To understand decision making environments, decision tree and basics of experimental design in accordance to VTU 14MBA14 Business Analytics subject

1. Decision Theory
14MBA14 Module 3
Dr. Surekha Prabhu
Professor& Head
Dept of Management Studies,
K.V.G. College of Engineering,
Sullia

2. Contents
Fundamentals of decision theory
Decision environment
Decision making under uncertainty
Decision making under risk
Decision tree
Experimental design-basics
References
Operations Research: Theory and Applications by J K
Sharma
http://www.r-tutor.com/elementary-statistics

3. Decision Theory represents a general approach to
decision making which is suitable for a wide range of
management decisions, including:
product and
service design
equipment
selection
location
planning
Decision Theory
Capacity
planning
Product –mix Credit policies

4. 4
Problem Formulation
• A decision problem is characterized by decision
alternatives, states of nature, and resulting
payoffs.
• The decision alternatives are the different
possible strategies the decision maker can
employ.
• The states of nature refer to future events, not
under the control of the decision maker, which
will ultimately affect decision results.
• States of nature should be defined so that they
are mutually exclusive and contain all possible
future events that could affect the results of all
potential decisions.

5. 5
Payoff Tables
• The consequence resulting from a specific
combination of a decision alternative and a
state of nature is a payoff.
• A table showing payoffs for all combinations
of decision alternatives and states of nature is
a payoff table.
• Payoffs can be expressed in terms of profit,
cost, time, distance or any other appropriate
measure.

6. Fundamentals of decision theory
Decision
alternatives
States of
nature
Payoff
Courses of
action or
strategies
An occurrence
over which
decision maker
has no control
Quantitative
measure of
the outcome

7. Three-egg omelette Problem
• You are preparing a three-egg omelette.
Having already broken two good eggs into the
pan, you are suddenly assailed by doubts
about the quality of the third. As yet
unbroken.egg, two things may happen: either
the egg is good or it is rotten.

8. Egg omelette problem
Events Probability Break 3rd egg
into pan
Break 3rd egg
into saucer &
inspect
Throw away 3rd
egg
Third egg is good 0.9 3-egg omlette 3-egg
omelette, one
saucer to wash
2-egg
omelette, one
good egg
destroyed
Third egg is rotten 0.1 No egg omlette
2 good eggs
destroyed
2-egg
omelette, one
saucer to wash
2-egg omelette
States of
nature
Acts (strategies)
Pay-offs

9. • Certainty - Environment in which
relevant parameters have known
values
• Risk - Environment in which
certain future events have
probable outcomes
• Uncertainty - Environment in
which it is impossible to assess
the likelihood of various future
events
Decision Environments

10. Risk vs. Uncertainty
• Risk
– Must make a decision for which the outcome is not known with
certainty
– Can list all possible outcomes & assign probabilities to the
outcomes
• Uncertainty
– Cannot list all possible outcomes
– Cannot assign probabilities to the outcomes
• Certainty
-is an environment in which future outcomes or state of nature are
known.
• Eg: Investment in Bank FD, there is CERTAINTY regarding
FUTURE PAYMENTS on maturity
• Investment in shares is risky
• Investment in shares FETCHING returns higher than FD in
another 2 years, is uncertain

11. Criteria of decision making under
uncertainity
0ptimism(Maximax or Minimin)
Pessimism(Maximin or Minimax)
Equal probabilities(Laplace)
Coefficient of optimism(Hurwicz)
Regret(Salvage)

12. Optimism (Maximax or Minimin criterion)
• Choose the alternative with the best possible
payoff
• Locate the maximum or minimum payoff
values corresponding to each alternatives
• The maximax is 7000 ,hence the company
should adopt strategy S1
Strategies
States of nature
N1 N2 N3
ROW
MAXIMUM
S1 7000 3000 1500 7000
S2 5000 4500 0 5000
S3 3000 3000 3000 3000

