Decision Theory and Decision TreeRepresented By:Laishram Priyadarshani Devi(Group Leader)Aradhana Pathak.Dhiraj Singh.Gaurav Kumar Singh.Gaurav Singh.Jagat jat

Introduction

Basic function of any manager in day-to –day performance of his job are planning, organising, monitoring and controlling .In all this function, he has to take a number of decisions, small or big.

Decisions are based on the criteria decided by the organisational objectives of business like utility, minimisation of cost or time, maximisation of profits.

There are number of external factors responsible to modify the decision and decision maker has to recognise factors like attitude or interest of stock holders or employees and unions.

Introduction ContdGovernment policies or change in Regulatory

framework may be a major factor playing its cards in major decision making processes.

Rationality of decision making and their improvement bring out the best in a Decision Maker.

Hence, deep analysis of pervious decisions and that of complexities of the given environment help the process of coherent, and effective decision making.

Quality of decision making depends on the input qualitatively and quantitatively.

Brief ContentsDEFINE DECISION THEORY.APPLICATIONS OF DECISION THEORY.APPROACH'S OF DECISION THEORY.CATEGORIES OF DECISION THEORY.TYPES OF DECISION MAKING ENVIRONMENT.DECISION TREES.STEPS IN DECISION TREE ANALYSIS.ADVANTAGES AND DISADVANTAGES OF

DECISION TREE

Important terminologies & conceptsDecision maker : The decision maker refers the

individuals or group of individuals responsible for making a choice of an appropriate courses of action amongst the available courses of action . For example , a CEO of a company may be accounatable to the share holder .

Course of action :it sometimes called actions, decision alternatives or strategies are the acts available to the decision makert.

State of nature :it is an exhaustive list of possible future events , i.e. ,a set of possible scenarios .

Payoff :it is the effectiveness associated with a particular combination of a course of action and state of nature.It measure the net benefit to the decision maker that accrues from a given combination of decision alternatives and events.

Assumption in formulation of payoff matrix:Both the number of feasible options and possible

states of nature is limited and finite.Each state of nature is mutually exclusive ,i.e.,only

one event wil occur for any given option.The results for each combination of an option and

state of nature are known and assumed to be stable and constant for given decision making scenario.

The decision objective is singular in nature and clearly identified .

There are no other constraints impose upon the decision issue.

Definition of Decision Theory:

A process which results in the selection from a set of alternative courses,that course of action which is considered to meet the objectives of the decision problem more satisfactorily then others as judged by the decision makers.

Or The process of logical and

quantitative analysis of all factors that influences the decision problem,assits the decision maker in analyzing these problems with several courses of action and consequences.

Steps in Decision Theory Approach

For better understanding: We are considering a manufacturing company that is

thinking of several alternatives method to increase its production to meet the increasing market demand.

The decision theory approach generally involves four steps:

1.List all the viable alternatives. 2.Identify the expected future events. 3.Construct a payoff table. 4.Select optimum decision criterion.

Step 1:List all the viable alternativesThe decision-maker list all the viable alternatives that can

be considered in the decision.

For the company considered above,it may be only three options.

Construct a new plant. Expand the present plant. Subcontract production for extra demand.

Step2:Identify the expected future events.

The decision maker list all the future events that may occur.Often it is possible to identify most of the events that can occur,the difficulty is to identify which particular event will occur.These future events are termed as states of nature or outcomes in decision theory.

For the manufacturing company considered above,the greatest uncertainity will be about product demand.

High demand. Moderate demand. Low demand. No demand.

Step 3:Construct a payoff table.

The decision -maker now constructs a payoff table or conditional gain or conditional profit for each possible combination or alternatives course of action and states of nature.

Table 1 represents 12 possible payoffs for the company’s expansion decision.

Table 1

Alternatives

States of nature(product demand)

High Moderate Low Nil

Expand Rs 50,000

Rs 25,000 -Rs 25,000 -Rs 45,000

Construct Rs 70,000

Rs 30,000 -Rs 40,000 -Rs 80,000

Subcontract Rs 30,000

Rs 15,000 -Rs 1,000 -Rs 10,000

Step 4:Select optimum decision criterion.

Finally,the decision maker will choose criterion which

results in larger payoff.

Decision-Making EnvironmentDecision are made under fours types of

environments that differ according to the degree of certainty.

1.Decision-making under conditions of certainty.

2.Decision-making under conditions of uncertainty.

3.Decision-making under condition of risk.

4.Decision-making under conditions of conflict.

Decision-Making Under Conditions of Certainty.

• In this environment,only one state of nature exists,the decision-maker simply pickes up the best payoff in that one column and chooses the associated alternative.

• Under the condition of certainty,the particular state of nature is associated with probability.

• Though the state of nature is only one,possible alternatives could be numerous.

