DECISION THEORY OF HRM

1. Decision Theory

2. Introduction
 Decision theory or decision analysis is an analytical and
systematic approach to decision making where the decision
maker has several feasible and viable decision alternatives
from which he or she has to select the best alternative on
the basis of some standards decided in advance
 The degree of certainty provides a foundation in developing
decision models to arrive at the best possible decisions. The
degree of certainty has two extreme points—complete
certainty and complete uncertainty. The region under these
two extreme points correspond to decision making under
risk. Problems based on the phenomenon of decision
making under risk are referred to as probabilistic problems.

3. Elements of Decision Analysis
 The state of nature is a future state of affairs that may
result from the choice of an alternative from the list of
available alternatives with the decision maker.
 In a decision problem, occurrences are chance occurrences.
All the chance occurrences are governed by probabilities.
 In probabilistic problems, it is assumed that duration is
finite. After any combination of an act and an event, there is
a final outcome. An outcome may be viewed in two ways:
payoff (reward) or loss. A tabular arrangement of payoffs is
referred to as payoff matrix. The values in the payoff matrix
are conditional because of the uncertain state of nature

4. Curd Pack Example
 Suppose a leading dairy products company produces fresh
curd packs weighing 200 grams every day. The expiry
period for the curd pack is 24 hours. The demand (number
of customers) for the curd pack is uncertain.
 The decision maker has to take decisions about the number
of curd packs to be produced every day because of the
uncertain environment. In other words, he has to take an
action. Action is in the control of a decision maker. In our
example (decision problem), a decision maker can take any
action (producing 100, 200, 300, or 400 curd packs). In this
example, the number of customers are uncertain, as are
possible events.
 Suppose the cost of producing each curd pack is Rs 10 and
it is sold for Rs 20. As one can understand very easily,
Payoff = Selling price – Cost. The number of customers and
the act and the payoff is exhibited in Table, which is known
as a payoff table.

5. Payoff table for the curd pack example

6. Opportunity Loss Table for the Curd Pack Example
The payoff table can also be constructed in the form of an
opportunity loss table. This table is also referred to as regret
table. The opportunity loss or regret can be defined as the
amount of payoff not realized by not selecting the optimum
course of action.
Opportunity loss = The relative pay off which a decision maker could have realized - the
Pay off which he has actually realized

7. Decision Making Under Uncertainty
A situation where the decision maker is unable to assess
the probability of any state of nature is referred to as
decision making under uncertainty.
 Laplace (Equally likely decision) criterion
 Maximin or minimax criterion
 Maximax criterion
 Hurwicz criterion
 Regret crieterion

8. Laplace (Equally likely Decision) Criterion
Laplace criterion is based on the simple principle that since
probabilities of the state of nature are unknown, various
events can be treated as equally likely. Under this
assumption, the expected payoff for each act is computed
first, followed by the mean of these expected payoff values.

9. Maximin Criterion
 Maximin criterion is a conservative approach to decision
making. The decision maker tries to avoid the worst
choice. In this approach, the minimum payoff over the
various events or possible states of nature is determined
by the decision maker and an act is selected for which the
Maximin payoff is the highest.
 In the curd pack example, minimum profits associated
with various act are given as below:
 According to the maximin criterion, act A1 is selected,
which generates the maximum profits when different acts
are compared.

10. Maximax Criterion
 Maximax criterion is an optimistic approach where a decision
maker determines the maximum payoff for each act and then an
act is selected which provides the highest returns.
 In the curd pack example, maximum profits associated with
various acts are given as below:
 Applying the maximax criterion, a decision maker
will select the strategy A5 which gives the overall
maximum of the different maximum payoffs
generated from different acts.

11. Hurwicz Criterion
Hurwicz who coined the Hurwicz approach, has introduced a coefficient of
optimism, generally denoted by alpha. Alpha varies on a scale ranging from 0 to
1.In this scale-0, indicates an extremely pessimistic approach to the future and
1 indicates an extremely optimistic approach to the future. Hence, alpha
represents the coefficient of optimism and (1- alpha) represent the coefficient
of pessimism.

12. Regret Criterion
 In regret criterion, a decision maker selects the course of action
that minimizes the maximum regret.
 In the curd pack example, from the opportunity loss table
maximum regret values can be selected as below:
 The regret value is minimum for act A3. Hence, the decision
maker will select act A3 by applying regret criterion.

13. Example A company is faced with the problem of a decline in its
sales turnover. To overcome this problem, it has decided to opt for
any of the four strategies: heavy advertisement (S1); increase in
number of sales executives (S2); adding new features to products
(S3), and increasing the price of the product (S4). Out of these four
acts, there may be four possible states of nature or events which
are a 40% increase in sales (E1); a 30% increase in sales (E2); a
25% increase in sales (E3); and a 22% increase in sales (E4). The
company executives have worked out the yearly net profit (in
thousand rupees) that would result if any of the four strategies are
selected.
ALPHA VALUE CAN BE TAKEN AS .6

14. Table : Payoff matrix for Example
On the basis of the five criteria for decision making
under uncertainty, suggest which act should be
adopted by the decision maker.

15. Solution
(i) Laplace (equally likely decision) criterion
(ii) Maximin or minimax criterion
Considering Laplace criterion, a decision maker can select
strategy S2.
According to the maximin criterion, strategy S3 is
selected which generates the maximum minimum net
profit among the different strategies.

