1. Lecture: Decision making under uncertainty Date: 07.07.14
Managerial Economics
Lecture: Decision making under uncertainty
Date:

2. Decisions and Decision Making
Decision = choice made from available alternatives
Decision Making = Process of identifying problems and opportunities and resolving them

3. Managerial Decision Making
Decision making is not easy
It must be done amidst of
ever-changing factors
unclear information
conflicting points of view

4. Categories of Decisions
Programmed Decisions
Situations occurred often enough to enable decision rules to be developed and applied in the future
Made in response to recurring organizational problems
Non-programmed Decisions – in response to unique, poorly defined and largely unstructured, and have important consequences to the organization

5. Decisions and Decision Making
Many decisions that managers deal with every day involve at least some degree of uncertainty and require non-programmed decision making
May be difficult to make
Made amid changing factors
Information may be unclear
May have to deal with conflicting points of view

6. Certainty, Risk, Uncertainty, Ambiguity
all the information the decision maker needs is fully available
Risk
decision has clear-cut goals
good information is available
future outcomes associated with each alternative are subject to chance

7. Certainty, Risk, Uncertainty, Ambiguity
managers know which goals they wish to achieve
information about alternatives and future events is incomplete
managers may have to come up with creative approaches to alternatives
Ambiguity
by far the most difficult decision situation
goals to be achieved or the problem to be solved is unclear
alternatives are difficult to define
information about outcomes is unavailable

8. Economic risk
Refers to the chance of loss because all possible outcomes and their probabilities are known
Business Risk
The chance of loss associated with a managerial decision
Uncertainty
When future outcomes can not be predicted with absolute accuracy but possibilities and probabilities are not known

9. Probability
Chance of occurrence
Probability Distribution
A list of possible events and probabilities
Payoff matrix
Table that shows outcomes associated with each possible state of nature

10. Payoff matrix
A firm will choose only one from two alternative projects
Each calling for an outlay of $10,000
Profits earned from the two projects are related to the general level of economic activity during the coming year

11. Payoff Matrix State of the economy Profits Recession $4000 $ 0
Project A Project B
Recession $4000 $ 0
Normal
Boom

12. Probability Distribution
A sales manager observes that there is a 70 % chance that a given customer will place a specific order versus a 30% chance that she will not
Event Probability of Occurrence
Receive order 0.7=70%
Do not receive order 0.3=30%
Total =100%

13. Decision Making: The Process of making a conscious choice between 2 or more alternatives producing most desirable consequences (benefits) relative to unwanted consequences (costs).
If Planning is truly Deciding in advance what to do, how to do it, when to do it and who is to do it, then Decision Making is an essential part of Planning

14. Categories of Decision Making
Decision Making Under Certainty: Linear Programming
Decision Making Under Risk: expected value, decision
trees, queuing theory, and simulation
Decision Making Under Uncertainty: Game Theory

15. Payoff (Benefit) Table - Decision Matrix
N N2 ……… Nj ……… Nn
P P2 ……… Pj ……… Pn
A O O12 ……… O1j ……… O1n
A O O22 ……… O2j ……… O2n
… … … ……… … …… …
Ai Oi Oi ……… Oij ……… Oin
Am Om Om ……… Omj …… Omn
Alternative
State of Nature / Probability
Outcome
Sum of n values of pj must be 1

16. N1 , N2 , Nj ……… Nn Decision alternatives, state of nature
A1, A2,…. Am Decision alternatives
N1 , N2 , Nj ……… Nn Decision alternatives, state of nature
P P2 ……… Pj ……… Pn Probability of occurrence
Om Om ……… Omj …… Omn Outcomes

17. Decision Making Under Certainty
Implies that we are certain
of the future state of nature
(or assume we are). Linear programming is a tool for the
decision making under certainty.
This means:-
the probability of pj of future Nj is 1 and all
other futures have zero probability

18. Each Nj has a known (or assumed) probability of pj and
Decision Making Under Risk
This means:-
Each Nj has a known (or assumed) probability of pj and
there may not be one state that results best outcome.

19. Probabilities pj of future states are unknown.
Decision Making Under Uncertainty
This means:-
Probabilities pj of future states are unknown.

