OR CHAPTER FOUR.pptx

Chapter Four
Decision Theory
Compiled by: Asmamaw T. (PhD)
5/8/2023 1

Introduction
• Decision theory represents a generalized approach to
decision making which often serves as the basis for a
wide range of managerial decision making.
• The decision model includes a list of courses of action
that are available and the possible consequences of each
course of action.
• An important factor in decision making is the degree of
certainty associated with consequences.
5/8/2023 2

Introduction
• The decisions are based on the criteria decided by the objective
of the organization
• Example : Maximization of profit or Minimization of cost,
time, wastage, etc
• Many decision making situations occur under conditions of
uncertainty.
• Example : The demand for a product may not be 500 units
next week, but 450 or 600 units, depending on the market
(which is uncertain).
5/8/2023 3

Characteristics of Decision Theory
• Decision theory problems are characterized by the
following:
1. A list of alternatives
2. A list of possible future states of nature
3. Payoffs associated with each alternative/state of nature
combinations
4. An assessment of the degree of certainty of possible
future events
5. A decision criterion
5/8/2023 4

1. List of alternatives: are a set of mutually exclusive
and collectively exhaustive decisions that are available
to the decision maker (some times, not always, one of
these alternatives will be to ‘do nothing’.)
2. States of nature: the set of possible future conditions,
or events, beyond the control of the decision maker, that
will be the primary determinants of the eventual
consequence of the decision.
• The states of nature, like the list of alternatives, must
be mutually exclusive and collectively exhaustive.
5/8/2023 5

3. Payoffs: the decision maker may have different payoffs
associated with different decision alternatives and states of nature
• The payoffs might be profits, revenues, costs, or other measures of
value.
• Usually the measures are financial. And, payoffs are estimated
values.
• The more accurate these estimates, the more useful they will be for
decision making purposes and the more likely, it is that the
decision maker will choose an appropriate alternative.
• The number of payoffs depends on the number of alternative/state
of nature combination.
5/8/2023 6

4. Degree of certainty: - the approach used by a decision maker
often depends on the degree of certainty that exists. There can
be different degrees of certainty.
• One extreme is complete certainty and the other is complete
uncertainty. Complete uncertainty exists when the likelihood
of the various states of nature are unknown.
• Between these two extremes is RISK, the term that implies
probabilities are known for the states of nature.
• Knowledge of the likelihood of each of the states of nature can
play an important role in selecting a course of action.
• Thus, if the decision maker feels that a particular state of
nature is highly likely, this will mean that the pay offs
associated with the state of nature are also highly likely.
5/8/2023 7

5. Decision Criteria: The process of selecting one
alternative from a list of alternatives is governed by a
decision criterion, which embodies the decision makers
attitude toward the decision as well the degree of
certainty that surrounds a decision.
• Some decision maker may have optimistic attitude,
where as others are pessimistic.
• Some wants to maximize gains, where as others are
more concerned with protecting against losses.
5/8/2023 8

Payoff Table
• A payoff table is a device a decision maker can use to
summarize and organize information relevant to a
particular decision.
• It includes a list of alternatives, the possible future
states of nature, and the payoffs associated with each of
the alternative/state of nature combinations.
• If probabilities for the states of nature are available,
these can also be listed.
• The general format of the table is illustrated in the next
slide:
5/8/2023 9

Payoff Table
State of Nature
S1 S2 S3
Alternatives A1
A2
A3
where:
Ai = the ith alternative
Sj = the jth states of nature
Vij = the value or payoff that will be realized if alternative i is
chosen and event j occurs.
V11 V12 V13
V21 V22 V23
V31 V32 V33
5/8/2023 10

Decision Making Process
1. Identify all possible state of nature i.e events available or affecting
the decision.
2. List out various course of action open to the decision maker. These
finite number of course of action will facilitate the decision maker to
decide under controlled parameters.
3. Identify the payoffs for various strategic solution under all known
events or state of nature . Variation of acts & events will be helpful
to identify the outcomes or pay-off for various combination.
4. Decision to choose from amongst these alternative under given
conditions with identified pay-offs.
 These steps may involve the judgment or any additional information
helping the decision making process.
5/8/2023 11

Decision making environment
Decision are made under four types of environment:
1. Decision making under condition of certainty
2. Decision making under condition of uncertainty
3. Decision making under condition of risk
5/8/2023 12

Decision Making Under Certainty
 The simplest of all circumstances occurs when decision making
takes place in an environment of complete certainty
 In this environment , only one state of nature exists for each
alternative i.e., there is complete certainty about the future .
 It is easy to analyze the situation and make good decision.
 Since the decision maker has perfect knowledge about the future
outcomes, he simply choose the alternative having optimum
payoff.
5/8/2023 13

