QUANTITATIVE
TECHNIQUES
LECTURE 2
FUNDAMENTALS OF DECISION
THEORY MODEL
September 2009
Learning Objectives
Students will be able to:
 List steps of the decision-making process.
 Describe the
environments.
types
of
decision-making
 Use probability values to make decisions under
risk.
 Make decisions under uncertainty & risk but
probability values are not known.
Steps in Decision Theory
•
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Define the problem and influencing factors.
List the possible alternatives.
Identify the possible outcomes.
List the payoff or profit of each combination of
alternatives and outcomes.
Evaluate the problem using one of the decision
theory models.
Select best alternative.
Implement the selected alternative.
Evaluate the decision’s effectiveness.
Step 1: Identifying the Problem
• Problem
– A discrepancy between an existing and desired
state of affairs.
• Characteristics of Problems
– There is pressure to solve the problem.
– The manager must have the authority, information,
or resources needed to solve the problem.
Step 2: Identifying Decision Criteria
• Decision criteria are factors that are important
(relevant) to resolving the problem.
Step 3: Allocating Weights to the
Criteria
• Decision criteria are not of equal importance.
Step 4: Developing Alternatives
• Identifying viable alternatives
Step 5: Analysing Alternatives
• Appraising each alternative’s strengths and
weaknesses
Step 6: Selecting an Alternative
• Choosing the best alternative
Step 7: Implementing the Decision
• Putting the chosen alternative into action.
Step 8: Evaluating the Decision’s
Effectiveness
• The soundness of the decision is judged by its
outcomes.
Components of Decision Making
• A decision-making includes several components: the
decisions themselves and “states of nature”.
• States of nature: is an actual event that may occur in the
future.
• To facilitate the analysis of these types of decision
situations so that the best decisions result, we use
“payoff tables”.
• Payoff table: a means of organising a decision situation,
including the payoffs from different decisions given the
various states of nature.
Decision Theory
Terms:
• Alternative: Course of action or choice.
Decision-maker chooses among alternatives.
• State of nature: An occurrence over which the
decision maker has no control.
Types of Decision-Making Environments
Decision making under conditions of certainty
1.
•
Decision-maker knows with certainty the
consequences of every alternative or decision choice
2.
Decision making under conditions of uncertainty
•
The decision-maker does not know the probabilities
of the various outcomes
3.
Decision making under conditions of risk
•
The decision-maker does know the probabilities of
the various outcomes that result from the choice of
particular alternatives.
Decision Making under Uncertainty
 Maximax (Optimistic approach)
 Maximin (Pessimistic approach)
 Criterion of realism (Hurwicz Criterion)
 Equally likely (Laplace)
 Minimax Regret
Decision Making Under Uncertainty
(without probabilities)
Decision-Making Criteria:
The Maximax Criterion-results in the maximum
of the maximum payoffs for every alternative
(Optimistic criterion)
The Maximin Criterion-results in the maximum
of the minimum payoffs for every alternative
(Pessimistic criterion)
 The Minimax Regret Criterion-minimises the
maximum regret.
•Regret is the difference between the payoff from the best
decision and all other decision payoffs.
The Hurwicz Criterion
•It is a compromise between the maximax and maximin
criteria.
•The coefficient of optimism, is a measure of the decision
maker’s optimism.
•The Hurwicz criterion multiplies the best payoff by , the
coefficient of optimism, and the worst payoff by 1 - , for
each decision, and the best result is selected.
 The Equal Likelihood Criterion
•weights each state of nature equally, assuming that the
states of nature are equally likely to occur.
•The equal likelihood criterion multiplies the decision
payoff for each state of nature by an equal weight.
 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.
Example 1
Suppose that a manufacturer of office equipment must
decide whether to expand his plant capacity now or wait
another year. His advisors tell him that if he expands now
and economic conditions remain good (p = 0.65), there will
be a profit of $369,000: if he expands now and there is a
recession (p = 0.35), there will be a loss of $90,000: if he
waits another year to expand and economic conditions
remain good, there will be a profit of $180,000: and if he
waits another year and there is a recession, there will be a
small profit of $18,000.
Construct a payoff table to present the above
information and choose the preferred decision.
Decision Table (Pay-off-table)
State of Nature
Alternative
Decision Making Under Risk
• Select alternative with largest expected
monetary value (EMV)
• EMV (alternative i) = (payoff of first state of
nature) x (prob. of first state of nature) +
(payoff of second state of nature) x (prob. of
second state of nature) +………….+ (payoff
of last state of nature) x (prob. of last state of
nature)
Expected Opportunity Loss (EOL)
 Alternative to maximising EMV is to minimise
expected opportunity loss (EOL is the cost of
not picking the best solution).
 First compute an opportunity loss table.
 Next, the EOL is computed for each alternative
by multiplying the opportunity loss by the
probability and adding these together.
 We then use the minimum EOL as the decision
criteria.
Expected Value of Perfect Information (EVPI)
• EVPI places an upper bound on what one
would pay for additional information.
• EVPI is the maximum you should pay to learn
the future.
EVPI = *EPPI - EMVmaximum
* where EPPI = (best outcome for first state of nature) x
(prob. of first state of nature) + (best outcome for 2nd
state of nature) x (prob. of 2nd state of nature)
+………..+ (best outcome for last state of nature) x
(prob. of last state of nature)
Decision Analysis
• The minimum EOL will always result in the
same decision (NOT value) as the maximum
EMV.
• The EVPI will always be equal to the
minimum EOL.
EVPI = EOLminimum
Characteristics of an Effective DecisionMaking Process
• It focuses on what is important.
• It is logical and consistent.
• It acknowledges both subjective and objective
thinking and blends analytical with intuitive thinking
• It requires only as much information and analysis as
is necessary to resolve a particular dilemma.
• It encourages and guides the gathering of relevant
information and informed opinion.
• It is straightforward, reliable, easy to use, and
flexible.
Example 2
• The table shown below is an example of a payoff
matrix. The A's stand for the alternative actions
available to the decision maker.
These actions
represent the controllable variables in the system. The
uncertain events or states of nature are represented by
the S's. Each S has an associated probability of its
occurrence, denoted P.
Actions/States
A1
S1
(P=0.25)
20
S2
(P=0.25)
60
S3
(P=0.25)
- 60
S4
(P=0.25)
20
A2
0
20
- 20
20
A3
50
-20
- 80
20
Calculate the following
• Hurwicz criterion;
• Laplace insufficient reason criterion;
• Maximax criterion;
• Maximin criterion;
• Expected Opportunity Loss
Example 3
The table below illustrates the 12 possible payoffs in the record and
tape company’s expansion decision.
Calculate the following
•
Hurwicz criterion (assume α = 0.45);
•
Laplace insufficient reason criterion;
•
Maximax criterion;
•
Maximin criterion;
•
Expected Opportunity Loss.
Decision maker’s alternatives (Rs)
State of nature
Expand
Build
Subcontract
High (0.2)
500,000
700,000
300,000
Moderate (0.3)
250,000
300,000
150,000
Low (0.35)
-250,000
-400,000
-10,000
Failure (0.15)
-450,000
-800,000
-100,000