1. QUANTITATIVE TECHNIQUES
Lecture 1
Decision Analysis
September 2009 1

2. Decision Making
Decision making is a vital part of our everyday lives. One decision may make the difference between a successful career and an unsuccessful one.
Decision theory is an analytic and systematic approach to the study of decision making.
What makes the difference between good and bad decisions?

3. Decision Theory
Decision theory treats decisions against nature. This refers to a situation where the result (return) from a decision depends on action of another player (nature).
For example, if the decision is to carry an umbrella or not, the return (get drench or not) depends on what action nature takes. It is important to note that, in this model, the returns accrue only to the decision maker. Nature does not care what the outcome is.

4. Various stages in decision making process
Perceiving the need for decision making
Determining the objectives
Collection of relevant information
Evaluating alternative courses of action
Choosing the best alternative

5. Decision Theory
The fundamental piece of data for decision theory problems is a payoff table:

6. Decision Theory
The entries rij are the payoffs for each possible combination of decision and state of nature. The decision process is the following.
The decision maker selects one of the possible decisions d1, d2, d3, , dn. Say di.
After this decision is made, a state of nature occurs. Say state j.
The return received by the decision maker is rij

7. Decision Theory
The question faced by the decision maker is: which decision to select?
The decision will depend on the decision maker's belief concerning what nature will do, that is, which state of nature will occur.
If we know which state of nature will occur, we simply select the decision that yields the largest return for the known state of nature. In practice, there may be infinitely many possible decisions.

8. Types of decision making situations
The types of decisions people make depend on how
much knowledge or information they have about
the situation. Three decision-making environments
are defined as follows:
Decision making under certainty,
Decision making under risk and
Decision making under uncertainty.

9. Decision making environments
Decision Making under Certainty: In the environment of decision making under certainty, decision makers know with certainty the consequence of every alternative or decision choice. Naturally, they will choose the alternative that will maximise their well-being or will result in the best outcome.

10. Decision Making under Risk: In decision making under risk, the decision maker knows the probability of occurrence of each outcome.
Objective: optimise the expected monetary value (EMV) and minimisation of expected loss.
Most popular methods used are EMV and EOL (Expected opportunity loss).

11. Decision Making under Uncertainty: In decision making under uncertainty, the decision maker does not know the probabilities of the various outcomes.

12. Decision Theory Decisions Under Risk
We make the assumption that there is more than one state of nature and that the decision maker knows the probability with which each state of nature will occur.
Let Pj be the probability that state j will occur. If the decision maker makes decision di, the expected return ERi is
ERi = ri1p1 + ri2p2 + ….. + rimpm.

13. Example 1
A newsboy buys papers from the delivery truck at the beginning
of the day. During the day, he sells papers. Leftovers papers at
the end of the day are worthless. Assuming that each paper
costs Rs and sells for Rs and that the following
probability distribution is known.
Po = Prob {demand = 0} = 0.2
P1 = Prob {demand = 1} = 0.4
P2 = Prob {demand = 2} = 0.3
P3 = Prob {demand = 3} = 0.1
(i). Construct a payoff table for the given situation.
(ii). How many papers should the newsboy buy from the
delivery truck?

14. Decision Theory
The fact that the newsboy must make his buying decision before demand is realised has a considerable impact on his revenues. If he could first see the demand being realised each day and then buy the corresponding number of newspapers for that day, his expected return would increase by an amount known as the expected value of perfect information (EVPI).
The expected value of perfect information indicates the expected gain from any such endeavor and thus places an upper bound on the amount that should be spent in gathering information.

15. Decision Trees Graphical display of decision process
Used for solving problems
With one set of alternatives and states of nature, decision tables can be used also
With several sets of alternatives and states of nature (sequential decisions), decision tables cannot be used
Expected Monetary Value (EMV) is criterion most often used. 15

16. Expected Monetary Value (EMV)
By using a decision table that contains conditional values and probability assessments for all states of nature, it is possible to determine the expected monetary value for each alternative if the decision could be repeated a large number of times.
The EMV for an alternative is just the sum of possible payoffs of the alternatives, each weighted by the probability of that payoff occurring.

