Managerial Decision Modeling
with Spreadsheets
Chapter 8
Decision Theory
Learning Objectives
• List steps of decision making process.
• Describe different types of decision making
environments.
• Make decisions under uncertainty when probabilities are
not known.
• Make decisions under risk when probabilities are known.
• Use Excel for problems involving decision tables.
• Develop accurate and useful decision trees.
• Use TreePlan to set up and analyze decision tree
problems with Excel.
• Revise probability estimates using Bayesian analysis.
• Understand the importance and use of utility theory in
decision making.
8.1 Introduction
• Decision theory is analytic and systematic approach to
study of decision-making.
• What makes difference between good and bad
decisions?
• Good decisions may be defined as:
–
–
–
–
Based on logic,
Considered all possible decision alternatives,
Examined all available information about future, and
Applied decision modeling approach.
• Bad decision may be defined as:
–
–
–
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Not based on logic,
Did not use all available information,
Did not consider all alternatives, and
Did not employ appropriate decision modeling techniques.
8.2 Five Steps of Decision Making
1. Clearly define problem at hand.
2. List all possible decision alternatives.
3. Identify possible future outcomes for each decision
alternative.
4. Identify payoff (usually, profit or cost) for each
combination of alternatives and outcomes.
5. Select one of decision theory modeling techniques,
apply decision model, and make decision.
Thompson Lumber Company
Step 1. Identifies problem as:
whether to expand product line by manufacturing and
marketing new product which is “backyard storage
sheds.”
Step 2. Generate decision alternatives available.
Decision alternative is defined as course of action or
strategy that may be chosen by decision maker.
Alternatives are to construct:
(1) large plant to manufacture storage sheds,
(2) small plant to manufacture storage sheds, or
(3) build no plant at all.
Step 3. Identify possible future outcomes of various
alternatives.
Thompson Lumber Company
Step 4. Express payoff resulting from each possible
combination of alternatives and outcomes.
Objective is to maximize profits.
Step 5. Select decision theory model and apply it to
data to help make decision.
Type of decision model available depends on
operating environment and amount of uncertainty and
risk involved.
Thompson Lumber Company
8.3 Types Of Decision Making
Environments
Type 1: Decision Making under Certainty. Decision maker
knows with certainty consequence of every decision alternative.
Type 2: Decision Making under Uncertainty. Decision maker
has no information about various outcomes.
Type 3: Decision Making under Risk. Decision maker has
some knowledge regarding probability of occurrence of each
outcome or state of nature.
Examples:
• Probability of being dealt club from deck of cards is 1/4.
• Probability of rolling 5 on die is 1/6.
8.4 Decision Making Under Uncertainty
• Criteria for making decisions under uncertainty.
1. Maximax.
2. Maximin.
3. Equally likely.
4. Criterion of realism.
5. Minimax regret.
• First four criteria calculated directly from decision
payoff table.
• Fifth minimax regret criterion requires use of
opportunity loss table.
Maximax Criterion
• Maximax criterion selects alternative maximizes
maximum payoff over all alternatives.
• First locate maximum payoff for each alternative.
• Select alternative with maximum number.
• Decision criterion locates alternative with highest
possible gain.
• Called optimistic criterion.
• Table shows maximax choice is first alternative:
"construct large plant."
• $200,000 payoff is maximum of maximum payoffs
for each decision alternative.
Maximax Criterion
Thompson Lumber Company
• Maximax criterion selects alternative that maximizes
maximum payoff over all alternatives.
• First alternative, "construct a large plant”, $200,000 payoff is
maximum of maximum payoffs for each decision alternative.
Maximin Criterion
• Maximin criterion finds alternative maximizes
minimum payoff over all alternatives.
• First locate minimum payoff for each alternative.
• Select alternative with maximum number.
• Decision criterion locates alternative that has least
possible loss.
• Called pessimistic criterion.
• Maximin choice, "do nothing," is shown in table.
• $0 payoff is maximum of minimum payoffs for each
alternative.
Maximin Criterion
Thompson Lumber Company
• Maximin criterion finds alternative maximizes minimum
payoff over all alternatives.
• First locate minimum payoff for each alternative, and select
alternative with maximum number.
Equally Likely (Laplace) Criterion
Thompson Lumber Company:
• Equally likely, also called Laplace, criterion finds
decision alternative with highest average payoff.