20. Decision Making Under Risk
There exist a number of possible future states of Nature Nj.
Each Nj has a known (or assumed) probability pj of occurring.
There may not be one future state that results in the best outcome for all alternatives Ai.
Examples of future states and their probabilities
Alternative weather (N1=rain, N2=good weather) will affect the
probability of alternative construction schedule; the probabilities P1 of
rain and p2 of good weather can be estimated from historical data
2. Alternative economic futures (boom and bust) determine the relative
Profitability of high risk investment strategy.

21.  (pjOij) Ei= Decision Making Under Risk n
Expected Values (Ei) : given the future states of nature and their
probabilities, the solution in decision making under risk is the
alternatives Ai that provides the highest expected value Ei, which is
defined as the sum of the products of each outcome Oij
times the probability pj that the associated state of nature Nj occurs n 
j=1
(pjOij)
Ei=
Choose the Alternative Ai giving
the highest expected value

22.  Example of Decision Making Under Risk Alternatives
Calculate Expected Values (Ei)
Example of Decision Making Under Risk
Not Fire
in your house
P1 = P2=0.001
Insure house $ $-200
Do not Insure house $-100,000
Alternatives
Fire
State of Nature
Probabilities n 
j=1
(pjOij)
Ei=
Would you insure your house or not?
E1=$-200
E1=0.999*(-200)+0.001*(-200)
E2=$-100
E2=0.999* *(-100,000)

23. Example: Consider that you own rights to a plot of land under which
there may or may not be oil. You are considering three alternatives:
Doing nothing (don’t drill), drilling your own expense of $
(Drill alone), and farming out, the opportunity to someone who will
drill the well and give you part of the profit if the well is successful.
Drilling your own a small Well will make $ profit and a Big well $.
Farm out alternative with Dry hole will not cost at all, but a small Well
Will make $ and a Big Well will make $ profit.
Constitute the Payoff table and calculate the expected value of each
alternative solve the problem.

24. $720,000 Alternative State of Nature / Probability
Decision Making Under Risk
Calculate Expected Values (Ei)
Well Drilling Example-Decision Making Under Risk
N1:Dry Hole N2 :Small Well N3:Big Well
P1= P2= P3=0.1
A1:Don’t Drill $ $ $0
A2:Drill Alone $-500, $300, $9,300,000
Alternative
State of Nature / Probability
A3:Farm Out $ $125, $1,250,000
Expected
Value
E1=0.6*0+0.3*0+ 0.1*0 $0
E2=0.6*(-500,000)+0.3*(300,000)+ 0.1*(9,300,000)
$720,000
E3=0.6*0+0.3*(125,000)+ 0.1*(1,250,000)
$162,000
$720,000
A2 is the solution if you are willing to risk $500,000

25. Decision Tree
The visual mapping of a sequential decision making process
A convenient way to represent decisions, chance events and possible outcomes in choices under risk and uncertainty
The diagram can incorporate all the specific objectives of the decision maker have been established
The structure of the tree emphasizes the ingredients , choices, outcomes and probabilities
The more precise the tree become, the more precise the more precise one’s thinking becomes about the problem

26. Decision Trees Decision Making Under Risk Decision node Ai Chance
Calculate Expected Values (Ei)
Decision Trees
Decision
node Ai
Chance
node Nj
Outcome
(Oij)
Probability
(Pj)
Expected Value Ei x =
No Fire:
(-200) x
(0.999) =
(-199.8) +
= $-200
Insure
(-200) x
(0.001) =
(-0.2)
Fire:
No Fire:
(0) x
(0.999) =
(0)
Don’t Insure +
=$-100
Fire:
(-100,000) x
(0.001) =
(-100)
Mathematical solution is identical,
visual representation is different

27. Simulation
First step
Construction of a mathematical model of the managerial decision-making that we want to simulate

28. Simulation
An aerospace engineer constructs a miniature model plane and wind tunnel to test the strength and resistance of the model plane to change in wind speed and direction
This modeling mimics the essential features of the essential features of the real-world situation

29. Simulation
The firm might construct a model for the strategy of expanding the output
The between the output of the commodity and its price, output, selling costs, revenues and taxes
Calculate the firm’s profit
Varying the value of each variable substituted into the model the firm can get an estimate of the effect of the change in the variable on the output of the model or profit of the firm

30. Simulation This refers to sensitivity analysis
To fully simulate the strategy to expand output, the firm needs the probability distribution of the concerned variables(output, commodity prices, input prices, depriciation……)
Randomly selected values of each variable of the model are then fed into the computer program to generate the present value of the firm’s profit is recorded

