### Chap 12

```Decision Analysis
Chapter 12
12-1
Chapter Topics
■ Components of Decision Making
■ Decision Making without Probabilities
■ Decision Making with Probabilities
■ Decision Analysis with Additional Information
■ Utility
12-2
Decision Analysis
Overview
 Previous chapters used an assumption of certainty with regards to
problem parameters.
 This chapter relaxes the certainty assumption
 Two categories of decision situations:
 Probabilities can be assigned to future occurrences
 Probabilities cannot be assigned to future occurrences
12-3
Decision Analysis
Components of Decision Making
■ A state of nature is an actual event that may occur in the future.
■ A payoff table is a means of organizing a decision situation,
presenting the payoffs from different decisions given the various
states of nature.
Table 12.1 Payoff table
12-4
Decision Analysis
Decision Making Without Probabilities
Figure 12.1 Decision
situation with real estate
investment alternatives
12-5
Decision Analysis
Decision Making without Probabilities
Table 12.2 Payoff table for the real estate investments
Decision-Making Criteria
maximax
maximin
minimax
minimax regret
Hurwicz
equal likelihood
12-6
Decision Making without Probabilities
Maximax Criterion
In the maximax criterion the decision maker selects the decision
that will result in the maximum of maximum payoffs; an
optimistic criterion.
Table 12.3
Payoff table illustrating a maximax decision
12-7
Decision Making without Probabilities
Maximin Criterion
In the maximin criterion the decision maker selects the decision
that will reflect the maximum of the minimum payoffs; a
pessimistic criterion.
Table 12.4 Payoff table illustrating a maximin decision
12-8
Decision Making without Probabilities
Minimax Regret Criterion
 Regret is the difference between the payoff from the best
decision and all other decision payoffs.
 Example: under the Good Economic Conditions state of nature,
the best payoff is \$100,000. The manager’s regret for choosing
the Warehouse alternative is \$100,000-\$30,000=\$70,000
Table 12.5 Regret table
12-9
Decision Making without Probabilities
Minimax Regret Criterion
 The manager calculates regrets for all alternatives under each
state of nature. Then the manager identifies the maximum
regret for each alternative.
 Finally, the manager attempts to avoid regret by selecting the
decision alternative that minimizes the maximum regret.
Table 12.6
Regret table illustrating the minimax regret decision
12-10
Decision Making without Probabilities
Hurwicz Criterion
 The Hurwicz criterion is a compromise between the maximax
and maximin criteria.
 A coefficient of optimism, , is a measure of the decision
maker’s optimism.
 The Hurwicz criterion multiplies the best payoff by  and the
worst payoff by 1- , for each decision, and the best result is
selected. Here,  = 0.4.
Decision
Apartment building
Values
\$50,000(.4) + 30,000(.6) = 38,000
Office building
\$100,000(.4) - 40,000(.6) = 16,000
Warehouse
\$30,000(.4) + 10,000(.6) = 18,000
12-11
Decision Making without Probabilities
Equal Likelihood Criterion
The equal likelihood ( or Laplace) criterion multiplies the
decision payoff for each state of nature by an equal weight, thus
assuming that the states of nature are equally likely to occur.
Decision
Apartment building
Values
\$50,000(.5) + 30,000(.5) = 40,000
Office building
\$100,000(.5) - 40,000(.5) = 30,000
Warehouse
\$30,000(.5) + 10,000(.5) = 20,000
12-12
Decision Making without Probabilities
Summary of Criteria Results
■ A dominant decision is one that has a better payoff than another
decision under each state of nature.
■ The appropriate criterion is dependent on the “risk” personality
and philosophy of the decision maker.
Criterion
Decision (Purchase)
Maximax
Office building
Maximin
Apartment building
Minimax regret
Apartment building
Hurwicz
Apartment building
Equal likelihood
Apartment building
12-13
Decision Making without Probabilities
Solution with QM for Windows (1 of 3)
Exhibit 12.1
12-14
Decision Making without Probabilities
Solution with QM for Windows (2 of 3)
Equal likelihood weight
Exhibit 12.2
12-15
Decision Making without Probabilities
Solution with QM for Windows (3 of 3)
Exhibit 12.3
12-16
Decision Making without Probabilities
Solution with Excel
=MIN(C7,D7)
=MAX(E7,E9)
=MAX(F7:F9)
=MAX(C18,D18)
=MAX(C7:C9)-C9
=C7*C25+D7*C26
=C7*0.5+D7*0.5
Exhibit 12.4
12-17
Decision Making with Probabilities
Expected Value
 Expected value is computed by multiplying each decision
outcome under each state of nature by the probability of its
occurrence.
Table 12.7 Payoff table with probabilities for states of nature
EV(Apartment) = \$50,000(.6) + 30,000(.4) = \$42,000
EV(Office) = \$100,000(.6) - 40,000(.4) = \$44,000
EV(Warehouse) = \$30,000(.6) + 10,000(.4) = \$22,000
12-18
Decision Making with Probabilities
Expected Opportunity Loss
■ The expected opportunity loss is the expected value of the
regret for each decision.
■ The expected value and expected opportunity loss criterion
result in the same decision.
EOL(Apartment) = \$50,000(.6) + 0(.4) = 30,000
EOL(Office) = \$0(.6) + 70,000(.4) = 28,000
EOL(Warehouse) = \$70,000(.6) + 20,000(.4) = 50,000
Table 12.8 Regret table with probabilities for states of nature
12-19
Expected Value Problems
Solution with QM for Windows
Expected values
Exhibit 12.5
12-20
Expected Value Problems
Solution with Excel and Excel QM (1 of 2)
Expected value for
apartment building
Exhibit 12.6
12-21
Expected Value Problems
Solution with Excel and Excel QM (2 of 2)
Exhibit 12.7
12-22
Decision Making with Probabilities
Expected Value of Perfect Information
■ The expected value of perfect information (EVPI) is the
maximum amount a decision maker would pay for additional
information.
■ EVPI equals the expected value given perfect information
minus the expected value without perfect information.
■ EVPI equals the expected opportunity loss (EOL) for the best
decision.
12-23
Decision Making with Probabilities
EVPI Example (1 of 2)
Table 12.9 Payoff table with decisions, given perfect information
12-24
Decision Making with Probabilities
EVPI Example (2 of 2)
■ Decision with perfect information:
\$100,000(.60) + 30,000(.40) = \$72,000
■ Decision without perfect information:
EV(office) = \$100,000(.60) - 40,000(.40) = \$44,000
EVPI = \$72,000 - 44,000 = \$28,000
EOL(office) = \$0(.60) + 70,000(.4) = \$28,000
12-25
Decision Making with Probabilities
EVPI with QM for Windows
The expected value, given
perfect information, in Cell F12
=MAX(E7:E9)
=F12-F11
Exhibit 12.8
12-26
Decision Making with Probabilities
Decision Trees (1 of 4)
A decision tree is a diagram consisting of decision nodes
(represented as squares), probability nodes (circles), and
decision alternatives (branches).
Table 12.10 Payoff table for real estate investment example
12-27
Decision Making with Probabilities
Decision Trees (2 of 4)
Figure 12.2 Decision tree for real estate investment example
12-28
Decision Making with Probabilities
Decision Trees (3 of 4)
■ The expected value is computed at each probability node:
EV(node 2) = .60(\$50,000) + .40(30,000) = \$42,000
EV(node 3) = .60(\$100,000) + .40(-40,000) = \$44,000
EV(node 4) = .60(\$30,000) + .40(10,000) = \$22,000
■ Branches with the greatest expected value are selected.