭ Operations Management ￭ Stevenson, 10e.

9. Causes for Poor Decisions
Mistakes in decision process
Bounded Rationality
Suboptimization
Copyright © 2009 The McGraw – Hill Companies, Inc. Publishing as McGraw – Hill / Irwin ￭ Operations Management ￭ Stevenson, 10e.

10. 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.
Copyright © 2009 The McGraw – Hill Companies, Inc. Publishing as McGraw – Hill / Irwin ￭ Operations Management ￭ Stevenson, 10e.

11. 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.

12. Copyright © 2009 The McGraw – Hill Companies, Inc. Publishing as McGraw – Hill / Irwin ￭ Operations Management ￭ Stevenson, 10e.

13. Decision Environments
Environment in
which it is
impossible to
asses the
likelihood of
various future
events.
Environment
in which
relevant
parameters
have known
values.
Environment at
which certain
future events have
probable
outcomes.
Risk
Copyright © 2009 The McGraw – Hill Companies, Inc. Publishing as McGraw – Hill / Irwin ￭ Operations Management ￭ Stevenson, 10e.

14. Decision Making Under Certainty
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.
Copyright © 2009 The McGraw – Hill Companies, Inc. Publishing as McGraw – Hill / Irwin ￭ Operations Management ￭ Stevenson, 10e.

15. Decision Making Under Certainty
Example 2.0
POSSIBLE FUTURE
DEMAND
Alternatives
Low
Small Facility
$10*
$10
$10
7
12
12
(4)
2
16
Medium Facility
Large Facility
Moderate
High
*Present value in $ millions.
What will you choose to build if the demand will be
low, moderate and high?
 If the demand will be low, just choose the small facility
with a payoff of $10 Million.
 If the demand is moderate choose to build a medium
facility with a payoff $12 Million.
 If the demand is high just build large facility with a $16
Million.
Copyright © 2009 The McGraw – Hill Companies, Inc. Publishing as McGraw – Hill / Irwin ￭ Operations Management ￭ Stevenson, 10e.

16. Decision Making Under Uncertainty
Decisions 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.
Copyright © 2009 The McGraw – Hill Companies, Inc. Publishing as McGraw – Hill / Irwin ￭ Operations Management ￭ Stevenson, 10e.

17. Decision Making Under Uncertainty
Example 3.1
POSSIBLE FUTURE
DEMAND
Alternatives
Low
Small Facility
$10*
$10
$10
7
12
12
(4)
2
16
Medium Facility
Large Facility
Moderate
High
*Present value in $ millions.
Using the maximin approach what will we choose?
The worst payoffs for the alternatives are:
Small Facility
:
$10 million
Medium Facility
:
7 million
Large Facility
:
(4) million
Hence, since $10 million is the best we choose to build
a small facility.
Copyright © 2009 The McGraw – Hill Companies, Inc. Publishing as McGraw – Hill / Irwin ￭ Operations Management ￭ Stevenson, 10e.

18. Decision Making Under Uncertainty
Example 3.2
POSSIBLE FUTURE
DEMAND
Alternatives
Low
Small Facility
$10*
$10
$10
7
12
12
(4)
2
16
Medium Facility
Large Facility
Moderate
High
*Present value in $ millions.
Using the maximax approach what will we choose?
The best payoffs for the
Small Facility
Medium Facility
Large Facility
alternatives are:
:
$10 million
:
12 million
:
16 million
The best overall payoff is the $16 million on the third
row. Hence, the maximax criterion leads to building a large
facility.
Copyright © 2009 The McGraw – Hill Companies, Inc. Publishing as McGraw – Hill / Irwin ￭ Operations Management ￭ Stevenson, 10e.

19. Decision Making Under Uncertainty
Example 3.3
POSSIBLE FUTURE
DEMAND
Low
Moderate
High
$10*
$10
$10
Alternatives
Small Facility
Medium Facility
7
Large Facility
(4)
*Present value in $ millions.
12
2
12
16
Using the laplace approach what will we choose?
Row in Total Row Average
(in $ Million ) (in $ Million)
$30
$10.00
31
10.33
14
4.67
Because the medium facility
has the highest average, it would
be chosen under the Laplace
criterion.
Copyright © 2009 The McGraw – Hill Companies, Inc. Publishing as McGraw – Hill / Irwin ￭ Operations Management ￭ Stevenson, 10e.

