The document discusses decision theory and decision-making under uncertainty. It defines key concepts in decision theory including decision maker, courses of action, states of nature, payoff, and expected monetary value. It describes three types of decision-making environments: certainty, risk, and uncertainty. Under risk, decisions are made using probability assessments and expected monetary value calculations. Several steps and concepts in decision making under risk are outlined, including constructing payoff matrices, calculating expected values, and opportunity loss analysis.

1. Operations Research
MBA-024

2. DECISION-MAKING
ENVIRONMENTS/DECISION THEORY
UNIT I

3. Decision Theory: Introduction
• The managerial activity includes broadly four
phases, namely, planning, organising,
directing and controlling.
• In performing all of these activities the
management has to face several such
situations where they have to make a choice
of the best among a number of alternative
courses of action.

4. • This choice making is technically termed as
decision-making.
• A decision is simply a selection from two or
more courses of action.
• Decision theory provides a rich set of concepts
and techniques to aid the decision maker in
dealing with complex decision problems.

5. Decision Theory: Definition
• A process which results in the selection from a
set of alternative courses of action, that
course of action which is considered to meet
the objectives of the decision problem more
satisfactorily than others as judged by the
decision maker.

6. Decision Theory: Applications
• Select the best from among several job offers.
• Select the most profitable investment portfolio.
• Determine whether or not to expand a
manufacturing facility.
• Determine whether a large plant, a small plant,
or no plant should be built.
• Decide whether to invest in a new plant,
equipment, research programme, marketing
facilities, etc.

7. Decision Theory: Steps
• Clearly identify and define the problem at
hand.
• Specify objectives and the decision criteria.
• Identify and evaluate the possible
alternatives.
• Formulate (or select) one of the mathematical
decision theory models.

8. Decision Theory: Steps
• Apply the model and select the ‘best’
alternative.
• Conduct a sensitivity analysis of the solution.
• Communication and implementation of
decision.
• Follow-up and feedback of results of decision.

9. Decision Theory: Concepts
• Decision Maker. An individual or a group of
individuals responsible for making the choice
of an appropriate course of action amongst
the available courses of action.
• Courses of Action. The alternative courses of
actions or strategies are the acts that are
available to the decision maker.

10. • States of Nature. The events or occurrences
which are outside the control of the decision
maker, but which determine the level of
success for a given decision.
• Payoff. Each combination of a strategy and
event is associated with a payoff, which
measures the net benefit to the decision
maker.

11. • Payoff Table. For a given problem, payoff
table lists the payoffs for each combination of
event and strategy.
• Regret/Opportunity Loss Table. An
opportunity loss is the loss incurred due to
failure of not adopting the best possible
strategy. For a given state of nature the
opportunity loss of possible strategy is the
difference between the payoff for that
strategy and the payoff for the best possible
strategy that could have been selected.

12. Types of Decision-Making
Environments
• Certainty. Complete and accurate knowledge
of the outcome of each alternative. There is
only one outcome for each alternative.
• Risk. Multiple possible outcomes for each
alternative. A probability of occurrence
attached to each possible outcome.
• Uncertainty. Multiple outcomes for each
alternative. But no knowledge of the
probability of their occurrence.

13. Decision-Making under Certainty
• The consequence of selecting each course of
action known with certainty.
• It is presumed that only one state of nature is
relevant for the purpose of the decision
maker.
• He identifies this state of nature, takes it for
granted and presumes complete knowledge
as to its occurrence.

14. Decision-Making under Certainty
• Some techniques used:
– System of equations.
– Linear programming.
– Integer programming.
– Dynamic programming.
– Queuing models.
– Inventory models.
– Capital budgeting analysis.
– Break even analysis.

15. Decision-Making under Risk
• The decision maker faces several states of
nature.
• He is supposed to have believable evidential
information, knowledge, experience or
judgement to enable him to assign probability
values to the likelihood of occurrence of each
state of nature.
• The course of action which has the largest
expected payoff value is selected.

16. Decision-Making under Risk
• The most widely used decision criterion is the
expected monetary value (EMV) or expected
payoff.
• The objective of decision making is to
optimise expected payoff.
• It means maximisation of expected profit or
minimisation of expected regret.

17. EMV
• Given a payoff table with payoffs and
probability assessments for all states of
nature, it is possible to determine EMV for
each course of action if the decision is
repeated a large number of times.
• The EMV for a given course of action is the
sum of possible payoffs of the alternatives,
each weighted by the probability of that
payoff occurring.

