DECISION THEORY WITH EXAMPLE
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This document discusses decision theory and decision making under uncertainty. It outlines the steps in decision theory as determining alternative actions, possible outcomes or states of nature, and constructing a payoff table to choose the alternative with the largest payoff. It describes four types of decision making environments - certainty, uncertainty, risk, and conflict - and gives criteria for decision making under uncertainty, including minimax, maximin, maximax, minimin, Laplace, and Hurwicz criteria. It provides an example applying these criteria to a farmer choosing which crop to plant.
DECISION THEORY WITH EXAMPLE
- 1. OPERATION RESEARCH DECISION THEORY PRESENTED BY: ANASUYA BARIK OPERATION RESEARCH 1
- 2. DECISION THEORY Steps involved in decision theory approach: •Determine the various alternative courses of actions from which the final decision has to be made. •Identify the possible outcomes, called the states of nature or events for the decision problem. •Construct a pay off table. •The decision maker chooses the criterion which results in largest pay off. OPERATION RESEARCH 2
- 3. Decision making environments: •Decision under certainty Whenever there exists only one outcome for a decision, we are dealing with this category •Decisions under uncertainty: When more than one outcome can result from any single decision i.e. more than one state of nature exists. •Decision under risk: The decision maker chooses from among several possible outcomes where the probability of occurrence can be stated objectively from the past data. •Decision under conflict: Neither states of nature are completely known nor are they completely uncertain. OPERATION RESEARCH 3
- 4. DECISION UNDER UNCERTAINTY: There are five criterion on the basis of which rules for making a decision is Formulated: Criterion of pessimism: • Minimax or Maximin • Maximin is a conservative approach to assume worst possible outcomes • Steps involved: Find minimum assured pay off for each alternative Choose the maximum of minimum values. • Minimax involves two steps: Determine maximum possible cost for each alternative Choose the alternative minimum of above costs OPERATION RESEARCH 4
- 5. Criterion of optimism: •Mimimin or maximax •Two extreme optimism •Decision makes ensures that he should not miss the opportunity to achieve the the greatest possible pay off or lowest possible cost •Steps involved: Determine maximum possible payoff Select a alterative which corresponds to maximum of above maximum pay off •Minimin of cost is done in similar manner OPERATION RESEARCH 5
- 6. Laplace criterion: • It is assumed that all states of nature will occur with equal probability •Probabilities of each state of nature is given by 1/( number of states of nature) •Steps involved: i. Assign equal probabilities to each payoff of a strategy ii. Determine the expected pay off value for each alternative. iii. Select the alternative which corresponds to the maximum payoff or minimum cost OPERATION RESEARCH 6
- 7. Criterion of realism or Hurwicz criterion: •Coefficient of optimism α •0<α<1 where o signifies total pessimism and 1 total optimism •Steps involved: i. Decide the coefficient of optimism and the coefficient of pessimism ii. Determine the maximum as well as minimum pay off for each alterative h= α x maximum for each alterative + (1-α) x minimum for each alterative iii. Select the alternative with highest value of h. OPERATION RESEARCH 7
- 8. Example: A farmer wants to decide which of the three crops he should plant on his 100 Acre farm. The profit from each is dependent on the rainfall during the growing seasons. The farmer has categorized the amount of rainfall as high, medium, low. His estimated profit for each is show in the table: Rainfall Crop A Crop B Crop C High 8000 3500 5000 Medium 4500 4500 5000 Low 2000 5000 4000 If the farmer wishes to plant only one crop, decide which will be his choice using •Maximax criterion •Maximin criterion •Hurwicz criterion •Laplace criterion OPERATION RESEARCH 8
- 9. Rainfall Crop A Crop B Crop C High 8000 3500 5000 Medium 4500 4500 5000 Low 2000 5000 4000 i. Maximax criterion: From table we observe that maximum pay off for each alternative are 8000, 5000 ad 5000 respectively. Maximum among these is 8000 corresponding to crop A. So this strategy chooses crop A . ii. Maximin criterion selects crop C iii. Hurwicz criterion: Assuming degree of optimism α = 0.6 ad therefore 1-α = 0.4 , the value of h is calculated in the table: Alternativ e Maximum pay off Minimum pay off OPERATION RESEARCH 9 h Crop A 8000 2000 5600 Crop B 5000 3500 4400 Crop C 5000 4000 4600
- 10. The maximum value is 5600 so this criterion selects crop A. iv. Laplace criterion: Assign equal probabilities i.e. 1/3. The expected pay off is calculated for each alterative: E (Crop A)=1/3(8000)+1/3(4500)+1/3(2000)= 4833 E (Crop B)=4333 E (Crop C)=4666 Hence this criterion also selects crop A. OPERATION RESEARCH 10
- 11. Thank you! OPERATION RESEARCH 11