13. Pessimism Maximin or Minimax criterion
• Choose the alternative with the best of the
worst possible payoffs
• Locate the minimum payoff values
corresponding to each alternatives
• The act/decision with higher minimum value
is 3000 ,hence the company should adopt S3
criterion strategy S3
Strategies
States of nature
N1 N2 N3
Row Minimum
S1 7000 3000 1500 3000
S2 5000 4500 0 0
S3 3000 3000 3000 3000

14. Laplace criterion(Equal probabilities)
• Under this assumption ,all states of nature are
equally likely.
• decision maker can compute the average
payoff for each row (the sum of the possible
consequences of each alternative is divided by
the number of states of nature) and, then,
select the alternative that has the highest row
average

15. LAPLACE CRITERION
Strategies
States of nature
N1 N2 N3
ROW
MAXIMUM
S1 7000 3000 1500 3,833.33
S2 5000 4500 0 3166.66
S3 3000 3000 3000 3000
The largest expected return is from Strategy S1, THE EXECUTIVE MUST
SELECT S1

16. Coefficient of optimism(Hurwicz)
• This criterion represents a compromise between the
optimistic and the pessimistic approach to decision
making under uncertainty.
• For each alternative select the largest &lowest
payoff values and multiply these with α and (1- α)
values respectively.
• Then calculate the weighted average using the
formula:
H Coefficient of optimism =
α (maximum in column)+ (1-α)(minimum in column)
• Select the best answer

17. Hurwicz Criterion
Strategy Maximum
pay-off
Minimum
pay-off
H
S1 7000 1500 4800
S2 5000 0 3000
S3 3000 3000 3000
Assuming degree of optimisim α = 0.6 and (1- α )=0.4
H Coefficient of optimism = α (maximum in column) +
(1-α)(minimum in column)
The maximum value is 4800, adopt S1

18. Regret (Salvage rule)
• This rule represents a pessimistic approach.
• The opportunity loss reflects the difference
between each payoff and the best possible payoff
in a column (it can be defined as the amount of
profit foregone by not choosing the best
alternative for each state of nature).
• For each course of action identify the maximum
regret value, record this no in a row
• Select the course of action with Smallest
anticipated opportunity loss value

19. Strategies
States of nature
N1 N2 N3
Row max
S1 7000 – 7000
= 0
4500-3000=
1500
3000-1500=1500 1500
S2 7000- 5000
= 2000
4500-4500=0 3000-0=3000 3000
S3 7000-3000 =
4000
4500-3000=
1500
3000-3000=0 4000
Col max 7000 4500 3000
The company should adopt minimum opportunity loss strategy S1
Strategies States of nature
N1 N2 N3
S1 7000 3000 1500
S2 5000 4500 0
S3 3000 3000 3000
Column max 7000 4500 3000

20. Decision table and tree
1
Outcome 1
outcome2
2
Outcome 3
outcome 4
States of nature
Strategies State 1 State 2
Strategy 1 Outcome 1 Outcome2
Strategy 2 Outcome 3 Outcome 4

21. Decision tree
• Decision tree is a network which exhibits
graphically the relationship between the different
parts of the complex decision process.
• It is a graphical model of each combination of
various acts and states of nature along with their
payoffs, probability distribution
• It is extremely useful in multistage situations
which involve a number of decisions ,each
depending on the preceding one.
• A decision tree analysis involves the construction
of a diagram that shows , at a glance, when
decisions are expected to be made- in what
sequence, their possible outcomes, &
corresponding payoffs.

22. • A DT consists of nodes, branches, probability estimates and
pay-offs
• Three types of “nodes”
– Decision nodes - represented by squares (□) It
represents a point of action where a decision maker
must select one alternative course of action among the
available
– Chance nodes - represented by circles (Ο) It indicates a
point of time where the decision maker will discover the
response to his decision
– Terminal nodes - represented by triangles (optional)
• Solving the tree involves pruning all but the best decisions
at decision nodes, and finding expected values of all
possible states of nature at chance nodes
• Create the tree from left to right
• Solve the tree from right to left

23. Decision tree example
Stay comfortable and dry
Bear unnecessary trouble of carrying umbrella
Get wet and uncomfortable
Remain dry and comfortable

24. 24
Elements of Decision Theory
• States of nature: The states of nature could be
defined as low demand and high demand.
• Alternatives: VGK could decide to build a small,
medium, or large Flour processing mill .
• Payoffs: The profit for each alternative under
each potential state of nature is going to be
determined.
We develop different models for this problem on the
following slides.