19. Steps for Calculating EMV
• Construct payoff table along with the
probabilities of the occurrence of each state
of nature.
• Calculate EMV for each course of action, as
shown earlier.
• Select the course of action that yields the
optimal EMV.

20. Expected Value with Perfect
Information
• The expected value with perfect information
is the expected or average return, in the long
run, if we have perfect information before a
decision has to be made.
• It is calculated by choosing the best
alternative for each state of nature and
multiplying its payoff with the probability of
that state of nature.

21. • Expected value with perfect information =
(Best outcome for 1st
state of nature) x
(Probability of 1st
state of nature) + (Best
outcome for 2nd
state of nature) x (Probability
of 2nd
state of nature) + … + (Best outcome for
last state of nature) x (Probability of last state
of nature)

22. Expected Value of Perfect
Information (EVPI)
• EVPI is the expected value with perfect
information minus the expected value without
perfect information, namely the maximum
EMV.

23. Expected Opportunity Loss (EOL)
• An alternative approach to maximising EMV is
to minimise EOL or expected value of regrets.

25. Suppose an electrical goods merchant buys, for resale
purposes in a market, electric irons in the range of 0 to
4. His resources permit him to buy nothing or 1 or 2 or 3
or 4 units. These are his alternative courses of action or
strategies. The demand for electric irons on any day is
something beyond his control and hence is a state of
nature. Let us presume that the dealer does not know
how many units will be bought from him by the
customers. The demand could be anything from 0 to 4.
The dealer can buy each unit of electric iron @ Rs.40
and sell it at Rs.45 each, his margin being Rs.5 per unit.
Assume the stock on hand is valueless. Portray in a
payoff table and opportunity loss table the quantum of
total margin (loss), that he gets in relation to various
alternative strategies and states of nature.

26. Payoff Matrix
Courses of Action
0 1 2 3 4
States
of
Nature
0 0-0=0 0-40=-40 0-80=-80 0-120=-120
1 0-0=0 45-40=5 45-80=-35
2 0-0=0 45-40=5 90-80=10
3 0-0=0 45-40=5 90-80=10
4 0-0=0 45-40=5 90-80=10

27. A person has the choice of running a hot snack stall
or an ice-cream and cold drink stall at Ooty. If the
weather is cool and rainy, he can expect to make a
profit of Rs.15000 and if it is warm he can expect to
make a profit of Rs.3000 by running a hot snack stall.
On the other hand, if his choice is to run an ice-
cream and cold drink stall, he can expect to make a
profit of R.18000 if the weather is warm and Rs.3000
if the weather is cool and rainy. There is 40% chance
of weather being warm in the coming season.
Should he opt for running the hot snack stall or an
ice-cream stall?

28. A newspaper boy has the following probabilities of
selling a magazine:
No. of copies sold Probability
10 0.10
11 0.15
12 0.20
13 0.25
14 0.30
Cost of copy is 30 paise and sale price is 50 paise. He
cannot return unsold copies. How many copies
should he order?

29. A dairy firm wants to determine the quantity of
butter it should produce to meet the demand. Past
records have shown the following demand pattern:
The stock levels are restricted to the range 15 to 50
kg due to inadequate storing facilities. Butter costs
Rs.40 per kg and is sold at Rs.50 per kg.
i.Construct a conditional profit table.
ii.Determine the action alternative associated with
maximization of expected profit.
iii.Determine EVPI.
Quantity required (kg) 15 20 25 30 35 40 50
No. of days demand occurred 6 14 20 80 40 30 10

30. Payoff Matrix
Courses of Action
15 20 25 30 35 40 50
States
of
Nature
15 150 -50 -250 -450 -650 -850 -1250
20 150 200 0 -200 -400 -600 -1000
25 150 200 250 50 -150 -350 -750
30 150 200 250 300 100 -100 -500
35 150 200 250 300 350 150 -250
40 150 200 250 300 350 400 0
50 150 200 250 300 350 400 500

31. Payoff Matrix (with probabilities)
Courses of Action
15 20 25 30 35 40 50 P
States
of
Nature
15 150 -50 -250 -450 -650 -850 -1250 0.03
20 150 200 0 -200 -400 -600 -1000 0.07
25 150 200 250 50 -150 -350 -750 0.1
30 150 200 250 300 100 -100 -500 0.4
35 150 200 250 300 350 150 -250 0.2
40 150 200 250 300 350 400 0 0.15
50 150 200 250 300 350 400 500 0.05