20. Decision Making Under Uncertainty
Example 3.4
POSSIBLE FUTURE
DEMAND
Alternatives
Small Facility
Medium Facility
Large Facility
Low
Moderate
High
$10*
$10
$10
7
12
12
(4)
2
16
*Present value in $ millions.
Using the minimax regret approach what will we choose?
Regrets (in $ Millions)
Alternatives
Low
Moderate
High
Worst
Small Facility
$0
$2
$6
$6
Medium Facility
3
0
4
4
Large Facility
14
10
0
14
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.
Copyright © 2009 The McGraw – Hill Companies, Inc. Publishing as McGraw – Hill / Irwin ￭ Operations Management ￭ Stevenson, 10e.

21. 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).
Copyright © 2009 The McGraw – Hill Companies, Inc. Publishing as McGraw – Hill / Irwin ￭ Operations Management ￭ Stevenson, 10e.

22. Decision Making Under Risk
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
Copyright © 2009 The McGraw – Hill Companies, Inc. Publishing as McGraw – Hill / Irwin ￭ Operations Management ￭ Stevenson, 10e.

23. Decision Making Under Risk
Example 4.0
POSSIBLE FUTURE
DEMAND
Alternatives
Low
Small Facility
$10*
$10
$10
7
12
12
(4)
2
16
Medium Facility
Large Facility
Moderate
High
*Present value in $ millions.
Using the EMV criterion, identify the best alternative for these
probabilities: low=.30,moderate=.50 and high=.20.
EVSmall =
EVMedium =
EVLarge =
.30($10)+.50($10)+.20($10) =
.30($7) +.50($12)+.20($12) =
.30($-4) +.50($2) +.20($16) =
$10
$10.5
$3
Hence, choose the medium facility because it has the
highest expected value.
Copyright © 2009 The McGraw – Hill Companies, Inc. Publishing as McGraw – Hill / Irwin ￭ Operations Management ￭ Stevenson, 10e.

24. Decision
Trees
Copyright © 2009 The McGraw – Hill Companies, Inc. Publishing as McGraw – Hill / Irwin ￭ Operations Management ￭ Stevenson, 10e.

25. Decision Trees
Copyright © 2009 The McGraw – Hill Companies, Inc. Publishing as McGraw – Hill / Irwin ￭ Operations Management ￭ Stevenson, 10e.

26. Decision Trees
Example 5.0
Determine the product of the chance probabilities and their respective
payoffs of the branches and the expected value of each initiative:
Copyright © 2009 The McGraw – Hill Companies, Inc. Publishing as McGraw – Hill / Irwin ￭ Operations Management ￭ Stevenson, 10e.

27. Decision Trees
Build Small
Low Demand
High Demand
.4($40) =
.6($55) =
$16
$33
Build Large
Low Demand
High Demand
.4($50) =
.6($70) =
$20
$42
______________________________________________________________________
Build Small
$16 + $33 = $49
Build Large
$20 + $42 = $62
Hence, the choice should be to build the large facility
because it has a larger expected value than the small facility.
Copyright © 2009 The McGraw – Hill Companies, Inc. Publishing as McGraw – Hill / Irwin ￭ Operations Management ￭ Stevenson, 10e.

28. Expected Value of Perfect Information (EVPI)
The difference between the
expected
payoff
with
perfect
information and the expected payoff
under risk.
Copyright © 2009 The McGraw – Hill Companies, Inc. Publishing as McGraw – Hill / Irwin ￭ Operations Management ￭ Stevenson, 10e.

29. Expected Value of Perfect Information (EVPI)
There are two ways to determine EVPI:
Expected
Payoff
Under
Certainty
Expected
Payoff
Under
Risk
EVPI
or
Copyright © 2009 The McGraw – Hill Companies, Inc. Publishing as McGraw – Hill / Irwin ￭ Operations Management ￭ Stevenson, 10e.

30. 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
Copyright © 2009 The McGraw – Hill Companies, Inc. Publishing as McGraw – Hill / Irwin ￭ Operations Management ￭ Stevenson, 10e.

31. 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.

32. Sensitivity Analysis
Copyright © 2009 The McGraw – Hill Companies, Inc. Publishing as McGraw – Hill / Irwin ￭ Operations Management ￭ Stevenson, 10e.

33. Copyright © 2009 The McGraw – Hill Companies, Inc. Publishing as McGraw – Hill / Irwin ￭ Operations Management ￭ Stevenson, 10e.