Example
• The following payoff table provides data about profits of the various
states of nature/alternative combination.
S1 S 2 S3
A1
A2
A3
• If we know that S2 will occur, the decision maker then can focus
on the first row of the payoff table. Because alternative A1 has
the largest profit (16), it would be selected.
4 16 12
5 6 10
-1 4 15
5/8/2023 14

Decision making under conditions of uncertainty
 Under complete uncertainty, the decision maker either is unable to
estimate the probabilities for the occurrence of the different states of
nature, or else s/he lacks confidence in available estimates of
probabilities, and for that reason, probabilities are not included in
the analysis.
 More than one states of nature exists but the decision maker lacks the
knowledge about the probabilities of their circumstances
 we shall consider four approaches to decision making under complete
uncertainty. These are:
1. Maximax
2. Maximin
3. Minimax regret
4. Insufficient reason
5/8/2023 15

Maximax (optimistic ) Criteria
• The decision maker selects the decision that will
result in the maximum of the maximum payoffs.
• The maximax is very optimistic.
• The decision maker assumes that the most
favorable state of nature for each decision
alternative will occur.
5/8/2023 16

• Example: The investor would optimistically assume
that good economic conditions will prevail in the
future. The best payoff for each alternative is
identified, and the alternative with the maximum of
these is the designated decision.
S1 S2 S3 Row Maximum
A1
A2
A3
4 16 12 16*
Maximum
5 6 10 10
-1 4 15 15
5/8/2023 17

• Decision: A1 will be chosen.
• Note: If the pay off table consists of costs instead of
profits, the opposite selection would be indicated: The
minimum of minimum costs (MiniMin).
• For the subsequent decision criteria we encounter, the
same logic in the case of costs can be used
5/8/2023 18

Maximin Criteria
This approach is the opposite of the previous one i.e. it
is pessimistic.
This strategy is a conservative one; it consists of
identifying the worst (minimum) payoff for each
alternative, and, then, selecting the alternative that has
the best (maximum) of the worst payoffs.
In effect, the decision maker is setting a floor on the
potential payoff by selecting maximum of the minimum;
the actual payoff can not be less than this amount.
 It involves selecting best of the worst.
5/8/2023 19

Maximin Criteria
Example:
S1 S2 S3 Row Minimum
A1
A2
A3
Decision: A2 will be chosen
Note: If it were cost, the conservative approach would
select the maximum cost for each decision and select the
minimum of these costs.
4 16 12 4
5 6 10 5*Maximum
-1 4 15 -1
5/8/2023 20

Minimax Regret
• In order to use this approach, it is necessary to develop an
opportunity loss table.
• The opportunity loss reflects the difference between each
payoff and the best possible payoff in a column (i.e., given a
state of nature).
• Hence, opportunity loss amounts are found by identifying
the best payoff in a column and, then, subtracting each
of the other values in the column from that payoff.
• Therefore, this decision avoids the greatest regret by
selecting the decision alternative that minimizes the
maximum regret.
5/8/2023 21

Minimax Regret
Example:
S1 S2 S3
A1
A2
A3
• opportunity loss table
S1 S2 S3
A1
A2
A3
4 16 12
5 6 10
-1 4 15
5-4=1 16-16=0 15-12=3 3*minimum
5-5=0 16-6=10 15-10=5 10
5-(-1)=6 16-4=12 15-15=0 12
5/8/2023 22

Minimax Regret
• A decision maker could select an alternative that
minimize the maximum possible regret.
• This requires identifying the maximum opportunity loss
in each row and, then, choosing the alternative that
would yield the best (minimum) of those regrets.
• Decision: A1 will be chosen
5/8/2023 23

Laplace (criteria of rationality)or
Baye’s criteria
The principle of insufficient reason offers a
method that incorporates more of the information.
It treats the states of nature as if each were equally
likely, and it focuses on the average payoff for
each row, selecting the alternative that has the
highest row average.
5/8/2023 24

Example
S1 S2 S3 S4 S5 Row average
A1
A2
A3
Decision: A1 is selected
 The basis for the criterion of insufficient reason is that under complete uncertainty,
the decision maker should not focus on either high or low payoffs, but should treat all
payoffs (actually, all states of nature), as if they were equally likely.
 Averaging row payoffs accomplishes this.
28 28 28 28 4 23.2*maximum
5 5 5 5 28 9.6
5 5 5 5 28 9.6
5/8/2023 25

The Hurwitz Criterion (Criterion of realism)
 The Hurwitz criterion strikes a compromise between the maximax
and maximin criterion.
 The principle underlying this decision criterion is that the decision
maker is neither totally optimistic, nor totally pessimistic.
 With Hurwitz criterion, the decision payoffs are weighted by a
coefficient of optimism, a measure of a decision maker’s optimism.
 The coefficient of optimism, which is defined as , is between zero and
one (0<  <1). If  = 1, then the decision maker is said to be
completely optimistic, if  = 0, then the decision maker is completely
pessimistic. Given this definition, if  is coefficient of optimism, 1- 
is coefficient of pessimism.
 The Hurwitz criterion requires that for each alternative, the maximum
payoff is multiplied by  and the minimum payoff be multiplied by 1-
.
5/8/2023 26

