1. 12-1 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall Decision Analysis Chapter 12

2. 12-2 ■Components of Decision Making ■Decision Making without Probabilities ■Decision Making with Probabilities ■Decision Analysis with Additional Information Chapter Topics Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

3. 12-3 Decision Analysis A set of alternative actions We may chose whichever we please A set of possible states of nature Only one will be correct, but we don’t know in advance A set of outcomes and a value for each Each is a combination of an alternative action and a state of nature Value can be monetary or otherwise

4. 12-4 Decision Analysis Certainty Decision Maker knows with certainty what the state of nature will be - only one possible state of nature Ignorance Decision Maker knows all possible states of nature, but does not know probability of occurrence Risk Decision Maker knows all possible states of nature, and can assign probability of occurrence for each state Note that the states of nature are mutually exclusive and collectively exhaustive

5. 12-5 Introduction to Decision Analysis Decisions Under Certainty  State of nature is certain (one state)  Select decision that yields the highest return Examples:  Product Mix  Blending / Diet  Distribution  Scheduling All the topics we have studied so far!

6. 12-6 Decision Making Under Certainty

7. 12-7 Decisions Under Uncertainty (or Risk)  State of nature is uncertain (several possible states) Examples:  Drilling for Oil  Developing a New Product  News Vendor Problem  Producing a Movie

8. 12-8 Table 12.1 Payoff Table ■A state of nature is an actual event that may occur in the future. ■A payoff table is a means of organizing a decision situation, presenting the payoffs from different decisions given the various states of nature. Decision Analysis Components of Decision Making Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

9. 12-9 Oil Drilling Problem Consider the problem faced by an oil company that is trying to decide whether to drill an exploratory oil well on a given site. Drilling costs $200,000. If oil is found, it is worth $800,000. If the well is dry, it is worth nothing. However, the $200,000 cost of drilling is incurred, regardless of the outcome of the drilling. State ofNature Decision Payoff Table

10. 12-10 Payoff Table Drilling costs $200,000. If oil is found, it is worth $800,000. If the well is dry, it is worth nothing. The prior probability that the site is wet is estimated at 40%. Payoff Table and Probabilities: All payoffs are in thousands of dollars StateofNature DecisionWetDry Drill600-200 Do not drill00 0.40.6

11. 12-11 Single vs. Multi-Criteria Decision Making Problems It is very important to make distinction between the cases whether we have a single or multiple criteria. A decision problem may have a single criterion like cost or profit. Examples of multi-criteria decision problems are: Buying a house Cost, proximity of schools, trees, nationhood, public transportation Buying a car Price, interior comfort, mpg, appearance, etc. Going to a college

12. 12-12 Decision Analysis Decision Making Without Probabilities Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall Figure 12.1

13. 12-13 Decision-Making Criteria maximaxmaximin minimax regretHurwiczequal likelihood Decision Analysis Decision Making without Probabilities Table 12.2 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

14. 12-14 Table 12.3 Payoff Table Illustrating a Maximax Decision In the maximax criterion the decision maker selects the decision that will result in the maximum of maximum payoffs; an optimistic criterion. Decision is to purchase office building. Decision Making without Probabilities Maximax Criterion Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

15. 12-15 Table 12.4 Payoff Table Illustrating a Maximin Decision In the maximin criterion the decision maker selects the decision that will reflect the maximum of the minimum payoffs; a pessimistic criterion. Decision is to purchase Apt. Building. Decision Making without Probabilities Maximin Criterion Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

16. 12-16 The Hurwicz criterion is a compromise between the maximax and maximin criterion. A coefficient of optimism, , is a measure of the decision maker’s optimism. (1-  is the coefficient of pessimism)  =1 (completely optimistic) – Maximax Criterion  = 0 (completely pessimistic )- Maximin Criterion The Hurwicz criterion multiplies the best payoff by  and the worst payoff by (1-  ), for each decision, and the best result is selected. Decision Values Apartment building $50,000(.4) + 30,000(.6) = 38,000 Office building $100,000(.4) - 40,000(.6) = 16,000 Warehouse $30,000(.4) + 10,000(.6) = 18,000 Decision Making without Probabilities Hurwicz Criterion Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

