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DECISION ANALYS

ISVinit 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 Hurwiczs alpha Criterion Savages minimax regret Criterion Laplaces 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.

y A decision problem is characterized by decision alternatives, states of nature, and resulting payoffs. y The decision alternatives are the different possible strategies the decision maker can employ. y 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 Accept

Frost 50,000

No Frost 50,000

Do Not Accept

15,000

70,000

Action Accept

Minimum Payoff 50,000

Maximin Value

Does Not Accept 15,000

According to Maximin criterion decision is to Accept the offer.

Action Accept Does Not Accept

Maximum Payoff 50000 70000 Maximax Value

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

Action Accept Does not Accept

Expected Payoff 50000 42500

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

Frost Accept Does not Accept Probability 50000 15000 1/7

No Frost 50000 70000 6/7

Expected Payoff 50000 62143

According to EMV criterion the recommended decision is do not accept the offer. The corresponding EP is Rs. 62143.

Action Accept Do Not Accept Action Accept Do Not Accept

Frost 0 35000 Maximum Regret 20000 35000

No Frost 20000 0

Minimax Regret

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

y Let

= 0.4 Weighted payoff 50000*0.4 + 50000*0.6 = 50000 70000* 0.4 + 15000* 0.6 = 37000

Action Accept Do not Accept

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

is 0.4,

y A Decision Tree is a chronological representation of the decision problem. y Each decision tree has two types of nodes; Round nodes correspond to the states of nature while Square nodes correspond to the decision alternatives. y The Branches leaving each round node represent the different states of nature while the branches leaving each square node represent the different decision alternatives. y 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.