32. Expected Monetary Value (EMV)
Courses of Action
15 20 25 30 35 40 50 P
States
of
Nature
15 150 -50 -250 -450 -650 -850 -1250 0.03
20 150 200 0 -200 -400 -600 -1000 0.07
25 150 200 250 50 -150 -350 -750 0.1
30 150 200 250 300 100 -100 -500 0.4
35 150 200 250 300 350 150 -250 0.2
40 150 200 250 300 350 400 0 0.15
50 150 200 250 300 350 400 500 0.05
EMV 150 192.5 217.5 217.5 117.5 -32.5 -407.5

33. EMVmax
Courses of Action
15 20 25 30 35 40 50 P
States
of
Nature
15 150 -50 -250 -450 -650 -850 -1250 0.03
20 150 200 0 -200 -400 -600 -1000 0.07
25 150 200 250 50 -150 -350 -750 0.1
30 150 200 250 300 100 -100 -500 0.4
35 150 200 250 300 350 150 -250 0.2
40 150 200 250 300 350 400 0 0.15
50 150 200 250 300 350 400 500 0.05
EMV 150 192.5 217.5 217.5 117.5 -32.5 -407.5

34. Opportunity Loss (Regret) Matrix
Courses of Action
15 20 25 30 35 40 50 P
States
of
Nature
15 0 200 400 600 800 1000 1400 0.03
20 50 0 200 400 600 800 1200 0.07
25 100 50 0 200 400 600 1000 0.1
30 150 100 50 0 200 400 800 0.4
35 200 150 100 50 0 200 600 0.2
40 250 200 150 100 50 0 400 0.15
50 350 300 250 200 150 100 0 0.05

35. Expected Opportunity Loss
(Regret)
Courses of Action
15 20 25 30 35 40 50 P
States
of
Nature
15 0 200 400 600 800 1000 1400 0.03
20 50 0 200 400 600 800 1200 0.07
25 100 50 0 200 400 600 1000 0.1
30 150 100 50 0 200 400 800 0.4
35 200 150 100 50 0 200 600 0.2
40 250 200 150 100 50 0 400 0.15
50 350 300 250 200 150 100 0 0.05
EOL 168.5 126 101 101 201 351 726

36. EOLmin
Courses of Action
15 20 25 30 35 40 50 P
States
of
Nature
15 0 200 400 600 800 1000 1400 0.03
20 50 0 200 400 600 800 1200 0.07
25 100 50 0 200 400 600 1000 0.1
30 150 100 50 0 200 400 800 0.4
35 200 150 100 50 0 200 600 0.2
40 250 200 150 100 50 0 400 0.15
50 350 300 250 200 150 100 0 0.05
EOL 168.5 126 101 101 201 351 726

37. EVPI (Method I)
• EVPI = EOLmin = 101

38. EVPI (Method II)
Courses of Action
15 20 25 30 35 40 50 P
States
of
Nature
15 150 -50 -250 -450 -650 -850 -1250 0.03
20 150 200 0 -200 -400 -600 -1000 0.07
25 150 200 250 50 -150 -350 -750 0.1
30 150 200 250 300 100 -100 -500 0.4
35 150 200 250 300 350 150 -250 0.2
40 150 200 250 300 350 400 0 0.15
50 150 200 250 300 350 400 500 0.05
EV with PI 150x0.03+200x0.07+250x0.1+300x0.4+350x0.2+400x0.15+500x0.05=318.5

39. EVPI (Method II)

40. An ice-cream retailer buys ice-cream at a cost of Rs.5
per cup and sells it for Rs.8 per cup; any ice-cream
remaining unsold at the end of the day can be
disposed of at a salvage price of Rs.2 per cup. Past
sales have ranged between 15 and 18 cups per day;
there is no reason to believe that sales volume will
take on any other magnitude in future. Find the
EVPI, if the sale history has the following
probabilities:
Market size 15 16 17 18
Probability 0.10 0.20 0.40 0.30

41. A television dealer finds that the cost of a TV in stock
for a week is Rs.30 and the cost of a unit shortage is
Rs.70. For one particular model of TV the probability
distribution of weekly sales is as follows:
How many units per week should the dealer order?
Also find the EVPI.
Weekly sales 0 1 2 3 4 5 6
Probability 0.1 0.1 0.2 0.25 0.15 0.15 0.05

42. Decision-Making under Uncertainty
• The probabilities are not known.
• No historical data available.
• Expected payoff cannot be calculated.
• Example: Introduction of a new product in the
market.
• The choice of a course of action depends
largely upon the personality of the decision-
maker or policy of the organisation.