31. Simulation
The probability distribution of the firm’s profits so generated can then be used to calculate the expected profit of the firm and the standard deviation of the distribution of the profit (As a measure of risk)
Using this information the firm determine the optimal strategy to adopt

32. Simulation Problem -Full scale simulation is expensive
-Only for the large projects when decision king is too complex to analyze with decision tree
But very powerful as consider all the interactions among all the variables

33. Decision Making Under Uncertainty
We do not know the probabilities pj of future states of nature Nj
Where more than one possible outcome to a decision
Probability of each possible outcome is not known
Decision making is necessarily subjective

34. Decision Making Under Uncertainty
Two specific decision rule
-Maximin criterion
-Minimax regret criterion

35. Decision Making Under Uncertainty
Maximin criterion postulates that the decision maker should determine the worst possible outcome of each strategy and then pick the strategy that provides the best of the worst possible outcomes

36. Decision Making Under Uncertainty
The firm could follow the strategy of introducing a new product
-Would provide a return of $20000 if succeeded
-lead to a loss of $10000 if failed
-Not to invest in the venture have zero profit or loss

37. Decision Making Under Uncertainty
Pay off matrix
State of nature
Strategy success failure maximin
Invest $ $ $10000
Do not invest *

38. Decision Making Under Uncertainty
Manger picks the strategy that provides the best (Maximum) of the worst(minimum) possible outcomes(maximin)
This is the decision of not investing as that has the maximum of the minimum payoffs
Pessimistic approach
Appropriate when the firm is strongly risk avert

39. Decision Making Under Uncertainty
Minimax regret criterion postulates that decision maker should select the strategy that minimizes the maximum regret or opportunity cost of the wrong decision whatever the state of nature that actually occurs
Regret is measured by the difference between the payoff of a given strategy and payoff of the best strategy under the same state of nature

40. Decision Making Under Uncertainty
If the best option is chosen no regret
If not the option that will incur the minimum regret

41. Decision Making Under Uncertainty
Pay off matrix
State of nature Regret matrix Maximum regret
Strategy success failure success failure
Invest $ $ $10000*
Do not invest 0 0 $ $20000

42. Decision Making Under Uncertainty
Decision Making Under Risk
Decision Making Under Uncertainty
N1:Dry Hole N2 :Small Well N3:Big Well
A1:Don’t Drill $ $ $0
A2:Drill Alone $-500, $300, $9,300,000
Alternative
State of Nature / Probability
A3:Farm Out $ $125, $1,250,000

43. Decision Making Under Uncertainty
Decision Making Under Uncertainty: Example
Coefficient of optimism
(Maximax) (Maximin)
Hurwicz Equally
Alternative Maximum Minimum (=0.2) Likely
Optimist Pessimist
Maximize [(best outcome)+(1-)(worst outcome)]
$1,450,000*
[0.2(9,300,000)+(1-0.2)(-500,000)]
A2:Drill Alone $9,300,000 * $-500,000
$3,033,333*
E2=-500, ,000+9,300,000 3
[0.2(1,250,000)+(1-0.2)(0)]
$250,000
A3:Farm Out $1,250, $0*
$458,333
E3=0+125,000+1,250,000 3

44. Alternative Alternative State of Nature / Probability
Decision Making Under Risk
Decision Making Under Uncertainty: Maximum Regret
N1:Dry Hole N2 :Small Well N3:Big Well
A1:Don’t Drill $ $ $0
A2:Drill Alone $-500, $300, $9,300,000
Alternative
State of Nature / Probability
A3:Farm Out $ $125, $1,250,000
N1:Dry Hole N2 :Small Well N3:Big Well
We do not know probabilities
A1:Don’t Drill $ $300, $9,300,000
A2:Drill Alone $500,
Alternative
State of Nature / Probability
A3:Farm Out $ $175, $8,050,000
Maximum
Regret
$9,300,000
$500,000
$8,050,000

45. Alternative State of Nature / Probability
Decision Making Under Uncertainty: Maximum Regret
State of Nature / Probability
Alternative
N1:Dry Hole N2 :Small Well N3:Big Well
Maximum
Regret
We do not know probabilities
A1:Don’t Drill $ $300, $9,300,000
$9,300,000
A2:Drill Alone $500,
$500,000
A2 is the solution.
We choose the minimum among maximum regrets.
A3:Farm Out $ $175, $8,050,000
$8,050,000