Methods: Linear programming. Transportation and assignment technique. Input-output analysis. Activity analysis. Economic order quantity.

Example:

If the company knew that the demand would be high,it would choose the alternative ’construct’ to get the highest payoff Rs 70,000,if it knew that the demand would be low,

it would choose alternative ’subcontract’ to keep the losses lowest to Rs 1000.

Alternatives

States of nature(product demand)

High Moderate Low Nil

Expand Rs 50,000 Rs 25,000 -Rs 25,000

-Rs 45,000

Construct Rs 70,000 Rs 30,000 -Rs 40,000

-Rs 80,000

Subcontract

Rs 30,000 Rs 15,000 -Rs 1,000 -Rs 10,000

Decision-Making under condition of uncertainty.

Under the condition of uncertainty,the decision-maker has a knowledge about the states that happens but lacks

the knowledge about the probablities of their occurrence.There are few decision criteria are available which could

be of help to the decision-maker.

They are as follows:

1.Maximax Criterion or Criterion of Optimism.

2.Maximin Criterion or Criterion of Pessimism.

3.Minimax Regret Criterion(Savage Criterion) .

4.Hurwicz Criterion(Criterion of Realism).

5.Laplace Criterion or Criterion of Rationality

(Bayes Criterion).

Minimax Criterion or Criterion of Optimism.

This criterion provides the decision-maker with optimistic criterion.He finds the maximum possible payoff for each possible alternative and then chooses the alternative with payoff within the group.

Maximum payoff =70,000

Alternatives

States of nature(product demand)

High Rs

Moderate Rs

Low Rs

NilRs

Maximum of row Rs

Expand 50,000 25,000 -25,000 -45,000 50,000

Contract 70,000 30,000 -40,000 -80,000 70,000

Subcontract

30,000 15,000 -1,000 -10,000 30,000

Maximin Criterion or Criterion of Pessimism(Wald Criterion).

This criterion provides the decision-maker with pessimistic criterion.

The decision-maker maximizes his minimum possible payoffs.He finds first the minimum possible payoff for each alternative

and then chooses the alternative with maximum payoff within the group.

Maximin=10,000

Alternatives

States of nature(product demand)

High Rs

Moderate Rs

Low Rs

NilRs

Minimum of row Rs

Expand 50,000 25,000 -25,000 -45,000 -45,000

Contract 70,000 30,000 -40,000 -80,000 -80,000

Subcontract

30,000 15,000 -1000 -10,000 -10,000

Minimax Regret Criterion(Savage Criterion) .

This decision criterion was developed by L.J.Savage.He pointed out that the decision-maker might experience regret after

the decision has been made and the states of nature i.e.events have occurred.

Thus the decision-maker should attempt to minimize regret before actually selecting a particular alternative.

The basic steps involved in this criterion are. Determine the amount of regret corresponding to each event for every

alternative.The regret for jth event corresponding to ith alternative is given by:

ith regret=(maximmum payoff-ith payoff)for jth event.

Determine the maximum regret amount for each alternative. Choose the alternative which corresponds to the minimum of the

maximum regrets.

This table shows that the company will minimize its regret to Rs 35,000 by selecting alternative ‘Expand’.

Minimax=35,0000

Alternative

States of nature(product demand)

High(Rs) Moderate Rs

LowRs

NilRs

Maximum of rowRs

Expand 20,000 5,000 24,000 35,000

35,000

Contract 0 0 39,000 70,000

70,000

Subcontract

40,000 15,000 0 0 40,000

Hurwicz Criterion(Criterion of Realism)/Weighted Average Criterion.

It is a compromise between the maximax and maximin decision criteria.

It is based on Hurwicz’s concept of coefficient of optimism.It allows the decision-maker to take into account both the maximum

and minimum for each alternative and assign them weights according to its degree of optimism(or pessimism).The alternative which maximizes the sum of weighted payoffs is then selected.

The basic steps involved in this criterion are. Choose an appropriate degree of optimism α,so that(1-α) represents

the degree of pessimism.α is called coefficient or index of optimism. Determine the maximum as well as minimum of each alternative and

obtain. P=α.maximum +(1-α).minimum.

Choose the alternative that yields the maximum value of P.

Assume α=0.8

When α=0,the criterion is too pessimistic.

When α=1,it is too optimistic.

A value of α =1/2 seems to be a reasonable choice.

Alternative

States of nature(product demand)

High Rs

ModerateRs

LowRs

NilRs

Maximum of rowRs

Minimum of rowRs

P=α.max+(1-α).min

Expand 50,000

25,000 -25,000

-45,000

50,000

-45,000

31,000

Contract 70,000

30,000 -40,000

-80,000

70,000

-80,000

40,000

Subcontract

30,000

15,000 -1000

-10,000

30,000

-10,000

22,000

Laplace Criterion or Criterion of Rationality(Bayes’ Criterion).