17. 12-17 Table 12.6 Regret Table Illustrating the Minimax Regret Decision Decision maker first selects the max payoff under each state of nature. Regret is the difference between the payoff from the best decision and all other decision payoffs (opportunity cost). The decision maker attempts to avoid regret by selecting the decision alternative that minimizes the maximum regret. Decision Making without Probabilities Minimax Regret Criterion Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

18. 12-18 The equal likelihood (or Laplace) criterion multiplies the decision payoff for each state of nature by an equal weight, thus assuming that the states of nature are equally likely to occur. Decision Values Apartment building $50,000(.5) + 30,000(.5) = 40,000 Office building $100,000(.5) - 40,000(.5) = 30,000 Warehouse $30,000(.5) + 10,000(.5) = 20,000 Decision Making without Probabilities Equal Likelihood Criterion Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

19. 12-19 ■A dominant decision is one that has a better payoff than another decision under each state of nature. ■The appropriate criterion is dependent on the “risk” personality and philosophy of the decision maker. Criterion Decision (Purchase) MaximaxOffice building MaximinApartment building Minimax regretApartment building HurwiczApartment building Equal likelihoodApartment building Decision Making without Probabilities Summary of Criteria Results Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

20. 12-20 Exhibit 12.1 Decision Making without Probabilities Solution with QM for Windows (1 of 3) Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

21. 12-21 Exhibit 12.2 Decision Making without Probabilities Solution with QM for Windows (2 of 3) Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

22. 12-22 Exhibit 12.3 Decision Making without Probabilities Solution with QM for Windows (3 of 3) Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

23. 12-23 Decision Criteria Expected Value A weighted average of all outcomes The weights are probabilities Gives the average value of the decision if it were made repeatedly Uses all the information concerning events and their likelihood

24. 12-24 Expected value is computed by multiplying each decision outcome under each state of nature by the probability of its occurrence. EV(Apartment) = $50,000(.6) + 30,000(.4) = 42,000 EV(Office) = $100,000(.6) - 40,000(.4) = 44,000 EV(Warehouse) = $30,000(.6) + 10,000(.4) = 22,000 Table 12.7 Decision Making with Probabilities Expected Value Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

25. 12-25 ■The expected opportunity loss is the expected value of the regret for each decision. ■Note that expected value and expected opportunity loss criterion result in the same decision. (Purchase office building) EOL(Apartment) = $50,000(.6) + 0(.4) = 30,000 EOL(Office) = $0(.6) + 70,000(.4) = 28,000 EOL(Warehouse) = $70,000(.6) + 20,000(.4) = 50,000 Table 12.8 Expected Opportunity Loss Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

26. 12-26 ■It is often possible to purchase additional information regarding future events and thus to make a better information. ■This additional information has some max value that represents the limit of what the decision maker would be willing to spend. ■The expected value of perfect information (EVPI) is the maximum amount a decision maker would pay for additional information. ■EVPI equals the expected value given perfect information minus the expected value without perfect information. ■EVPI equals the expected opportunity loss (EOL) for the best decision. Expected Value of Perfect Information Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

27. 12-27 Table 12.9 Payoff Table with Decisions, Given Perfect Information Decision Making with Probabilities EVPI Example (1 of 2) Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

28. 12-28 ■EV of Decision with perfect information: $100,000(.60) + 30,000(.40) = $72,000 ■EV of Decision without this perfect information: EV(office) = $100,000(.60) - 40,000(.40)= $44,000 EVPI = $72,000 - 44,000 = $28,000 EOL(office) = $0(.60) + 70,000(.4) = $28,000 Decision Making with Probabilities EVPI Example (2 of 2) Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

29. 12-29 Decision Analysis Example Problem Solution (1 of 9) Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

30. 12-30 Decision Analysis Example Problem Solution (2 of 9) a.Determine the best decision without probabilities using the 5 criteria of the chapter. 1.Maximax 2. Maximin 3. Minimax Regret 4. Hurwicz (α=.3) 5. Equal Likelihood a.Determine best decision with probabilities assuming.70 probability of good conditions,.30 of poor conditions. Use expected value and expected opportunity loss criteria. b.Compute expected value of perfect information. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

