DECISION THEORY

“ The one word that makes a good manager – decisiveness.”

What is Decision Theory?

“ A process of best selection from a set of alternative courses of action, that course Of action which is supposed to meet objectives up to satisfaction of the decision maker “

Without a clear direction we slow down, uncertain of where to head. Decision theory provides direction with clarity that allows for focused effort and speed.

Courses of Action: A set of predermined rules

The Decision Maker refers to ‘Individual’ or a ‘group of individual’ responsible for making the choice of an appropriate course of action amongst the available course of action.

Decision AlternativesThere is a finite number of

decision alternatives available to the decision maker at each point in time When a decision is made.

These alternatives are also called Courses of action ( Actions, acts, or Strategies ) and are not only under control but are also known to the decision maker.

States of Nature

These are the future conditions (also called consequences, events or scenarios) that are not under the control of decision maker.

A state of nature can be a state of economy (e.g. inflation) , a weather condition, a political development, etc. These are the result of an ’act of God’ or result of many situations pushing in various directions.

States of Nature

The states of nature may be described numerically such as , demand of 100 units of an item or non – numerically such as employees strike, etc.

The states of Nature are mutually exclusive and collectively exhaustive (total) With respect to any decision problem.

Pay off

A numerical value (Out Come) resulting from each possible combination of alternatives and states of nature is called payoff . A tabular arrangement of these values is known as payoff matrix.

States of Nature

Courses of Action

A1 A2 …. An

N1 a11 a12 … a1n

N2 a21 a22 … a2n

N3 a31 a22 …. a3n

. . . … .

. . . … .

Nm am1 am2 … a mn

Pay off matrix example.

Yield in kg per

hectare

Weather

Dry(E1) Moderate(E2) Damp(E3)Price

Rs.Per Kg

paddy (A1) 500 1700 4500 1.25

Ground Nut (A2) 800 1200 1000 4.00

Tobacco(A3) 100 300 200 15.00Courses of action

States of Nature

Regret or Opportunity loss

Opportunity loss is incurred due to failure of not adopting most favourable course of action or strategy.

The difference between the highest possible profit for a state of nature and the actual profit obtained for the particular action taken is known as opportunity loss.

Types of DECISION-MAKING Environments

1. Decision under certainty

2. Decision Under Uncertainty (W/0 probability)

3. Decision under Risk (With probability)

1. Decision under certainty

In this case the decision maker has the complete knowledge of consequence of every decision choice with certainty.

Example. Break even point analysis, wherein

precise information about the cost and sales revenue is known, and liner programming , wherein the required resource , available resources, and the costs/profits associated with it are known.

2. Decision Under Uncertainty

(With out Probability) The decision situations where there

is no way in which the decision maker can assess the probabilities of the various states of nature are called decisions under uncertainty.

Example. A new product is introduced in the

market. A new plant is set up.

3. Decision under Risk (With probability)

In this case decision maker

Supposed to believe Authentic information, knowledge, past experience or happenings to enable him to assign probability values to the likelihood of occurrence of each state of nature.

Decision Making Under Uncertainty

The five commonly used criteria for decision making under uncertainty are:

1. the optimistic approach (Maxi-max)

2. the conservative approach (Maxi-min)

3. the minimax regret approach (Mini-max regret)

4. Equally likely (Laplace criterion)

5. Criterion of realism with (Hurwicz criterion)

1. Optimistic Approach

The optimistic approach would be used by an optimistic decision maker.

The decision with the largest possible payoff is chosen.

If the payoff table was in terms of costs, the decision with the lowest cost would be chosen.

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Example: CAL Condominium Complex

A developer must decide how large a luxury condominium complex to build – small, medium, or large. The profitability of this complex depends upon the future level of demand for the complex’s condominiums.

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CAL Condos: Elements of Decision Theory

States of nature: The states of nature could be defined as low demand and high demand.

Alternatives: CAL could decide to build a small, medium, or large condominium complex.

Payoffs: The profit for each alternative under each potential state of nature is going to be determined.

CAL Condos: Payoff Table

Alternatives Low HighSmall 8 8Medium 5 15Large -11 22

States of Nature

(payoffs in millions of dollars)

THIS IS A PROFIT PAYOFF TABLE

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CAL Condos: Optimistic Decision (maximax )

If the optimistic approach is selected:STATES OF NATURE

BESTAlternatives Low High PROFITSmall 8 8 8Medium 5 15 15Large -11 22 22

Maximax payoff

Maximax

decision

2. Conservative Approach

The conservative approach would be used by a conservative decision maker.

