Group Members Abdul Mulla

Dipti BharwadaPrachi JadhavVaibhav Patki

Vinit Singh

• A good decision is one that is based on logic, considers all available data and possible alternatives, and applies the qualitative and quantitative approaches to solve them

• Decision Analysis (DA) provides structure and guidance for thinking systematically about hard decisions

• It allows a decision maker to take action with confidence gained through a clear understanding of the problem

• Decision Analysis helps to improve the quality of the resulting decisions

The Five commonly used decision criteria are as follows:

• Maximin Criterion

• Maximax Criterion

• Hurwicz’s alpha Criterion

• Savage’s minimax regret Criterion

• Laplace’s Criterion

• Decision making under Certainty or Deterministic situation

• Decision making under Risk or Stochastic situation

• Decision making under Uncertainty

• Conflict and Competitive situation (Games)

Decision Making under Certainty

In this case the decision maker tends to maximize returns or minimize costs. The decision taken is such that it satisfies such criteria in a problem where he knows the outcomes with certainty.

Decision Making under Uncertainty

In this case the problem is uncertain i.e. , the decision maker cannot estimate or anticipate the probability of occurrence of the events with each decision alternatives.

• Decision Making under Risk

In this case the decision maker can anticipate the probability of occurrence of events that he cannot control which is called State of Nature associated with each decision alternative.

A decision problem is characterized by decision alternatives, states of nature, and resulting payoffs.

The decision alternatives are the different possible strategies the decision maker can employ.

The states of nature refer to future events, not under the control of the decision maker, which may occur. States of nature should be defined so that they are mutually exclusive and collectively exhaustive.

• The consequence resulting from a specific combination of a decision alternative and a state of nature is a payoff.

• A table showing payoffs for all combinations of decision alternatives and states of nature is a payoff table.

• Payoffs can be expressed in terms of profit, cost, time, distance or any other appropriate measure.

• In the fall farmer is offered Rs. 50000 for his Apple crop, which will be harvested in the beginning of the following year. If the farmer accepts the offer, the money is his regardless of the quality or quantity of the harvest. If the farmer does not accept the offer, he must sell his oranges in the open market after they are harvested. Under normal conditions, the farmer can anticipate receiving Rs. 70000 on the open market for his harvest. If he experiences a Frost, however then much of his harvest will be ruined & he can anticipate receiving only Rs. 15000 in the open market.

• Determine recommended decisions, using each of the criterion under the situation of uncertainty. ( for Hurwicz- alpha criterion, use alpha= 0.4)

• Determine recommended decision under the appropriate criterion if in the past, the farmer has lost much of his harvest to frost 1 out of every 7 years.

Action Frost No Frost

Accept 50,000 50,000

Do Not Accept

15,000 70,000

Action Minimum Payoff

Accept 50,000

Does Not Accept

15,000

According to Maximin criterion decision is to Accept the offer.

Maximin Value

Action Maximum Payoff

Accept 50000

Does Not Accept 70000 Maximax Value

According to Maximax Criterion recommended decision is to Not Accept the offer.

Action Expected Payoff

Accept 50000

Does not Accept

42500

According to Laplace Criterion the recommended decision is to Accept the offer.

Frost No Frost Expected Payoff

Accept 50000 50000 50000

Does not Accept

15000 70000 62143

Probability 1/7 6/7

According to EMV criterion the recommended decision is do not accept the offer.

The corresponding EP is Rs. 62143.

Action Frost No Frost

Accept 0 20000

Do Not Accept 35000 0

Action Maximum Regret

Accept 20000

Do Not Accept 35000

According to the Savage Criterion recommended decision is to Accept the offer.

Minimax Regret

Let α = 0.4

Action Weighted payoff

Accept 50000*0.4 + 50000*0.6 = 50000

Do not Accept 70000* 0.4 + 15000* 0.6 = 37000

According to Hurwicz- alpha Criterion when α is 0.4, the recommendation is to Accept the offer.

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. Squares or Rectangles depict decision nodes.

Accept the

offer

Do not Accept the

offer

Frost

Frost

No Frost

No Frost

50,000

50,000

15,000

70,000

15,000*1

/7

70,000*6/7

62,14

3+

50,000

62,143

• Are simple to understand and interpret. People are able to understand decision tree models after a brief explanation.

• Have value even with little hard data. Important insights can be generated based on experts describing a situation (its alternatives, probabilities, and costs) and their preferences for outcomes.