31. 12-31 Step 1 (part a): Determine decisions without probabilities. Maximax Decision: Maintain status quo DecisionsMaximum Payoffs Expand $800,000 Status quo1,300,000 (maximum) Sell 320,000 Maximin Decision: Expand DecisionsMinimum Payoffs Expand$500,000 (maximum) Status quo-150,000 Sell 320,000 Decision Analysis Example Problem Solution (3 of 9) Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

32. 12-32 Minimax Regret Decision: Expand DecisionsMaximum Regrets Expand$500,000 (minimum) Status quo650,000 Sell 980,000 Hurwicz (  =.3) Decision: Expand Expand $800,000(.3) + 500,000(.7) = $590,000 Status quo$1,300,000(.3) - 150,000(.7) = $285,000 Sell $320,000(.3) + 320,000(.7) = $320,000 Decision Analysis Example Problem Solution (4 of 9) Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

33. 12-33 Equal Likelihood Decision: Expand Expand $800,000(.5) + 500,000(.5) = $650,000 Status quo $1,300,000(.5) - 150,000(.5) = $575,000 Sell $320,000(.5) + 320,000(.5) = $320,000 Step 2 (part b): Determine Decisions with EV and EOL. Expected value decision: Maintain status quo Expand $800,000(.7) + 500,000(.3) = $710,000 Status quo $1,300,000(.7) - 150,000(.3) = $865,000 Sell $320,000(.7) + 320,000(.3) = $320,000 Decision Analysis Example Problem Solution (5 of 9) Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

34. 12-34 Expected opportunity loss decision: Maintain status quo Expand $500,000(.7) + 0(.3) = $350,000 Status quo 0(.7) + 650,000(.3) = $195,000 Sell $980,000(.7) + 180,000(.3) = $740,000 Step 3 (part c): Compute EVPI. EV given perfect information = 1,300,000(.7) + 500,000(.3) = $1,060,000 EV without perfect information = $1,300,000(.7) - 150,000(.3) = $865,000 EVPI = $1.060,000 - 865,000 = $195,000 Decision Analysis Example Problem Solution (6 of 9) Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

35. 12-35 35 Decision Trees The Payoff Table approach is useful for a non- sequential or single stage. Many real-world decision problems consists of a sequence of dependent decisions. Decision Trees are useful in analyzing multi- stage decision processes.

36. 12-36 Decision Trees Two types of Node Decision Node Represent decision points Decision are made by the organisation Outcome Node Linked to possible outcomes These are uncontrollable

37. 12-37 37 A Decision Tree is a chronological representation of the decision process. The tree is composed of nodes and branches. Characteristics of a decision tree A branch emanating from a state of nature (chance) node corresponds to a particular state of nature, and includes the probability of this state of nature. Decision node Chance node Decision 1 Cost 1 Decision 2 Cost 2 P(S 2 ) P(S 1 ) P(S 3 ) P(S 2 ) P(S 1 ) P(S 3 ) A branch emanating from a decision node corresponds to a decision alternative. It includes a cost or benefit value.

38. 12-38 Example

39. 12-39 Example

40. 12-40 Example

41. 12-41 41 Work backward from the end of each branch. At a state of nature node, calculate the expected value of the node. At a decision node, the branch that has the highest ending node value represents the optimal decision. The Decision Tree Determining the Optimal Strategy

42. 12-42 A decision tree is a diagram consisting of decision nodes (represented as squares), probability nodes (circles), and decision alternatives (branches). Table 12.10 Payoff Table for Real Estate Investment Example Decision Making with Probabilities Decision Trees (1 of 4) Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

43. 12-43 Figure 12.2 Decision Tree for Real Estate Investment Example Decision Making with Probabilities Decision Trees (2 of 4) Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

44. 12-44 ■The expected value is computed at each probability node: EV(node 2) =.60($50,000) +.40(30,000) = $42,000 EV(node 3) =.60($100,000) +.40(-40,000)= $44,000 EV(node 4) =.60($30,000) +.40(10,000) = $22,000 ■Branches with the greatest expected value are selected. Decision Making with Probabilities Decision Trees (3 of 4) Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