For each decision the minimum payoff is listed and then the decision corresponding to the maximum of these minimum payoffs is selected. (Hence, the minimum possible payoff is maximized.)

If the payoff was in terms of costs, the maximum costs would be determined for each decision and then the decision corresponding to the minimum of these maximum costs is selected. (Hence, the maximum possible cost is minimized.)

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CAL Condos: Conservative Decision ( Max-min)

If the conservative approach is selected:STATES OF NATURE

WORST Alternatives Low High PROFIT Small 8 8 8 Medium 5 15 5 Large -11 22 -11

Maxi-min payoff

Maxi-min

decision

The decision with the best profit from the column of worst profits is selected.

3. Mini-max Regret Approach

The minimax regret approach requires the construction of a regret table or an opportunity loss table.

This is done by calculating for each state of nature the difference between each payoff and the largest payoff for that state of nature.

Then, using this regret table, the maximum regret for each possible decision is listed.

The decision chosen is the one corresponding to the minimum of the maximum regrets.

4.Laplace Criterion: Assume equal amount of probabilities Computation of expected value for each decision

choice

5. Hurwic’z Criterion:

First, select coefficient of realism, a, with a value between 0 and 1.

When a is close to 1, decision maker is optimistic about future, and when a is close to 0, decision maker is pessimistic about future.

Payoff = a (maximum payoff) + (1-a) x(minimum

payoff)

Decision-making under conditions of Risk ( with probability )

If the availability of information for a decision environment is partial, then a decision under such an environment is called ‘decision under risk’. The available information will be given in the form of probability distribution.

Expected Money value (EMV)

Expected opportunity loss (EOL)

Expected value of perfect Information (EVPI)

Expected Money value (EMV)

Expected opportunity loss (EOL)

Expected value of perfect Information

(EVPI)

Decision Tree

Decision Tree

A Visual Representation of Choices, Consequences, Probabilities, and Opportunities.

A Way of Breaking Down Complicated Situations Down to Easier-to-Understand Scenarios.

Easy Example

A Decision Tree with two choices.

Go to Graduate School to get my MBA.

Go to Work “in the Real World”

Decision Trees A decision tree is a chronological representation

of the decision problem. Each decision tree has two types of nodes;

round nodes correspond to the states of nature while square nodes correspond to the decision alternatives.

The branches leaving each round node represent the different states of nature while the branches leaving each square node represent the different decision alternatives.

At the end of each limb of a tree are the payoffs attained from the series of branches making up that limb.

Notation Used in Decision Trees

A box is used to show a choice that the manager has to make.

A circle is used to show that a probability outcome will occur.

Lines connect outcomes to their choice

or probability outcome.

What are some of the costs we should take into account when deciding whether or not to go to business school?

• Tuition and Fees

• Rent / Food / etc.

• Opportunity cost of salary

• Anticipated future earnings

Simple Decision Tree Model

Go to Graduate School to get my MBA.

Go to Work “in the Real World”

2 Years of tuition: $55,000, 2 years of Room/Board: $20,000; 2 years of Opportunity Cost of Salary = $100,000 Total = $175,000.

PLUS Anticipated 5 year salary after Business School = $600,000.

NPV (business school) = $600,000 - $175,000 = $425,000

First two year salary = $100,000 (from above), minus expenses of $20,000.

Final five year salary = $330,000

NPV (no b-school) = $410,000

Go to Business School

Example – Joe’s Garage

Joe’s garage is considering hiring another mechanic. The mechanic would cost them an additional $50,000 / year in salary and benefits. If there are a lot of accidents in Providence this year, they anticipate making an additional $70,000 in net revenue. If there are not a lot of accidents, they could lose $20,000 off of last year’s total net revenues. Because of all the ice on the roads, Joe thinks that there will be a 70% chance of “a lot of accidents” and a 30% chance of “fewer accidents”. Assume if he doesn’t expand he will have the same revenue as last year.

Draw a decision tree for Joe and tell him what he should do.

Example 2 - Answer

Hire new mechanic

Cost = $50,000

Don’t hire new mechanic

Cost = $0

70% chance of an increase in accidents

Profit = $70,00030% chance of a decrease in accidents

Profit = - $20,000

• Estimated value of “Hire Mechanic” = NPV =.7(70,000) + .3(- $20,000) - $50,000 = - $7,000

• Therefore you should not hire the mechanic

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