1. QUANTITATIVE TECHNIQUES
LECTURE 2
FUNDAMENTALS OF DECISION THEORY MODEL
September 2009

2. Learning Objectives Students will be able to:
List steps of the decision-making process.
Describe the types of decision-making environments.
Use probability values to make decisions under risk.
Make decisions under uncertainty & risk but probability values are not known.

3. Steps in Decision Theory
Define the problem and influencing factors.
List the possible alternatives.
Identify the possible outcomes.
List the payoff or profit of each combination of alternatives and outcomes.
Evaluate the problem using one of the decision theory models.
Select best alternative.
Implement the selected alternative.
Evaluate the decision’s effectiveness.

4. Step 1: Identifying the Problem
A discrepancy between an existing and desired state of affairs.
Characteristics of Problems
There is pressure to solve the problem.
The manager must have the authority, information, or resources needed to solve the problem.

5. Step 2: Identifying Decision Criteria
Decision criteria are factors that are important (relevant) to resolving the problem.
(investments required); (chance of failure); (growth of the firm)
Step 3: Allocating Weights to the Criteria
Decision criteria are not of equal importance.

6. Step 4: Developing Alternatives
Identifying viable alternatives
Step 5: Analysing Alternatives
Appraising each alternative’s strengths and weaknesses

7. Step 6: Selecting an Alternative
Choosing the best alternative
Step 7: Implementing the Decision
Putting the chosen alternative into action.

8. Step 8: Evaluating the Decision’s Effectiveness
The soundness of the decision is judged by its outcomes.

9. Components of Decision Making
A decision-making includes several components: the
decisions themselves and “states of nature”.
States of nature: is an actual event that may occur in the
future.
To facilitate the analysis of these types of decision
situations so that the best decisions result, we use
“payoff tables”.
Payoff table: a means of organising a decision situation,
including the payoffs from different decisions given the
various states of nature.

10. Decision Theory Terms: Alternative: Course of action or choice.
Decision-maker chooses among alternatives.
State of nature: An occurrence over which the
decision maker has no control.

11. Types of Decision-Making Environments
1. Decision making under conditions of certainty
Decision-maker knows with certainty the consequences of every alternative or decision choice
2. Decision making under conditions of uncertainty
The decision-maker does not know the probabilities of the various outcomes
Decision making under conditions of risk
The decision-maker does know the probabilities of the various outcomes that result from the choice of particular alternatives.

12. Decision Making under Uncertainty
Maximax (Optimistic approach)
Maximin (Pessimistic approach)
Criterion of realism (Hurwicz Criterion)
Equally likely (Laplace)
Minimax Regret

13. Decision Making Under Uncertainty (without probabilities)
Decision-Making Criteria:
The Maximax Criterion-results in the maximum of the maximum payoffs for every alternative (Optimistic criterion)
The Maximin Criterion-results in the maximum of the minimum payoffs for every alternative (Pessimistic criterion)

14. It is a compromise between the maximax and maximin criteria.
The Minimax Regret Criterion-minimises the
maximum regret.
Regret is the difference between the payoff from the best decision and all other decision payoffs.
The Hurwicz Criterion
It is a compromise between the maximax and maximin criteria.
The coefficient of optimism, is a measure of the decision maker’s optimism.
The Hurwicz criterion multiplies the best payoff by , the coefficient of optimism, and the worst payoff by 1 - , for each decision, and the best result is selected.

15. Summary of Criteria Results
The Equal Likelihood Criterion
weights each state of nature equally, assuming that the states of nature are equally likely to occur.
The equal likelihood criterion multiplies the decision payoff for each state of nature by an equal weight.
Summary of Criteria Results
A dominant decision is one that has a better payoff than another decision under each state of nature
The appropriate criterion is dependent on the “risk” personality and philosophy of the decision maker.

16. Example 1 Suppose that a manufacturer of office equipment must
decide whether to expand his plant capacity now or wait
another year. His advisors tell him that if he expands now
and economic conditions remain good (p = 0.65), there will
be a profit of $369,000: if he expands now and there is a
recession (p = 0.35), there will be a loss of $90,000: if he
waits another year to expand and economic conditions
remain good, there will be a profit of $180,000: and if he
waits another year and there is a recession, there will be a
small profit of $18,000.
Construct a payoff table to present the above
information and choose the preferred decision.

17. Decision Table (Pay-off-table)

18. Decision Making Under Risk
Select alternative with largest expected monetary value (EMV)
EMV (alternative i) = (payoff of first state of nature) x (prob. of first state of nature) + (payoff of second state of nature) x (prob. of second state of nature) +………….+ (payoff of last state of nature) x (prob. of last state of nature)

19. Expected Opportunity Loss (EOL)
Alternative to maximising EMV is to minimise expected opportunity loss (EOL is the cost of not picking the best solution).
First compute an opportunity loss table.
Next, the EOL is computed for each alternative by multiplying the opportunity loss by the probability and adding these together.
We then use the minimum EOL as the decision criteria.

20. Expected Value of Perfect Information (EVPI)
EVPI places an upper bound on what one would pay for additional information.
EVPI is the maximum you should pay to learn the future.
EVPI = *EPPI - EMVmaximum
* where EPPI = (best outcome for first state of nature) x
(prob. of first state of nature) + (best outcome for 2nd
state of nature) x (prob. of 2nd state of nature)
+………..+ (best outcome for last state of nature) x
(prob. of last state of nature)

21. Decision Analysis EVPI = EOLminimum
The minimum EOL will always result in the same decision (NOT value) as the maximum EMV.
The EVPI will always be equal to the minimum EOL.
EVPI = EOLminimum

22. Characteristics of an Effective Decision-Making Process
It focuses on what is important.
It is logical and consistent.
It acknowledges both subjective and objective thinking and blends analytical with intuitive thinking
It requires only as much information and analysis as is necessary to resolve a particular dilemma.
It encourages and guides the gathering of relevant information and informed opinion.
It is straightforward, reliable, easy to use, and flexible.

23. Example 2
The table shown below is an example of a payoff matrix.  The A's stand for the alternative actions available to the decision maker.  These actions represent the controllable variables in the system.  The uncertain events or states of nature are represented by the S's.  Each S has an associated probability of its occurrence, denoted P. 
Actions/States S1
(P=0.25) S2 S3 S4 A1 20 60
- 60 A2
- 20 A3 50
-20
- 80

24. Calculate the following
Hurwicz criterion; 
Laplace insufficient reason criterion; 
Maximax criterion; 
Maximin criterion; 
Expected Opportunity Loss

25. Decision maker’s alternatives (Rs)
Example 3
The table below illustrates the 12 possible payoffs in the record and
tape company’s expansion decision.
Calculate the following
Hurwicz criterion (assume α = 0.45); 
Laplace insufficient reason criterion; 
Maximax criterion; 
Maximin criterion; 
Expected Opportunity Loss.
Decision maker’s alternatives (Rs)
State of nature
Expand
Build
Subcontract
High (0.2)
500,000
700,000
300,000
Moderate (0.3)
250,000
150,000
Low (0.35)
-250,000
-400,000
-10,000
Failure (0.15)
-450,000
-800,000
-100,000