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

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

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: A 1 : Develop a small amount of acreage (500 acres) A 2 : Develop a medium amount of acreage (2500 acres) A 3 : Develop a large amount of acreage (5000 acres)

5. ABC Land Development Corp. Three possible states of nature that ABC anticipates as possibilities: S 1 : Low customer demand S 2 : Medium customer demand S 3 : High customer demand

6. Decision Table Projected profit depends on the decision alternative and the state of nature that occurs. S1S1 S2S2 S3S3 A1A1350030002700 A2A210001250012400 A3A3-500-25025000 Which decision alternative would you choose?

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

8. Decision Making Under Uncertainty 1.Maximax (optimistic) 2.Maximin (pessimistic) 3.Criterion of realism (Hurwicz) 4.Equally likely (Laplace) 5.Minimax regret There are several criteria for making decisions under uncertainty

9. Maximax (optimistic) approach S1S1 S2S2 S3S3 A1A1350030002700 A2A210001250012400 A3A3-500-25025000 Max of row 3500 12500 25000 Max of maximums 25000 Find the maximum payoff for each decision alternative (row). Select the decision alternative with the maximum maximum – MAXIMAX. Determines the best possible outcome for ABC

10. S1S1 S2S2 S3S3 A1A1350030002700 A2A210001250012400 A3A3-500-25025000 Min of row 2700 1000 -500 Max of minimums 2700 Find the minimum payoff for each decision alternative (row). Select the decision alternative with the maximum minimum - MAXIMIN Determines the best of the worst possible outcome for ABC Maximin (pessimistic) approach

11. S1S1 S2S2 S3S3 A1A1350030002700 A2A210001250012400 A3A3-500-25025000 Criteria of Realism (α=0.8) 3340 10200 19900 Max of realism 19900 Weighted average = ( α ) (maximum in row) + (1 – α )(minimum in row) Determines compromise between optimistic and pessimistic Criterion of Realism (Hurwicz)

12. Equally likely (Laplace) approach S1S1 S2S2 S3S3 A1A1350030002700 A2A210001250012400 A3A3-500-25025000 Average 3067 8083 8633 Max of average 8633 Find the average payoff for each decision alternative (row). Select the decision alternative with the maximum average. Determines the highest average outcome.

13. Minimax Regret S1S1 S2S2 S3S3 A1A13500-350012500-300025000-2700 A2A23500-100012500-1250025000-12400 A3A33500-(-500)12500-(-250)25000-25000 Create Opportunity Loss Tables. S1S1 S2S2 S3S3 A1A10950022300 A2A22500012600 A3A34000127500

14. Minimax Regret S1S1 S2S2 S3S3 A1A10950022300 A2A22500012600 A3A34000127500 Max 22300 12750 12600 Minimax 12600 Determines the highest average outcome.

15. Which is the best decision? ApproachDecision Maximax (optimistic) A3A3 Maximin (pessimistic) A1A1 Realism A3A3 Equally Likely A2A2 Minimax Regret A2A2

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 S 1 )*P(S 1 ) + (payoff of S 2 )*P(S 2 ) +…..+ (payoff of S n )*P(S n )

17. Decision-making with probabilities What if ABC estimates the likelihood of each state of nature occurring. S 1 : Low customer demand P(S 1 ) = 0.2 S 2 : Medium customer demandP(S 2 ) = 0.5 S 3 : High customer demand P(S 3 ) = 0.3 Would this change your decision previously made?

18. Expected Monetary Value Approach S1S1 S2S2 S3S3 A1A1350030002700 A2A210001250012400 A3A3-500-25025000 Expected value 3010 10170 7275 Max of expected values – Max EV 10170 EMV (500 acres) = (0.2)(3500) + (0.5)(3000) + (0.3)(2700) = 3010 Represents the average best (with probabilities) outcome for ABC.0.20.50.3

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) S1S1 S2S2 S3S3 A1A1350030002700 A2A210001250012400 A3A3-500-25025000 0.20.50.3 EVwPI = 0.2(3500) + 0.5(12500) + 0.3(25000) =14450

21. Expected Opportunity Loss Expected opportunity loss (EOL) is the cost of not picking the best solution 1.First construct an opportunity loss table 2.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 S1S1 S2S2 S3S3 A1A10950022300 A2A22500012600 A3A34000127500 EOL 22300 12750 12600 Minimum EOL 12600 Construct opportunity loss table. EOL (2500 acres) = (0.2)(2500) + (0.5)(0) + (0.3)(12600) = 42800.20.50.3

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