It is based upon what is known as the principle of insufficient reason.

Since the probabilities associated with the occurrence of various events are unknown,there is not enough information to conclude that these probabiliteis will be different.

This criterion assigns equal probabilities to all the events of each alternative decisions and selects the alternative associated with the maximum expected payoff

n denotes the number of events. P’s denotes the payoffs. Expected value is represented by: 1/n(P1+P2+…….+Pn)

Thus the alternative ‘subcontract’ results in maximum average payoff of Rs 8,500.

Alternatives

States of nature(Product demand)

HighRs

ModerateRs

LowRs

NilRs

Expected payoffRs

Expand 50,000 25,000 -25,000

-45,000

1000/4[50+25-25-45]=-1,200

Contract 70,000 30,000 -40,000

-80,000

1000/4[70+30-40-80]=-5,000

Subcontract

30,000 15,000 -1000 -10,000

1000/4[30+15-1-10]=8500

Decision Making Under Conditions of Risk

Most business decisions may have to be made under conditions of risk.

More than one states of nature exist and the decision-maker has sufficient information to assign probabilities to each of these states.

These probabilities could be obtained from the past records or from simply the subjective judgement of the decision-maker.

Number of decision criteria are available,some are: Expected Value Criterion. Expected Opportunity Loss Criterion. Expected Value of Perfect Information.

Expected value criterion: This criterion requires the calculation of the expected

value of each decision alternative which is the sum of the weighted payoffs for that alternative, where the weights are the probabilities assigned to the states of the nature that can happen. Also called as expected monetary value(EMV)criterion.

Expected opportunity loss(EOL) criterion:It is an alternative approach is to minimize expected

opportunity loss.EOL represents the amount by which maximum possible profit will be reduced under various possible stock action. The course of action that minimises this losses or reductions is the optimal decision alternatives.

Expected value of perfect information(EVPI): when the situation is probabilistic, there is no control on the occurrences of a given state of nature. If the decision maker had exact information, the situation would be entirely different i.e., with more authentic and exact information available, the decision quality would improve.

EVPI=Best outcome of first state of nature)x(Probability of first state of nature)+………..+ (Best outcome of last state of nature)x(Probability of last state of nature()

EVPI=EPPI – EMV

EPPI=Expected Profit with Perfect Information

EMV=Expected Monetary Value

Application of decision-makingSelect the best from among several job offers.Select the most profitable investment portfolio.Select the best way to build a modern electronic

component.Determine the number of personal computers(PCs)

to order for an office supply store.Determine whether or not to expand a medical or

manufacturing facility.Determine if a large plant, small plant, or no plant

should be built.Decide if it is worthwhile to hire a marketing research

team to gather additional data.

Application of decision-makingDecide whether to lease, sub-contract or manufacture

or select a quality control plan.Decide whether to invest in a new plant, equipment,

etc.Decide about the area of design and development of

new and improved product and equipment.

Decision Trees.

A decision tree is a graphical representation of the decision alternatives,states of nature,probabilities attached to the states of nature and conditional benefits and losses.

It consist of a network of nodes and branches.Two types of nodes are used:

Decision node represented by a square.

State of nature node represented by a circle.Alternative courses of action originate from the decision

node as main branches.

Steps in Decision Tree Analysis.Identify the decision points and the alternative course of

action at each decision point systematically.At each decision point,determine the probability and payoff

associated with each course of action.Commencing from the extreme right end,compute the

expected payoffs(EMV)for each course of action.Choose the course of action that yields the best payoff for

each of the decisions.Proceed backwards to the next stage of decision points.Repeat above steps till the first decisions is reached.Finally,identify the courses of action to be adopted from the

beginning to the end under different possible outcomes for the situation as a whole.

Advantages of the Decision tree approach. It structures the decision process and helps decision- making

in an orderly,systematic and sequential manner. It requires the decision-maker to examine all possible

outcomes,whether desirable or undesirable. It communicates the decision-making process to others in an

easy and clear manner,illustrating each assumption about the future.

It displays the logical relationship between the parts of a complex decision and identifies the time sequence in which the various actions and subsequent events would occur.

It is especially useful in situations wherin the initial decision and its outcome affects the subsequent decisions.

It can be applied in various fields such as introduction of new product,marketing,make or buy decisions,investment decision etc.

Disadvantages of the Decision tree approach.

Decision tree diagrams more complicated as the number of the decisions alternatives increases and more variables are introduced.

It becomes highly complicated when interdependent alternatives and dependent variables are present in the problem.

It assumes the utility of money is linear with money.It analyses the problem in terms of expected values and

thus yield an ‘average’ valued solution.There is often inconsistency in assigning probabilities for

different events.

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