• Calculate average payoff for every alternative.
• Pick alternative with maximum average payoff.
• Assumes all probabilities of occurrence for states of
nature are equal.
• Equally likely choice is second alternative, "construct
a small plant."
• Strategy shown in table has maximum average payoff
($40,000) over all alternatives.
Equally Likely (Laplace) Criterion
Thompson Lumber Company
• Equally likely criterion finds decision alternative with highest
average payoff.
• Calculate average payoff for every alternative.
• Pick alternative with maximum average payoff.
Criterion of Realism (Hurwicz)
• Often called weighted average, the criterion of
realism (or Hurwicz) decision criterion is
compromise between optimistic and pessimistic
decision.
• Select coefficient of realism, a, with value between 0
and 1.
– When a is close to 1, decision maker is optimistic
about future.
– When a is close to 0, decision maker is pessimistic
about future.
Criterion of Realism
Formula for criterion of realism =
a x (maximum payoff for alternative) +
(1-a) x (minimum payoff for alternative)
• Assume coefficient of realism a = 0.80.
• Best decision would be to construct a large plant.
• Alternative has highest weighted average payoff:
$124,000 = (0.80)($200,000) + (0.20)(- $180,000).
Criterion of Realism
Thompson Lumber Company
Coefficient of realism a = 0.80.
$124,000 = (0.80)($200,000) + (0.20)(- $180,000).
Minimax Regret Criterion
• Final decision criterion is based on opportunity loss.
• Opportunity loss, also called regret, is difference
between optimal payoff and actual payoff received.
• Develop opportunity loss table.
• Determine opportunity loss of not choosing best
alternative for each state of nature.
• Opportunity loss for any state of nature, or any
column, calculated by subtracting each outcome in
column from best outcome in same column.
Minimax Regret Criterion
Thompson Lumber Company
• Best outcome for favorable market is $200,000 as
result of first alternative, "construct a large plant."
• Subtract all payoffs in column from $200,000.
• Best outcome for unfavorable market is $0 as result
of third alternative, "do nothing."
• Subtract all payoffs in column from $0.
• Table illustrates computations and shows complete
opportunity loss table.
Minimax Regret Criterion
Thompson Lumber Company
• Table illustrates computations and shows complete opportunity
loss table.
Minimax Regret Criterion
Thompson Lumber Company
• Once opportunity loss table has been constructed, locate
maximum opportunity loss within each alternative.
• Pick alternative with minimum number.
• Minimax regret choice is second alternative, "construct a
small plant." Regret of $100,000 is minimum of maximum
regrets over all alternatives.
8.5 Decision Making Under Risk
• Common for decision maker to have some idea about
probabilities of occurrence of different outcomes or
states of nature.
• Probabilities may be based on decision maker’s
personal opinions about future events, or on data
obtained from market surveys, expert opinions, etc.
• When probability of occurrence of each state of nature
can be assessed, problem environment is called
decision making under risk.
Expected Monetary Value
• Given decision table with conditional values (payoffs) and
probability assessments, determine expected monetary value
(EMV) for each alternative.
• Computed as weighted average of all possible payoffs for
alternative, where weights are probabilities of different states
of nature:
EMV (alternative i) =
(payoff of first state of nature) x (probability of first
state of nature) +
(payoff of second state of nature) x (probability of second
state of nature) + . . . +
(payoff of last state of nature) x (probability of last
state of nature)
Expected Monetary Value
Thompson Lumber Company
• Probability of favorable market is same as probability of
unfavorable market.
• Each state of nature has a 0.50 probability.
Expected Opportunity Loss
• Alternative approach in decision making under risk is to
minimize expected opportunity loss (EOL).
• Opportunity loss, also called regret, refers to difference
between optimal profit or payoff and actual payoff received.
• EOL for an alternative is sum of all possible regrets of
alternative, each weighted by probability of state of nature for
that regret occurring.
EOL (alternative i) = (regret of first state of nature)
x (probability of first state of nature)
+ (regret of second state of nature)
x (probability of second state of nature)
+ . . . + (regret of last state of nature)
x (probability of last state of nature)
EOL Decision
Thompson Lumber Company
• EOL values are computed as shown.
