Operations Research chapter 5.- decision theory ppt
- 1. Chapter Five Chapter Five Decision Theory Model
- 2. Decision theory Decision theory The decision making refers to the selection of an act from amongst various alternatives, the one which is judged to be the best under given circumstances. Decision theory is used to determine the best alternative under incomplete and uncertain future conditions. To analyze a set of complex situations with many alternatives and many different possible consequence
- 3. Decision Theory Process Decision Theory Process a) Identify possible future conditions called states of nature b) Develop a list of possible alternatives, one of which may be to do nothing c) Determine the payoff associated with each alternative for every future condition d) If possible, determine the likelihood of each possible future condition e) Evaluate alternatives according to some decision criterion and select the best alternative
- 4. State of nature State of nature Are actual event that may occur in the future and which are beyond the control of the decision maker State of nature are factors which influence a choice of alternatives but their occurrences are knowing during decision making Example • Demand level of a product • Market condition • Whether condition etc
- 5. Pay off table Pay off table • A payoff table is a tool that provides information about consequences associated with each alternative/state of nature combination usually related to potential profit or loss.
- 6. Decision making environment/ Decision making environment/ Degree of certainty Degree of certainty 1. Decision-making under certainty •There is complete certainty about the future •The decision-maker knows with certainty the consequences of every alternative and Wich state of nature will happen 2. Decision-making under uncertainty •The decision-maker does not know the probabilities of the various outcomes and which state of nature will happen 3. Decision-making under risk (with probability) •The decision-maker does know the probabilities of the various outcomes and state of nature
- 7. Decision criteria Decision criteria Criteria under complete uncertainty 1. Maximin 2. Maximax 3. Minimax regret 4. Hurwicz 5. Equal likelihood Criteria under probability 1. Expected monitory value(EMV) 2. Expected opportunity Loss(EOL)
- 8. Criteria.. Criteria.. Maximin: The maximin strategy is a conservative one; it consists of identifying the worst (minimum) payoff for each alternative and then selecting the alternative that has the best (maximum) of the worst payoffs. In effect, the decision maker is setting a floor for the potential payoff; the actual payoff cannot be less than this amount. Maximax The maximax approach is the opposite of the previous one: The best payoff for each alternative is identified, and the alternative with the maximum of these is the designated decision. Minimax Regret An approach that takes all payoffs into account. To use this approach, it is necessary to develop an opportunity loss table that reflects the difference between each payoff and the best possible payoff in a column (i.e., given a state of nature). Hence, opportunity loss amounts are found by identifying the best payoff in a column and then subtracting each of the other values in the column from that
- 9. The Hurwicz (Realism) Criterion (Weighted The Hurwicz (Realism) Criterion (Weighted Average or Realism Criterion) Average or Realism Criterion) • The approach offers the decision maker a compromise between the maximax and the maximin criteria. – Requires the decision maker to specify a degree of optimism, in the form of a coefficient of optimism α, with possible values of α ranging from 0 to 1.00. – The closer the selected value of α is to 1.00, the more optimistic the decision maker is, and the closer the value of α is to 0, the more pessimistic the decision maker is.
- 10. Shortly Shortly • Maximin - Choose the alternative with the best of the worst possible payoffs • Maximax - Choose the alternative with the best possible payoff • Laplace - Choose the alternative with the best average payoff of any of the alternatives • Minimax Regret - Choose the alternative that has the least of the worst regrets
- 11. Approaches to Incorporating Probabilities in the Approaches to Incorporating Probabilities in the Decision Making Process Decision Making Process • Expected Monetary Value (EMV) approach – Provides the decision maker with a value that represents an average payoff for each alternative. • Expected Opportunity Loss (EOL) – The opportunity losses for each alternative are weighted by the probabilities of their respective states of nature to compute a long-run average opportunity loss, and the alternative with the smallest expected loss is selected as the best choice. • Expected Value of Perfect Information (EVPI) – Expected value of perfect information: the difference between the expected payoff under certainty and the expected payoff under risk
- 12. Example 1 Example 1 Suppose that an investor wants to construct one of the following facilities (small, medium, or large facility). The profit from each facility depends on the future market demand, which could be low, moderate, or high. His estimated profit for each alternative under each state of nature is shown in the table. A decision is being made concerning which size facility should be constructed
- 20. Expected opportunity loss(EOL) Expected opportunity loss(EOL)
- 23. Example 2 Example 2 • 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 season. The farmer has categorized the amount of rainfall as high, medium, and low. His estimated profit for each is shown in the table. Alternatives State of nature High Medium Low Crop A 8000 3500 5000 Crop B 4500 4500 5000 Crop C 2000 5000 4000 If the farmer wishes to plant only crop, decide which should be his best crop under each criteria?
- 24. Example 3 Example 3 Suppose that a real estate developer must decide on a plan for developing a certain piece of property. After careful consideration, the developer has identified the following list of acceptable alternatives: 1.Apartment building 2.Office building 3.Commercial building Suppose that the developer identified the following state of nature 1. Low demand 2. Moderate demand 3. High demand
- 25. Payoff Table for Real Estate Developer Payoff Table for Real Estate Developer ( ( Profit per year in Birr) Profit per year in Birr) State Of Nature( Demand Level) Alternatives (Types of building) High Moderate Low Apartment 500 320 200 Office 750 300 100 Commercial 400 100 -125