25. 25
VGK Flour mill : Payoff Table
Alternatives
Low High
Small 8 8
Medium 5 15
Large -11 22
States of Nature
(Profits in LAKHS of Rs )
THIS IS A PROFIT PAYOFF TABLE

26. 1
n
i i
i
E( X ) Expected value of X p X

  
Decision making under risk
Expected monetary value
Where Xi is the ith outcome of a decision, pi is the
probability of the ith outcome, and n is the total
number of possible outcomes
 Each possible state of nature has an assumed
probability pi
 States of nature are mutually exclusive
 Probabilities must sum to 1
 Determine the expected monetary value (EMV) for
each alternative

27. EMV Example
1. EMV(A1) = (.5)($200,000) + (.5)(-$180,000) = $10,000
2. EMV(A2) = (.5)($100,000) + (.5)(-$20,000) = $40,000
3. EMV(A3) = (.5)($0) + (.5)($0) = $0
States of Nature
Favorable Unfavorable
Alternatives Market Market
Construct large plant (A1) $200,000 -$180,000
Construct small plant (A2) $100,000 -$20,000
Do nothing (A3) $0 $0
Probabilities .50 .50
Best Option

28. Expected Opportunity Loss (EOL)
• It is the opposite of EMV
• EOL is defined as the difference between the
highest profit or pay-off and the actual profit due
to choosing a particular course of action in a
particular state of nature
• The conditional opportunity loss (EOL) for a
particular course of action is determined by taking
the difference between the payoff value of the
most favourable course of action and some other
course of action.

30. act Cold weather Warm weather
Sell cold drinks 60-40= 20 90-90 =0
Sell ice cream 60-60 = 0 90-40 =50
Sell cold drinks 0.3 x 20 + 0.7 x 0 = 6
Sell ice cream 0.3 x 0 + 0.7 x 50 = 35
Opportunity loss matrix
EOL for each alternative course of action is computed as below
Since EOL is minimum in case of selling cold drinks ,this is the best act
Sell cold drinks 0.3 x 40 + 0.7 x 90 = 75
Sell ice cream 0.3 x 60 + 0.7 x 40 = 46
Since EMV is more for selling cold drinks, it is recommended

31. Expected Value of Perfect Information
Expected value of perfect information: the
difference between the expected payoff under
certainty and the expected payoff under risk
Expected value of
perfect information
Expected payoff
under certainty
Expected payoff
under risk
=
-
EVPI is defined as the maximum amount one would
pay to obtain perfect information about the state of
nature that would occur.

32. EXPERIMENTAL DESIGN
Experiment some management examples
Sales Productivity
Experiment
Will an increase in the average number of sales
calls per customer from six to eight per year
significantly improve sales?
Shelf Space Experiment Will decreasing the shelf space allocated to brand
X detergent by 25 percent significantly lower its
sales?
Direct Mail Experiment Will it be worthwhile to mail last year's donors an
attractive (but expensive) brochure describing the
company’s activities and soliciting higher
contributions for this year?
Pricing Experiment Can a company improve the profitability of its
fashion clothing line by increasing its price by 10
percent?

33. Experiment
• An experiment is a procedure in which a
company manipulates one (or sometimes
more than one) independent or cause
variable and collects data on the
dependent or effect variable while
controlling for other variables that may
influence the dependent variable

34. Variables are measures
that change .
The independent variable
is the variable that is
purposely changed. It is
the manipulated
variable.
The dependent variable
changes in response to
the independent
variable. It is the
responding variable.
Independent
variables
increase in the
average number
of sales calls per
customer
decreasing the
shelf space
allocated to brand
X detergent
mail last year's
donors an
attractive
brochure
Dependent
variables
sales
sales
higher
contributions

35. Constants &control in an Experiment
What are constants in an experiment?
Factors that are kept the same and not allowed to change
What is a control?
The part of the experiment that serves as the standard of
comparison.
It is the unchanged part of the experiment that detects the
effects of hidden variables
Levels of the Independent Variable
How many different levels of the independent variable
should we test?

