Welcome Unit 4 Seminar

1. WelcomeUnit 4 Seminar MM305 Wednesday 8:00 PM ET Quantitative Analysis for Management Delfina Isaac

2. Following Up Determining Alternative Courses of Action Implementing the Decision Analyzing the Alternatives Selecting the Best Alternatives Six Steps in Decision Making Identifying the Problem

3. Decision theory models • Decision alternatives – this is a course of action that may be chosen by the decision maker. • States of nature – an occurrence that affects the outcome of the decision; decision maker has no control over the states of nature • Payoff – benefit that occurs when a specific decision is made and a specific state of nature occurs.

4. ABC Land Development Corp. ABC Land owns 5000 acres that are zoned to be developed as recreational home sites. Three development decision alternatives are being considered:  A1: Develop a small amount of acreage (500 acres) A2: Develop a medium amount of acreage (2500 acres) A3: Develop a large amount of acreage (5000 acres)

5. ABC Land Development Corp. Three possible states of nature that ABC anticipates as possibilities: S1: Low customer demand S2: Medium customer demand S3: High customer demand

6. Decision Table Projected profit depends on the decision alternative and the state of nature that occurs. Which decision alternative would you choose?

7. Types of Decision-Making Environments Type 1: Decision making under certainty Decision maker knows with certaintythe consequences of every alternative or decision choice Type 2: Decision making under uncertainty The decision maker does not knowthe probabilities of the various outcomes Type 3: Decision making under risk The decision maker knows the probabilities of the various outcomes

8. Decision Making Under Uncertainty There are several criteria for making decisions under uncertainty • Maximax (optimistic) • Maximin (pessimistic) • Criterion of realism (Hurwicz) • Equally likely (Laplace) • Minimax regret

9. Maximax (optimistic) approach Determines the best possible outcome for ABC Max of row 3500 12500 25000 25000 Max of maximums Find the maximum payoff for each decision alternative (row). Select the decision alternative with the maximum maximum – MAXIMAX.

10. Maximin (pessimistic) approach Determines the best of the worst possible outcome for ABC Min of row 2700 1000 -500 2700 Max of minimums Find the minimum payoff for each decision alternative (row). Select the decision alternative with the maximum minimum - MAXIMIN

11. Criterion of Realism (Hurwicz) Determines compromise between optimistic and pessimistic Criteria of Realism (α=0.8) 3340 10200 19900 19900 Max of realism Weighted average = (α) (maximum in row) + (1 – α)(minimum in row)

12. Equally likely (Laplace) approach Determines the highest average outcome. Average 3067 8633 8083 8633 Max of average Find the average payoff for each decision alternative (row). Select the decision alternative with the maximum average.

13. Minimax Regret Create Opportunity Loss Tables.

14. Minimax Regret Determines the highest average outcome. Max 22300 12600 12750 12600 Minimax

15. Which is the best decision?

16. Decision Making Under Risk • Decision making when there are several possible states of nature and we know the probabilities associated with each possible state • Most popular method is to choose the alternative with the highest expected monetary value (EMV) EMV (alternative i) = (payoff of S1)*P(S1) + (payoff of S2)*P(S2) +…..+ (payoff of Sn)*P(Sn)

17. Decision-making with probabilities What if ABC estimates the likelihood of each state of nature occurring. S1: Low customer demand P(S1) = 0.2 S2: Medium customer demand P(S2) = 0.5 S3: High customer demand P(S3) = 0.3 Would this change your decision previously made?

18. Expected Monetary Value Approach Represents the average best (with probabilities) outcome for ABC. Expected value 3010 10170 7275 10170 Max of expected values – Max EV EMV (500 acres) = (0.2)(3500) + (0.5)(3000) + (0.3)(2700) = 3010

19. Expected Value of Perfect Information (EVPI) • EVPI places an upper bound on what you should pay for additional information EVPI = EVwPI – Maximum EMV • EVwPI is the long run average return if we have perfect information before a decision is made

20. Expected Value with Perfect Information (EVwPI) EVwPI = 0.2(3500) + 0.5(12500) + 0.3(25000) =14450

21. Expected Opportunity Loss • Expectedopportunityloss (EOL) is the cost of not picking the best solution • First construct an opportunity loss table • For each alternative, multiply the opportunity loss by the probability of that loss for each possible outcome and add these together • Minimum EOL will always result in the same decision as maximum EMV • Minimum EOL will always equal EVPI

22. Expected Opportunity Loss Construct opportunity loss table. EOL 22300 12600 12750 12600 Minimum EOL EOL (2500 acres) = (0.2)(2500) + (0.5)(0) + (0.3)(12600) = 4280

23. Sensitivity Analysis Sensitivity analysis examines how our decision might change with different input data Examines the effects of various probabilities for the states of nature on the expected values for the decision alternatives.

24. Using Excel QM to Solve Decision Theory Problems