16. Solution
(iii) Maximax or minimin criterion
Applying the maximax criterion, a decision maker will select the
strategy S3, which provides the maximum payoff among the various
strategies.
(iv) Hurwicz criterion
In order to use the Hurwicz criterion, the decision maker selects alpha as 0.6, that is, (1
– alpha = 0.4).

17. Solution
So, according to the Hurwicz criterion, a decision maker will select
strategy S3 which gives the maximum Hurwicz criterion value of
630.

18. Decision Making Under Risk
 Decision making under risk is a situation where more than
one state of nature exists and the decision maker has
sufficient information to assign probability values to the
likelihood of occurrence of each of these states.
 The three approaches a decision maker uses to evaluate
various courses of action and select the best course of
action are as follows:
 Expected monetary value (EMV)
 Expected opportunity loss (EOL)
 Expected value of perfect information (EVPI)

19. Expected Monetary Value (EMV)
Expected monetary value (EMV) is the sum of the payoffs for
each course of action multiplied by the probabilities associated
with each state of nature.

20. Example
Suppose that in Previous Example, the probability of occurrence of
various states of nature are also provided as indicated in Table below .
On the basis of the expected monetary value (EMV) criterion, what
decision should be taken by the decision maker?

21. Solution
Expected monetary values (EMV) for selecting the best act are computed in Table
From Table, it can be observed that the maximum expected
monetary value is obtained for strategy (act) S2. Hence, a
decision maker will select the strategy S2.

22. Expected Opportunity Loss (EOL)
Expected opportunity loss (EOL) criterion is another approach
based on which a decision can be taken., the expected
opportunity loss (EOL) can be computed as below:

23. Example
Suppose in, the probability of occurrence of various states of nature are also
provided as indicated in Table.
On the basis of the expected opportunity loss (EOL)
criterion, what
decision should be taken by the decision maker?

24. Solution
 For different acts (strategies), the expected opportunity loss (EOL) can be
computed as below:
 A decision maker will select an act (strategy) which will
minimize the expected opportunity loss or expected regret.
 It can be noticed that for act (strategy) S2, the expected
regret value is minimum (150). Hence, on the basis of the
expected opportunity loss (EOL) criterion, a decision maker
will select strategy S2.

25. Expected Value of Perfect Information (EVPI)
Expected value of perfect information (EVPI) is referred to as the
difference between the expected payoff with perfect information (EPPI)
and the maximum expected payoff (EP) computed under uncertainty.
Example : The payoffs with some probabilities associated with events
(states of nature) for the curd pack example is exhibited in Table 19.18.
Calculate the expected value of perfect information (EVPI).

26.  So, the expected payoff with perfect information (EPPI) is the sum of all the
elements in the last column of Table.
 Expected payoff with perfect information (EPPI) = 2500
 Maximum expected payoff (EP) is the expected monetary value (EMV),
which is already computed as 1400.
 Hence, expected value of perfect information (EVPI) = Expected payoff with
perfect information (EPPI) – Maximum expected payoff (EP) = 2500 – 1400
=1100

27. Decision Trees
 A decision tree can be referred to as a graphic model of a
decision process. In other words, a decision tree is a graphic
representation of a sequence strategy–nature of state
combination available to a decision maker.
 Example : A consumer durables company wants to diversify into
other sectors of business. The company can choose to diversify
into four different fields— the fast moving consumer goods
sector, the consumer electronics sector, the concept selling
sector, and the print media. The company has sought advice
from a reputed consultancy firm. The advice received from the
consultancy in terms of probability statements are as below:

28. Example
 Fast moving consumer goods sector: Chances are 20% that the net
profit of the company will decline by 10% in first three years; chances
are 45% that the company will breakeven (no profit no loss) in the first
three years, and chances are 35% that the net profit of the company will
increase by 20%.
 Consumer electronics sector: Chances are 15% that the net profit of the
company will decline by 15% in the first three years; chances are
55% that the company will breakeven (no profit no loss) in the first three
years, and chances are 30% that the net profit of the company will
increase by 15%.
 Concept selling: Chances are 25% that the net profit of the company will
decline by 20% in the first three years; chances are 35% that the
company will breakeven (no profit no loss) in the first three years, and
chances are 40% that the net profit of the company will increase by 15%.
 Print media: Chances are 35% that the net profit of the company will
decline by 25% in the first three years; chances are 35% that the
company will breakeven (no profit no loss) in the first three years, and
chances are 30% that net the profit of the company will increase by 20%.
Construct a decision tree and using the expected value criterion,
select the alternative with the highest expected payoff.

29. Solution
Decision tree

30. Solution

31. Ex
A company is engaged in the process of launching a new
product. The top mgt of the company has 3 options in
terms of launching the product in 3 sales zones: North
region (N), South region (S) and East region (E). The
management has decided to take the final decision on
the basis of the demand for the product, which is divided
into 3 categories: High demand, medium demand and
low demand. On the basis of past demand and
management’s view, the respective probab. Of 3 kinds of
demand are estimated to be .45, .35 and .20.
The table on next page indicates the estimated profit (in
thousand Rs.) for various combination of events and acts

32. Demand Probability North
Region
South
Region
East
Region
High .45 100 -60 -120
Medium .35 80 -20 40
Low .20 60 150 135
Construct a Decision tree and using the expected
value criterion, select the alternatives with the
highest expected pay off