45. 12-45 Figure 12.3 Decision Tree with Expected Value at Probability Nodes Decision Making with Probabilities Decision Trees (4 of 4) Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

46. 12-46 Decision Analysis Example Problem Solution (1 of 9) Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

47. 12-47 Decision Tree Example Problem Solution (2 of 9) a.Determine best decision with probabilities assuming.70 probability of good conditions,.30 of poor conditions. b.Develop a decision tree with expected value at the nodes. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

48. 12-48 Step 4 (part d): Develop a decision tree. Decision Analysis Example Problem Solution (7 of 9) Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

49. 12-49 Decision Making with Probabilities Sequential Decision Trees (1 of 4) ■Note that when a decision requires only a single desicion not series of decisions to be made over time, an expected value payoff table will yield the same results as a decision tree. ■If a decision making problem requires series of decisions to be made over time, then the best method to use is DECISION TREES. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

50. 12-50 Sequential Decision Trees Lets modify real estate investment example to include a ten-year period in which several decisions are made over time. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

51. 12-51 Sequential Decision Tree The first decision facing the investor is whether to purchase an apartment building or land. If the investor purchases the apartment building, two states of nature are possible: Either the population of the town will grow (with a probability of.60) or the population will not grow (with a probability of.40). Either state of nature will result in a payoff. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

52. 12-52 Sequential Decision Tree On the other hand, if the investor chooses to purchase the land, and if population growth occurs for a 3- year period, then investor will make another decision regarding the development of the land: Either apartments will be built (with addiditional cost) or the land will be sold. If no population growth occurs for a 3-year period, then either the land will be developed commercially (with additional cost) or the land will be sold. What is the best decision to take???? Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

53. 12-53 Figure 12.4 Sequential Decision Tree Decision Making with Probabilities Sequential Decision Trees (2 of 4) Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

54. 12-54 Figure 12.5 Sequential Decision Tree with Nodal Expected Values Decision Making with Probabilities Sequential Decision Trees (3 of 4) Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

55. 12-55 Decision Making with Probabilities Sequential Decision Trees (4 of 4) ■Decision is to purchase land; highest net expected value ($1,160,000). ■Payoff of the decision is $1,160,000. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

56. 12-56 A newsvendor can buy the Wall Street Journal newspapers for 40 cents each and sell them for 75 cents. However, he must buy the papers before he knows how many he can actually sell. If he buys more papers than he can sell, he disposes of the excess at no additional cost. If he does not buy enough papers, he loses potential sales now and possibly in the future. Suppose that the loss of future sales is captured by a loss of goodwill cost of 50 cents per unsatisfied customer. Constructing the Payoff Table for The Newsvendor Problem

57. 12-57 The demand distribution is as follows: P 0 = Prob{demand = 0} = 0.1 P 1 = Prob{demand = 1} = 0.3 P 2 = Prob{demand = 2} = 0.4 P 3 = Prob{demand = 3} = 0.2 Each of these four values represent the states of nature. The number of papers ordered is the decision. The returns or payoffs are as follows:

58. 12-58 State of Nature (Demand) 0 1 2 3Decision 0 0 -50 -100 -150 1 -40 35 -15 -65 2 -80 -5 70 20 3 -120 -45 30 105 Payoff = 75(# papers sold) – 40(# papers ordered) – 50(unmet demand) Where 75¢ = selling price 40¢ = cost of buying a paper 50¢ = cost of loss of goodwill

59. 12-59 Now, the ER is calculated for each decision: State of Nature (Demand) 0 1 2 3Decision 0 0 -50 -100 -150 -85 1 -40 35 -15 -65 -12.5 2 -80 -5 70 20 22.5 3 -120 -45 30 105 7.5 ER Prob. 0.1 0.3 0.4 0.2 ER 1 = -40(0.1) + 35(0.3) – 15(0.4) – 65(0.2) = -12.5ER 2 = -80(0.1) – 5(0.3) + 70(0.4) + 20(0.2) = 22.5ER 3 = -120(0.1) – 45(0.3) + 30(0.4) – 105(0.2) = 7.5ER 0 = 0(0.1) – 50(0.3) – 100(0.4) – 150(0.2) = -85 Of these four ER’s, choose the maximum, and order 2 papers