Managerial Economics Lecture: Decision making under uncertainty Date: 07.07.14

Managerial Economics

Lecture: Decision making under uncertainty

Date: 07.07.14

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Decisions and Decision Making

• Decision = choice made from available alternatives

• Decision Making = Process of identifying problems and opportunities and resolving them

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Managerial Decision Making

• Decision making is not easy

• It must be done amidst of – ever-changing factors – unclear information – conflicting points of view

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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

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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

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Certainty, Risk, Uncertainty, Ambiguity

● Certainty● 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

Certainty, Risk, Uncertainty, Ambiguity

● Uncertainty● 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

• Economic risk Refers to the chance of loss because all possible

outcomes and their probabilities are known• Business RiskThe chance of loss associated with a managerial

decision• UncertaintyWhen future outcomes can not be predicted

with absolute accuracy but possibilities and probabilities are not known

• ProbabilityChance of occurrence• Probability DistributionA list of possible events and probabilities• Payoff matrixTable that shows outcomes associated with each

possible state of nature

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

Payoff Matrix

• State of the economy Profits Project A Project B

Recession $4000 $ 0

Normal 5000 5000Boom 6000 12000

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 1.0=100%

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

Categories of Decision MakingDecision Making Under Certainty: Linear ProgrammingDecision Making Under Risk: expected value, decision trees, queuing theory, and simulationDecision Making Under Uncertainty: Game Theory

Payoff (Benefit) Table - Decision Matrix

N1 N2 ……… Nj ……… Nn

P1 P2 ……… Pj ……… Pn

A1 O11 O12 ……… O1j ……… O1n

A2 O21 O22 ……… O2j ……… O2n

…. …. … ……… … …… …

Ai Oi1 Oi2 ……… Oij ……… Oin …. …. … ……… … …… …

Am Om1 Om2 ……… Omj …… Omn

AlternativeState of Nature / Probability

Outcome

Sum of n values of pj must be 1

A1, A2,…. Am Decision alternatives

N1 , N2 , Nj ……… Nn Decision alternatives, state of nature

P1 P2 ……… Pj ……… Pn Probability of occurrence

Om1 Om2 ……… Omj …… Omn Outcomes

Decision Making Under Certainty

Implies that we are certainof 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

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.

Decision Making Under Uncertainty

This means:- Probabilities pj of future states are unknown.


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

1. Alternative weather (N1=rain, N2=good weather) will affect the probability of alternative construction schedule; the probabilities P1 ofrain 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.


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

n

j=1

(pjOij)Ei=

Decision Making Under Risk Calculate Expected Values (Ei)

E1=0.999*(-200)+0.001*(-200) E1=$-200

E2=0.999*0+0.001*(-100,000) E2=$-100

Example of Decision Making Under Risk

Not Fire in your house

P1 =0.999 P2=0.001

Insure house $-200 $-200

Do not Insure house 0 $-100,000

Alternatives

Fire in your house

State of Nature

Probabilities

Would you insure your house or not?

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 500000$ (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 300000$ profit and a Big well9300000$. Farm out alternative with Dry hole will not cost at all, but a small WellWill make 125000$ and a Big Well will make 1250000$ profit. Constitute the Payoff table and calculate the expected value of each alternative solve the problem.


Well Drilling Example-Decision Making Under Risk

N1:Dry Hole N2 :Small Well N3:Big Well

P1=0.6 P2=0.3 P3=0.1

A1:Don’t Drill $0 $0 $0

A2:Drill Alone $-500,000 $300,000 $9,300,000


A3:Farm Out $0 $125,000 $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

$720,000A2 is the solution if you are willing to risk $500,000

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


Decision Trees

Insure

Don’t Insure

No Fire:

Fire:

No Fire:

Fire:

Decision node Ai

Chance node Nj

Outcome (Oij)

Probability (Pj)

Expected Value Ei

(-200) (0.999)

x =

x = (-199.8)

(-200) (0.001)x = (-0.2)

(0) (0.999)x = (0)

(-100,000) (0.001)x = (-100)

+

+

= $-200

=$-100

Mathematical solution is identical, visual representation is different

Simulation

• First stepConstruction of a mathematical model of the

managerial decision-making that we want to simulate

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

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

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

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

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


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


• Two specific decision rule-Maximin criterion-Minimax regret criterion


• 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


• 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


• Pay off matrix State of natureStrategy success failure

maximinInvest $20000 -$10000 -$10000

Do not invest 0 00*


• 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


• 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


• If the best option is chosen no regret• If not the option that will incur the minimum

regret


• Pay off matrix State of nature Regret matrix Maximum regret

Strategy success failure success failure

Invest $20000 -$10000 0 10000 $10000*

Do not invest 0 0 $20000 0 $20000





A2:Drill Alone $-500,000 $300,000 $9,300,000


A3:Farm Out $0 $125,000 $1,250,000


Decision Making Under Uncertainty: Example

A2:Drill Alone $9,300,000 * $-500,000

Alternative Maximum Minimum (=0.2) Likely

A3:Farm Out $1,250,000 $0*

Hurwicz Equally

$3,033,333*

E2=-500,000+300,000+9,300,000 3

$458,333

E3=0+125,000+1,250,000 3

Coefficient of optimism

(Maximax) (Maximin)

Maximize [(best outcome)+(1-)(worst outcome)]

$1,450,000*

[0.2(9,300,000)+(1-0.2)(-500,000)]

[0.2(1,250,000)+(1-0.2)(0)]

$250,000

Optimist Pessimist


Decision Making Under Uncertainty: Maximum Regret



A2:Drill Alone $-500,000 $300,000 $9,300,000


A3:Farm Out $0 $125,000 $1,250,000


We do not know probabilities

A1:Don’t Drill $0 $300,000 $9,300,000

A2:Drill Alone $500,000 0 0


A3:Farm Out $0 $175,000 $8,050,000

Maximum Regret

$9,300,000

$500,000

$8,050,000

Decision Making Under Uncertainty: Maximum Regret


We do not know probabilities

A1:Don’t Drill $0 $300,000 $9,300,000

A2:Drill Alone $500,000 0 0


A3:Farm Out $0 $175,000 $8,050,000

Maximum Regret

$9,300,000

$500,000

$8,050,000

A2 is the solution.We choose the minimum among maximum regrets.

Documents

Managerial Economics Lecture: Decision making under uncertainty Date: 07.07.14