17. Expected Monetary Value (EMV)
EMV (alternative i) = (payoff of first state of nature) * (probability of first state of nature) + (payoff of second state of nature) * (probability of second state of nature) + …… (payoff of last state of nature) * (probability of last state of nature).

18. Analysing Problems with Decision Trees
Define the problem
Structure or draw the decision tree
Assign probabilities to the states of nature
Estimate payoffs for each possible combination of alternatives and states of nature
Solve the problem:
Compute expected values for each state-of-nature node moving right to left.
Select decisions that maximize expected value. 18

19. Terms:
Alternative: Course of action or choice.
State of nature: An occurrence over which the decision maker has no control.
Symbols used in decision tree:
: A decision node from which one of several alternatives may be selected.
: A state of nature node out of which one state of nature will occur.

20. Decision Tree 1 2 State 1 State 2 Outcome 1 Outcome 2 Outcome 3
Alternative 1
Alternative 2
Decision Node
Outcome 1
Outcome 2
Outcome 3
Outcome 4
State of Nature Node 20

21. Example 2
A company has a new product which is expected to have great potential.
At the moment the company has two courses of action open to the
marketing department either test the market or drop the product. If the
department test the product, it will cost Rs. 50,000 and the response could
be positive or negative with the probabilities of 0.70 and 0.30 respectively.
If it is positive, they could either market it with full scale, then the result
might be low, medium or high demand and the respective net payoffs
would be -Rs, 100,000, Rs. 100,000 or Rs. 500,000. These outcomes have
probabilities of 0.25, 0.55 and 0.20 respectively. If the result of the test
marketing is negative they have decided to drop the product. If, at any
point, they drop the product there is a net gain of Rs. 25,000 from the scale
of scrap. All financial values have been discounted to the present.
Draw a decision tree for the problem and indicate the most preferred
decision.

22. Sensitivity Analysis
Investigates how our decision making might change with different input data.
Involves the changing of weights (for example, efficiency, sustainability or equity goals) or parameters (for example, prices, unit cost, probability of research success, probability of adoption) in a decision making algorithm in order to gain information about the "robustness" of the decision making process.
We can analyse the dependence of our results on our initial assumptions. This analysis can be conducted either through group analysis and discussion, or by means of mathematical procedures in which either the measurement methods or the criteria weights are modified.
However, before we start any investigation we first define an important variable: P = probability, which must be between 0 and 1.

23. Example 3
The decision that Omega Computer Manufacturing
Company Ltd. identifies is whether or not to expand his
product line by manufacturing and marketing a new
product, liquid-cooled motherboards. The management of
this company has to generate the alternatives that are
available to them and the alternatives are: (1) to construct a
large plant to manufacture the motherboards, (2) to
construct a small plant, or (3) construct no plant at all. The
company determines that there are only two possible
outcomes: first, the market for the motherboards could be
favorable, meaning there is a high demand for the product,
or it could be unfavorable, meaning there is a low demand.

24. Favourable Market (Rs.) Unfavourable Market (Rs.)
Decision
State of nature
Favourable Market (Rs.)
Unfavourable Market (Rs.)
Construct a large plant
200,000
-180,000
Construct a small plant
100,000
-20,000
Do nothing
Management’s best estimates of the probabilities of a
favourable or an unfavourable market are both 0.5.
Which strategy should be chosen by the management?
Evaluate the EVPI.

25. Example 4
Company ABC has developed a new line of products. Top management is
attempting to decide on the appropriate marketing and production strategy. Three
strategies are being considered, which are referred as A (aggressive), B (basic) and
C (cautious). The market conditions under study are denoted by S (strong) or W
(weak). Management’s best estimate of the net profits (in millions of Rs.) in each
case are given in the following table.
Management’s best estimates of the probabilities of a strong or a weak market are
0.45 and 0.55 respectively.
Which strategy should be chosen by the management? Conduct also a
sensitivity analysis for the given situation to determine the limits for the
alternatives.
Decision
State of nature S W A 30 -8 B 20 7 C 5 15