• Using minimum EOL as decision criterion, best decision would
be second alternative, "construct a small plant" with an EOL of
$60,000.
• Minimum EOL will always result in same decision alternative
as maximum EMV.
Expected Value of Perfect Information
• Expected value with perfect information is expected or average
return, if one has perfect information before decision has to be
made.
• Choose best alternative for each state of nature and multiply its
payoff times probability of occurrence of that state of nature:
Expected value with perfect information (EV with PI) =
(best payoff for first state of nature)
x (probability of first state of nature)
+ (best payoff for second state of nature)
x (probability of second state of nature)
+ . . . + (best payoff for last state of nature)
x (probability of last state of nature)
EVPI = EV with PI - maximum EMV
EV with PI and EVPI
• Best outcome for state of nature "favorable market" is
"build a large plant" with a payoff of $200,000.
• Best outcome for state of nature "unfavorable market" is
"do nothing," with payoff of $0.
• Expected value with perfect information
(EV with PI) = ($200,000)(0.50) + ($0)(0.50)
= $ 100,000.
• If one had perfect information, an average payoff of
$100,000 if decision could be repeated many times.
• Maximum EMV or expected value without perfect
information, is $40,000.
• EVPI = EV with PI - maximum EMV
= $100,000 - $40,000 = $60,000.
8.6 Decision Trees
• Any problem presented in decision table can be
graphically illustrated in decision tree.
• All decision trees are similar in that they contain
decision nodes (or points) and state of nature nodes
(or points).
• These nodes are represented using following symbols:
 = A decision node.
Arcs (lines) originating from decision node denote all
decision alternatives available at that node.
О = A state of nature (or chance) node.
Arcs (lines) originating from a chance node denote all
states of nature that could occur at that node.
Decision Tree
Thompson Lumber Company
• Tree usually begins with decision node.
• Decision is determine whether to construct large plant, small
plant, or no plant.
• Once decision is made, one of two possible states of nature
(favorable or unfavorable market) will occur.
Folding Back a Decision Tree
Thompson Lumber Company
• In folding back decision tree, use following two rules:
– At each state of nature (or chance) node, compute expected
value using probabilities of all possible outcomes at that
node and payoffs associated with outcomes.
– At each decision node, select alternative that yields better
expected value or payoff.
Reduced Decision Tree
Thompson Lumber Company
• Using rule for decision nodes, select alternative with highest
EMV.
• Corresponds to alternative to build small plant.
• Resulting EMV is $40,000.
Decision Trees for Multi-stage
Decision Making Problems
Decision Tree With EMVs Shown
Thompson Lumber Company
Expected Value of Sample Information
• One way of measuring value of market information is
to compute the expected value of sample
information (EVSI), as follows:
8.8 Estimating Probability
Values Using Bayesian Analysis
• There are many ways of getting probability data for
problem.
• Numbers (e.g., 0.78, 0.22, 0.27, 0.73 ) can be
assessed by manager based on experience and
intuition.
• They can be derived from historical data or
computed from other available data using Bayes’
theorem.
Calculating Revised Probabilities
• Assume following four conditional probabilities
were known.
Market Survey Reliability in Predicting
Actual States of Nature
Market Survey Reliability in Predicting
Actual States of Nature
Probability Revisions Given
Positive Survey
Probability Revisions Given
Negative Survey
Potential Problems in Using
Survey Results
• Survey results or pilot studies are done before actual decision
is made.
• Bayes’ analysis used to help determine correct conditional
probabilities
• Need to have data about surveys and accuracy.
• Cannot get data about those situations in which decision was
not to build a plant or not to take some course of action.
• Probabilities are based only on cases in which decision to
build a plant or take some course of action is actually made.
• Conditional probability information is not quite as accurate as
desired.
Summary
• Introduced decision theory to study decision making.
• Studied (1) decision making under certainty, (2) decision
making under uncertainty, and (3) decision making under
risk.
• Identified best alternatives using criteria: maximax, maximin,
equally likely, criterion of realism, and minimax regret.
• Discussed computation and use: expected monetary value
(EMV), expected opportunity loss (EOL), and expected value
of perfect information (EVPI).
• Decision trees were used for larger decision problems in
which decisions had to be made in sequence.
• Computed expected value of sample information (EVSI).
• Bayesian analysis used to revise or update probability values.