43. Decision Criteria under condition
of Uncertainty
• Maximin.
• Maximax.
• Minimax Regret.
• Hurwicz Criterion.
• Baye’s/Laplace’s Criterion.

44. Criterion of Pessimism (Maximin)
• Also called ‘Waldian Criterion.’
• Determine the lowest outcome for each
alternative.
• Choose the alternative associated with the
best of these.

45. Criterion of Optimism (Maximax)
• Suggested by Leonid Hurwicz.
• Determine the best outcome for each
alternative.
• Select the alternative associated with the best
of these.

46. Minimax Regret Criterion
• Attributed to Leonard Savage.
• For each state, identify the most attractive
alternative.
• Place a zero in those cells.
• Compute opportunity loss for other alternatives.
• Identify the maximum opportunity loss for each
alternative.
• Select the alternative associated with the lowest
of these.

47. Criterion of Realism (Hurwicz
Criterion)
• A compromise between maximax and
maximin criteria.
• A coefficient of optimism α (0≤α≤1) is
selected.
• When α is close to 1, the decision-maker is
optimistic about the future.
• When α is close to 0, the decision-maker is
pessimistic about the future.

48. Hurwicz Criterion
• Select the strategy which maximises:

49. Laplace Criterion
• Assign equal probabilities to each state.
• Compute the expected value for each
alternative.
• Select the alternative with the highest
alternative.

50. A firm manufactures three types of products. The fixed
and variable costs are given below:
The likely demand (units) of the products is given below:
•Poor demand: 3000
•Moderate demand: 7000
•High demand: 11000
If the sale price of each type of product is Rs.25, then
prepare the payoff matrix.
Product Fixed cost (Rs.) Variable cost per unit (Rs.)
A 25000 12
B 35000 9
C 53000 7

51. A farmer wants to decide which of the three crops he should plant on his 100-acre
farm. The profit from each is dependent on the rainfall during the growing season.
The farmer has categorized the amount of rainfall as high, medium and low. His
estimated profit for each is shown in the Table below:
If the farmer wishes to plant only one crop, decide which should be his ‘best crop,’
using
a.Maximax criterion
b.Maximin criterion
c.Hurwicz criterion (farmer’s degree of optimism being 0.6)
d.Laplace criterion
e.Minimax regret criterion.
Rainfall Estimated conditional profit (Rs.)
Crop A Crop B Crop C
High 8000 3500 5000
Medium 4500 4500 5000
Low 2000 5000 4000

52. A manufacturer makes a product, of which the principal
ingredient is a chemical X. At the moment, the
manufacturer spends Rs.1000 per year on the supply of X,
but there is a possibility that the price may soon increase
to four times its present figure because of a worldwide
shortage of the chemical. There is another chemical Y,
which the manufacturer could in conjunction with a third
chemical Z, in order to give the same effect as chemical X.
Chemicals Y and Z would together cost the manufacturer
Rs.3000 per year; but their prices are unlikely to rise.
What action should the manufacturer take? Apply the
maximin and minimax regret criteria for decision-making
and give two sets of solutions.
If the coefficient of optimism is 0.4, find the course of
action that minimizes the cost.

53. Decision Tree Approach
• Using a decision tree the decision problem,
alternative courses of action, states of nature
and the likely outcomes are diagrammatically
depicted.
• A decision tree consists of a network of nodes,
branches, probability estimates and payoffs.
• Nodes are of two types: decision-node
(square) and chance node (circle).

54. • Alternative courses of action originate from
decision nodes as main branches (decision
branches).
• At the terminal of each decision branch, there is
a chance node.
• Chance events emanate from chance nodes in
the form of sub-branches (chance branches).
• The respective payoffs and the probabilities
associated with the alternative courses and
chance events are shown alongside the chance
branches.
• At the terminal of the chance branches expected
payoffs are shown.

55. Types of Decision Trees
• Deterministic.
• Probabilistic.
• These can further be subdivided into single
stage and multistage trees.
• A single stage deterministic decision tree
involves making only one decision under
conditions of certainty (no chance events).