36. Writing A Statement of the
Problem for the
Experiment
It should state: “The Effect of the Independent
Variable on the Dependent Variable”.
What should it state?

37. An Introduction to Experimental Design
 A factor is a variable that the experimenter has
selected for investigation (the independent variable).
 A treatment is a level of a factor.
 Experimental units are the objects of interest
in the experiment.
 A completely randomized design is an
experimental design in which the treatments are
randomly assigned to the experimental units.

38. Fast food Franchise must decide which menu
item to market. Are the three Menu items equally
effective?
A Completely Randomized Experimental Design
Factor . . . New menu
Treatments . . . Item 1, Item 2 , Item 3
Experimental units . . . Franchise restaurants
Response variable . . . sales volume
A fast food franchise is test marketing 3 new menu items. To find out
if they the same popularity, 18 franchisee restaurants are randomly
chosen for participation in the study. In accordance with the
completely randomized design, 6 of the restaurants are randomly
chosen to test market the first new menu item, another 6 for the
second menu item, and the remaining 6 for the last menu item.

39. Item1 Item2 Item3
22 52 16
42 33 24
44 8 19
52 47 18
45 43 34
37 32 39
Suppose the following table represents the sales figures of the 3 new
menu items in the 18 restaurants after a week of test marketing.
Purpose is to….
test whether the mean
sales volume for the 3
new menu items are all
equal.

40. Randomized Block Design
• In a randomized block design, there is only
one primary factor under consideration in the
experiment. Similar test subjects are grouped
into blocks. Each block is tested against all
treatment levels of the primary factor at
random order. This is intended to eliminate
possible influence by other extraneous factors.

41. Item1 Item2 Item3
R1 31 27 24
R2 31 28 31
R3 45 29 46
R4 21 18 48
R5 42 36 46
R6 32 17 40
A fast food franchise is test marketing 3 new menu items. To find
out if they have the same popularity, 6 franchisee restaurants are
randomly chosen for participation. For the randomized block
design, each restaurant will be test marketing all 3 new menu
items. A restaurant will test market only one menu item per
week, and it takes 3 weeks to test market all menu items. The
testing order of the menu items for each restaurant is randomly
assigned
Purpose is to….
test whether the mean
sales volume for the 3 new
menu items are all equal.

42. Factorial Experiments
 In some experiments we want to draw conclusions
about more than one variable or factor.
 Factorial experiments and their corresponding results
are valuable designs when simultaneous conclusions
about two or more factors are required.
 For example, for a levels of factor A and b levels of
factor B, the experiment will involve collecting data
on ab treatment combinations.
 The term factorial is used because the experimental
conditions include all possible combinations of the
factors.

43. Factorial Design
• A fast food franchise is test marketing 3 new
menu items in North Indian & South Indian
States. To find out if they the same popularity, 12
franchisee restaurants from each part are
randomly chosen for participation in the study. In
accordance with the factorial design, within the
12 restaurants from north India, 4 are randomly
chosen to test market the first new menu item,
another 4 for the second menu item, and the
remaining 4 for the last menu item. The 12
restaurants from North India are arranged
likewise.

44. Following tables represent the sales figures of the 3
new menu items after a week of test marketing
• Item1 Item2 Item3
N1 25 39 36
N2 36 42 24
N3 31 39 28
N4 26 35 29
Item1 Item2 Item3
S1 51 43 42
S2 47 39 36
S3 47 53 32
S4 52 46 33
Purpose is to……….
test whether the mean
sales volume for the
new menu items are all
equal
Decide also whether the
mean sales volume of
the two regions differs.