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CHAPTER 13

CHAPTER 13. Decision Theory. Chapter 13. Decision Theory. Decision process calls for: Identification of states of nature, or events Identification of courses of action, or acts

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CHAPTER 13

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  1. CHAPTER 13 Decision Theory

  2. Chapter 13 Decision Theory Decision process calls for: • Identification of states of nature, or events • Identification of courses of action, or acts • Determination of the pay-off function depicting outcomes of various combinations of acts and events (pay-offs resulting from various act-event combinations can be either gains/losses or costs) • Choosing, on the basis of some criterion, from among different alternatives Quantitative Techniques in Management by N.D.Vohra

  3. Pay-off and Regret Tables • A conditional pay-off table is set up either using given detailed information or through an algebraically expressed pay-off function • A conditional regret matrix can also be set up as follows: • When pay-offs are represented as gains: For every event, consider each act one by one and find excess of largest pay-off (coming from optimal act) over pay-off from the act in consideration • When pay-offs are represented as costs: For every event, consider each act one by one and find excess of pay-off from the act in consideration over the smallest pay-off (coming from optimal act) Quantitative Techniques in Management by N.D.Vohra

  4. Decision Rules • Decisions under Uncertainty • Laplace Principle: uses equal likelihood of various acts • Maximinor Minimax Principle: pessimists’ criterion • Maximax or Minimin Principle: optimists’ criterion • Hurwicz Principle: uses decision-maker’s degree of optimism • Savage Principle: uses regret values Quantitative Techniques in Management by N.D.Vohra

  5. Decision Rules • Decisions under Risk • Maximum likelihood principle: for event with highest probability, choose the act with best pay-off • Expectation principle: choose the act with best expected pay-off (highest in case of gains and lowest in case of costs) • Expected regret principle: choose the act with lowest expected regret value; decision identical to one under expectation principle Quantitative Techniques in Management by N.D.Vohra

  6. EVPI EVPI: Expected Value of Perfect Information • EVPI = Expected regret of optimal action Also, • In case of gains as pay-offs: • EVPI = EPPI minus Expected pay-off under optimal action • EPPI = Expected Pay-off under Perfect Information • In case of costs as pay-offs: • EVPI = Expected pay-off under optimal action minus ECPI • ECPI = Expected Cost under Perfect Information Quantitative Techniques in Management by N.D.Vohra

  7. Posterior Analysis • Uses additional given information in taking decisions • Using given information, prior probabilities are revised and posterior probabilities calculated • Decision taken using posterior probabilities • Expected Value of Sample Information, EVSI = Expected pay-off with given information minus Expected pay-off without given information • Efficiency of EVSI = {EVSI/EVPI}×100 Quantitative Techniques in Management by N.D.Vohra

  8. Decision Trees • Used where sequential decision-making is involved • Decision trees are drawn taking appropriate decision nodes (where decision-maker has control) and chance nodes (where decision-maker has no control) • Optimal sequence of decisions is determined by rolling back technique and using the expected value criterion Quantitative Techniques in Management by N.D.Vohra

  9. Utility Theory • Uses utility as basis of decision-making rather than monetary values with the notion that people have different utility for money • Utility is measured in arbitrarily defined units, called utils • For a given decision-maker, utility function is defined which depicts utility to him/her for various monetary values • Uses the criterion of expected utility for taking decisions Quantitative Techniques in Management by N.D.Vohra

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