56. • In a multi stage deterministic tree a sequence
or chain of decisions are to be made.
• A problem involving only one decision to be
made under conditions of risk or uncertainty
(more than one chance events) can be
represented using a single stage probabilistic
decision tree.
• In the above problem, if a sequence of
decisions is required, a multi stage
probabilistic decision tree is required.

57. D1
C1
Decision node
(course of action)
Outcome 1
(payoff)
Outcome 2
Outcome 3
Outcome 4
Outcome 5
Chance node
(state of nature)

60. Drawing a Decision Tree:
Conventions
• Identify all decisions (and their alternatives) to
be made and the order in which they must be
made.
• Identify the chance events or states of nature
that might occur as a result of each decision
alternative.
• Develop a tree diagram showing the sequence
of decisions and chance events.

61. • Estimate probabilities that the possible events
will occur as a result of the decision
alternatives.
• Obtain outcomes (usually expressed in
economic terms) of the possible interactions
among decision alternatives and events.
• Calculate the expected value of all possible
decision alternatives.
• Select the decision alternative (or course of
action) offering the most attractive expected
value.

62. Roll-Back Technique
• Used for analysing a decision tree.
• Proceeds from the last decision in the sequence
and works back to the first for each of the
possible decisions.
• Two rules concerning this technique:
– If branches emanate from a circle, the total expected
payoff may be calculated by summing up the
expected values of all the branches.
– If branches emanate from a square, we calculate the
total expected payoff for each branch emanating from
that square and the branch with the highest expected
benefit gives the solution.

63. Decision Tree: Advantages
• Useful for portraying the interrelated, sequential and
multidimensional aspects of a decision problem.
• Focuses attention on the critical elements in a decision
problem.
• Especially useful in cases where an initial decision and
its outcome affect the subsequent decisions.
• Enables the decision maker to see the various
elements of the decision problem in a systematic way.
• Complex managerial problems can be explicitly
defined.
• Can be applied in various fields.

64. Decision Tree Approach: Applications
• Introduction of a new product.
• Marketing strategy.
• Make or buy decisions.
• Pricing assets acquisition.
• Investment decisions.

65. A company owns a lease on a property. It may
sell the lease for Rs.12000 or it may drill the said
property for oil. Various possible drilling results
are as under along with the probabilities of
happening and rupee consequences:
Possible Result Probability Rupee Consequence
Dry well 0.10 -100000
Gas well 0.40 45000
Oil & gas well 0.30 98000
Oil well 0.20 199000

66. D1
C1
Rs.12000
(Rs.100000)
Rs.45000
Rs.98000
Rs.199000
sell the lease
drill for oil
outcome of drilling
dry well (p=0.1)
gas well (p=0.4)
oil & gas well (p=0.3)
oil well (p=0.2)

68. Mr. X of ABC Ltd. wants to introduce a new product in the
market. He has a choice of two different research and
development plans A and B. A costs Rs.10 lakh and has 40%
chance of success whereas B costs Rs.5 lakh with 30% chance
of success. In the event of success, Mr. X has to decide whether
to advertise the product heavily or lightly. Heavy advertising will
cost Rs.4 lakh and give a 0.7 probability of full acceptance and
0.3 probability of partial acceptance by the market. Light
advertising will cost Rs.1 lakh with a probability 0.5 of full
acceptance and 0.5 probability of partial acceptance. Full market
acceptance of the product developed as per plan A would be
worth Rs.40 lakh and as per plan B would be worth Rs.30 lakh.
Partial acceptance in both the cases will be worth Rs.20 lakh.
Which plan should Mr. X adopt and what sort of advertising
should be done for marketing the product? Solve the problem
with the help of a decision tree.

69. D1
C2
C1
D2
D3
C3
C6
C4
C5

70. D1
C2
C1
D2
D3
C3
C6
C4
C5
A(Rs.10,00,000)B(Rs.5,00,000)
Failure (P=0.6)
Failure (P=0.7)
Success (P=0.4)
Success (P=0.3)
HA (4,00,000)
LA(1,00,000)
LA (1,00,000)
HA(4,00,000)
FA (P=0.7)
PA (P=0.3)
FA (P=0.5)
PA (P=0.5)
FA (P=0.7)
PA (P=0.3)
FA (P=0.5)
PA (P=0.5)
Rs.40,00,000
Rs.40,00,000
Rs.30,00,000
Rs.30,00,000
Rs.20,00,000
Rs.20,00,000
Rs.20,00,000
Rs.20,00,000
Rs.0
Rs.0