This document discusses decision theory and provides examples of how to analyze decisions using various decision making criteria. It defines decision theory as providing a rational approach to dealing with problems involving uncertainty. Some key decision making criteria discussed include expected monetary value (EMV), expected value of perfect information (EVPI), Maximax, Maximin, Laplace criterion, Hurwicz criterion, opportunity loss matrix, and Savage principle. Worked examples applying these criteria to hypothetical business decisions are provided.

1. Decision Theory
Prof. Anjali M Kulkarni

2. Decision Theory
•“an analytic and systematic approach to
the study of decision making”
 Bad decisions:
 •not based on reasoning
 •do not consider all available data and
possible alternatives
 •do not employ a quantitative approach
Decision Theory Good decisions:
•based on reasoning
•consider all available data and possible
alternatives
•employ a quantitative approach
–A good decision may occasionally result in an unexpected outcome; it is still a good
decision if made properly
–A bad decision may occasionally result in a good outcome if you are lucky; it is still a
bad decision

3. What is Decision Theory?
 Decision theory provides a rational approach to
the managers in dealing with problems confronted
with partial, imperfect or uncertain future
conditions.
 Ex: A manufacturing company has several
alternative methods to increase its production to
meet the increasing market demand may have the
following options :

4. Decision Theory
Ex: A manufacturing company has several alternative methods to increase
its production to meet the increasing market demand may have the
following options :
 List all the viable alternatives
 Expand the present plant
 Construct a new plant
 Subcontract production for extra demand

5. Table 1 : 12 possible payoffs for the
manufacturing company’s expansion decision
Events/Outcomes
States of
Nature(Demand)
(E)
Acts or Alternatives or Options(A)
Expand Diversify Subcontract
High 50000 70000 30000
Moderate 25000 30000 15000
Low -25000 -40000 -1000

6. Problem
 Determine EMV, EVPI, Maximax, Maximin, Laplace
Criterion, Hurwicz Criterion (α = 0.6), Opportunity Loss
Matrix, Savage Principle for the following payoffs:
Product
Acceptance
Probabilities Sales of Product Lines in lakhs
Soap Detergent Tooth Paste
High 0.30 30 45 20
Medium 0.50 60 30 40
Low 0.20 25 10 70

7. Solution
 EMV(Expected Monetary Value)
 The EMV for each decision-making alternative is obtained by
multiplying the conditional profits by assigned probabilities and
adding the resulting conditional values.
 EMV [Soap] = 0.30 * 30 + 0.5 * 60 + 0.20 * 25 = 44
 EMV [Detergent] = 0.30 * 45 + 0.5 * 30 + 0.20 * 10 = 30.5
 EMV [Tooth Paste] = 0.30 * 20 + 0.5 * 40 + 0.20 * 70 = 40
 Conclusion
 The alternative that yields the highest EMV is selected. The highest
EMV is Soap which yields the highest sales.

8. EVPI (Expected Value of Perfect Information )
 EVPI is obtained by multiplying with the associated
probabilities and the highest value in each row
 In the first row of the pay-off table, the highest value is
45. similarly it is multiplied with the other values
 EVPI = 0.30 * 45 + 0.5 * 60 + 0.20 * 70 = Rs. 57.5
 Conclusion
 The decision-maker spends Rs. 57.5 to obtain the perfect
information about the best alternative among the product
lines that yields the highest sales.

9. Maximax
 Select the decision that results in the maximum of the maximum rewards
 A very optimistic decision criterion
 –Decision maker assumes that the most favorable state of nature for each action will
occur
 Most risk prone agent
 Maximax Calculation
 Identify the highest value in each column and select the highest value
 Soap = 60, Detergent = 45, Tooth Paste = 70
 Conclusion
 Tooth Paste is considered as an alternative having highest value

10. Maximin
 Select the decision that results in the maximum of the minimum rewards
 A very pessimistic decision criterion
 –Decision maker assumes that the minimum reward occurs for each decision alternative
 –Select the maximum of these minimum rewards
 Most risk averse agent
 Maximin Calculation
 Identify the smallest value in each column and select the highest value
 Soap = 25, Detergent = 10, Tooth Paste = 20
 Conclusion
 Soap is considered as an alternative having highest value

11. Laplace Criterion
 1/n[ P1 + P2 + .. + Pn] [where n is the number of events, P1, P2 are the
expected payoff’s]
Product Lines Mean (Expected) Payoff
Soap (30 + 60 + 25)/3 = 38.33
Detergent (45 + 30 + 10)/3 = 28.33
Tooth Paste (20 + 40 + 70)/3 = 83.33
Conclusion
Tooth Paste is considered as an alternative having highest value.

12. Hurwicz Criterion (α = 0.6)
Product Lines Max Min Criterion Value
= α . maximum + ( 1 – α ) .
minimum
Soap 60 25 0.6 * 60 + 0.4 * 25 = 46
Detergent 45 10 0.6 * 45 + 0.4 * 10 = 31
Tooth Paste 70 20 0.6 * 70 + 0.4 * 20 = 50
Conclusion
Tooth Paste is considered as an alternative having highest value.

13. Opportunity Loss or Regret Table
 The Opportunity Loss or Regret table can be obtained by subtracting from the
highest profit value in each row with the remaining elements
 In the first row of the Payoff-table, the highest element is 45. In the second
row of the Payoff-table, the highest element is 60. In the third row of the
Payoff-table, the highest element is 70.
Product Acceptance
Sales of Product Lines in lakhs
Soap Detergent Toothpaste
High 15 0 25
Medium 0 30 20
Low 55 60 0

14. Savage Principle
 From the Opportunity Loss Table or Regret Table, the maximum value in each
column is identified. From all the maximum regret values in each of the
columns the minimum among the maximum regret is selected.
 In the first column it is 55, in the second column it is 60 and in third column,
it is 25.
 From all the maximum values, the minimum value is selected.
 The minimum value is 25.
 Conclusion
 Tooth Paste is considered as an alternative having smallest value

15. Practice Problems in Decision Theory
Q.1
 Determine EMV, EVPI, Maximax, Maximin, Laplace Criterion, Hurwicz Criterion
(α = 0.3), Opportunity Loss Matrix, Savage Principle for the following payoffs
Demand
Probabilities Profit of Product Lines in lakhs
T. V Refrigerator Washing Machine
High 0.35 120 75 40
Medium 0.25 50 80 20
Low 0.40 55 30 30

16. Q.2
 Determine EMV, EVPI, Maximax, Maximin, Laplace Criterion, Hurwicz Criterion
(α = 0.7), Opportunity Loss Matrix, Savage Principle for the following payoffs
Demand
Probabilities Sales in lakhs
Expand Diversify Sub Contract
High 0.60 30 80 25
Medium 0.15 65 70 90
Low 0.25 35 15 40