Example
S1 S2 S3 Max row
A1
A2
A3
If  = 0.4 for the above example,
A1 = (0.4x16) + (0.6x4) = 8.8
A2 = (0.4x10) + (0.6x5) = 7
A3 = (0.4x15) + (0.6x-1) = 5.6
• Decision: A1 is selected
4 16 12 16
5 6 10 10
-1 4 15 15
5/8/2023 27

The Hurwitz Criterion (Criterion of realism)
 A limitation of Hurwicz criterion is the fact that  must be
determined by the decision maker.
 Regardless of how the decision maker determines , it is still a
completely a subjective measure of the decision maker’s degree
of optimism.
 Therefore, Hurwicz criterion is a completely subjective
decision making criterion.
5/8/2023 28

Decision Making Under Risk
 The decision making criteria just presented previously were
based on the assumption that no information regarding the
likelihood of the states of the nature was available.
 Thus, no probabilities of occurrence were assigned to the states of
nature, except in the case of the equal likelihood criterion.
 It is often possible for the decision maker to know enough about
the future state of nature to assign probabilities to their
occurrences.
5/8/2023 29

Decision Making Under Risk
• The term risk is often used in conjunction with partial
uncertainty, presence of probabilities for the occurrence of
various states of nature.
• The probabilities may be subjective estimates from managers or
from experts in a particular field, or they may reflect historical
frequencies.
• If they are reasonably correct, they provide the decision maker
with additional information that can dramatically improve the
decision making process.
• Given that probabilities can be assigned, several decision criteria
are available to aid the decision maker.
• Following are different approaches to make decision under Risk
5/8/2023 30

A. Expected Monetary Value (EMV)
 The EMV approach provides the decision maker with a value which represents an
average payoff for each alternative. The best alternative is, then, the one that has
the highest EMV.
 The average or expected payoff of each alternative is a weighted average:
𝐸𝑀𝑉𝑖 = =
𝑖=1
𝐾
𝑃𝑖𝑉𝑖𝑗
Where:
EMVi = the EMV for the ith alternative
Pi = the probability of the ith state of nature
Vij = the estimated payoff for alternative i under state of nature j.
Note: the sum of the probabilities for all states of nature must be 1.
5/8/2023 31

Example
Probability 0.20 0.50 0.30
S1 S2 S3 Expected payoff
A1
A2
A3
Decision: A1 will be chosen
4 16 12 12.40*maximum
5 6 10 7
-1 4 15 6.3
5/8/2023 32

B. Expected Opportunity Loss (EOL)
The table of opportunity loss is used rather than a
table of payoffs.
Hence, the opportunity losses for each alternative are
weighted by the probabilities of their respective state of
nature to compute a long run average opportunity loss,
and the alternative with the smallest expected loss is
selected as the best choice.
5/8/2023 33

Example
S1 S2 S3
A1
A2
A3
EOL (A1) = 0.20(1) + 0.50(0) + 0.30(3) = 1.10 *minimum
EOL (A2) = 0.20(0) + 0.50(10) + 0.30(5) = 6.50
EOL (A3) = 0.20(6) + 0.50(12) + 0.30(0) = 7.20
Note: The EOL approach resulted in the same alternative as the
EMV approach (Maximizing the payoffs is equivalent to
minimizing the opportunity losses).
4 16 12
5 6 10
-1 4 15
5/8/2023 34

C. Expected Value of Perfect Information
(EVPI)
• It can some times be useful for a decision maker to
determine the potential benefit of knowing for certain
which state of nature is going to prevail.
• The EVPI is the measure of the difference between the
certain payoffs that could be realized under a condition
involving risk.
• If the decision maker knows that S1 will occur, A2
would be chosen with a payoff of $5. Similarly for S2 $16
(for A1) and for S3, $15 (with A3) would be chosen.
5/8/2023 35

C. Expected Value of Perfect Information
(EVPI)
Hence, the expected payoff under certainty (EPC) would be:
EPC = 0.20(5) + 0.50(16) + 0.30(15) = 13.50
The difference between this figure and the expected payoff under
risk (i.e., the EMV) is the expected value of perfect information.
Thus:
EVPI = EPC - EMV
= 13.50 -12.40 = 1.10
• Note: The EVPI is exactly equal to the EOL. The EOL indicates
the expected opportunity loss due to imperfect information,
which is another way of saying the expected payoff that could be
achieved by having perfect information.
5/8/2023 36

OR CHAPTER FOUR.pptx

More Related Content

Similar to OR CHAPTER FOUR.pptx (20)

More from AynetuTerefe2 (11)

Recently uploaded (20)

OR CHAPTER FOUR.pptx