Decision Science Chapter 2 Decision Analysis

1. Decision Science Chapter 2 Decision Analysis

2. Decision Analysis • For evaluating and choosing among alternatives • Considers all the possible alternatives and possible outcomes

3. Five Steps in Decision Making • Clearly define the decision problem • List all possible alternatives • Identify all possible outcomes for each alternative • Identify the payoff for each alternative & outcome combination • Use a decisionmodelingtechnique to choose an alternative

4. Al MNAR Co. Example • Decision: Whether or not to make and sell storage sheds • Alternatives: • Build a large plant • Build a small plant • Do nothing • Outcomes: Demand for sheds will be high, moderate, or low

5. 4. Payoffs

6. 5. Apply a decision modeling method a) Decision making under certainty using • Maximax • Maximin • Criterion of realism • Equally likely • Minimax regret b) Decision making under risk 1. EMV 2. EOL 3. EVwPI and EVPI c) Decision making under uncertainty

7. a) Decision making under certainty • Probabilities of the possible outcomes are not known • Decision making methods: • Maximax • Maximin • Criterion of realism • Equally likely • Minimax regret

8. a1- MaximaxCriterion • The optimistic approach • Assume the best payoff will happen for each alternative the right decision under Maximax Large plant $ 200,000

9. a2- MaximIN Criterion • The pessimistic approach • Assume the worst payoff will occur for each alternative the right decision under MaximIN No plant $ 0

10. a3- Realism Criterion (Hurwicz criterion) • Uses the coefficient of realism (α) to estimate the decision maker’s optimism • 0 <α< 1 α x (max payoff for alternative) + (1- α) x (min payoff for alternative) = Realism (Hurwicz) payoff for alternative

11. Suppose Realism (Hurwicz) criterion α = 0.45 (for MAX) 1- α = 1- 0.45 = 0.55 (for MIN)

12. Suppose α = 0.45

13. The right decision under Realism (Hurwicz) Small plant $ 29,500

14. a4- Equally Likely Criterion (Laplace) Assumes all outcomes equally likely and uses the average payoff The right decision under Laplace Large plant $ 60,000

15. A5- Minimax Regret Criterion • Regret or opportunity loss measures much better we could have done Regret = (best payoff) – (actual payoff) The best payoff for each outcome is highlighted

16. Minimax Regret Criterion We want to minimize the amount of regret The right decision under Minimax Regret Small plant $ 110,000

17. b) Decision Making Under Risk • Where probabilities of outcomes are available • Expected Monetary Value (EMV) uses the probabilities to calculate the average payoff for each alternative EMV (for alternative i) = ∑(probability of outcome) x (payoff of outcome)

18. B1- Expected Monetary Value (EMV) The right decision under EMV Large plant $ 86,000

19. B2- Expected Opportunity Loss (EOL) • How much regret do we expect based on the probabilities? EOL (for alternative i) = ∑(probability of outcome) x (regret of outcome)

20. B2- Expected Opportunity Loss (EOL) The best payoff for each outcome is highlighted

21. B2- Expected Opportunity Loss (EOL)

22. The right decision under EOL Large plant $ 24,000

23. Perfect Information • Having Perfect Information would allow choosing the best payoff outcome Expected Value With Perfect Information (EVwPI) The expected value when perfect information is available EVwPI = ∑ (probability of outcome) x ( best payoff of outcome) Expected Value of Perfect Information (EVPI) • EVPI an increase in value as a result of perfect information • EVPI = EVwPI – EMV

24. Payoffs in blue would be chosen based on perfect information (knowing demand level) EVwPI = $110,000

25. Expected Value of Perfect Information EVPI = EVwPI – EMV = $110,000 - $86,000 = $24,000 • The “perfect information” increases the expected value by $24,000 • Would it be worth to obtain the perfect information when it costs $ 30,000? • Answer is NO Because cost is greater than EVPI