1. DECISION MODELING WITH MICROSOFT EXCEL Copyright 2001 Prentice Hall Publishers and Ardith E. Baker DECISION Chapter 8 ANALYSIS Part 2

2. DECISION ANALYSIS Decision Trees: Marketing Cellular Phones A _________is a graphical device for analyzing decisions under ______(models in which the decisions and the probabilities on the states of nature are specified). Decision trees are especially useful when there is a ___________of decisions. We will use TreePlan ( http://www.treeplan.com ), a spreadsheet______, which draws decision trees in a spreadsheet. _______Theorem will be used to incorporate new information into the process.

3. ALTERNATE MARKETING AND PRODUCTION STRATEGIES The design and product-testing phase has just been completed for Sonorola’s new line of cellular phones. Three major alternatives are being considered on a marketing and production strategy for this product: A 1. Aggressive (A) Major ________________from the firm Major capital________________ Large ______________of all models Major _________marketing campaign

4. B 2. Basic (B) Move current production to_________ C 3. Cautious (C) Use excess _________on existing phone lines to produce new products SW Management decides to __________the level of demand as either strong (S) or weak (W). Modify current line in_________ Inventories for only most _______items Only local or _________advertising Minimum of new tooling Production satisfies___________ Advertising at the discretion of local dealer

5. Here is the spreadsheet model: Managements best estimate of the probability of a strong or weak market. B The optimal decision if you are _____________is to select B which yields the highest expected payoff.

6. CREATING A DECISION TREE This marketing model can also be represented by a decision tree. In decision trees: A __________represents a point at which a decision must be made. Each line (branch) leading from the square represents a possible__________. Each line (______) leading from the circle represents a possible outcome. A ___________represents an event (a situation when the __________is not certain).

7. In order to create the decision tree in Excel, the TreePlan add-in must be loaded. To do this, double-click on Treeplan.xla. After loading the add-in, select the Decision Tree option from the Tools pull-down menu.

8. In the resulting dialog, click on New Tree. By default, a _______is displayed with 2 decision nodes. To add another node, click on the decision node and hit Ctrl-t to bring up a _______in which you can select the Add Branch option.

9. After labeling the three branches, replace the ___________node with a random event node by clicking on the terminal node and hitting Ctrl-t to bring up the menu from which you will select Change to event node and two____________.

10. Here is the resulting decision tree: By default, the probabilities for each of the 2 random events are 0.5.

11. Repeat the last few steps for the remaining decisions. The resulting decision tree is:

12. APPENDING THE PROBABILITIES AND TERMINAL VALUES Now we must _________some additional information in order to use this decision tree to find the __________decision. Assign the _____________(the return associated with each terminal position). Additionally, _____________will be assigned to each branch emanating from each circular node.

13. First change the probabilities from 0.5 to:

14. Next, change the terminal values:

15. Using a decision tree to find the optimal solution is called “_________the tree.” FOLDING BACK To solve a decision tree, one works backward (i.e., from right to left) by ___________the tree. First the __________branches are folded back by calculating an expected value for each terminal node. For example, Expected terminal value = 30(0.45) + (-8)(0.55) = 9.10

16. Once the expected terminal values are calculated, management must choose the ___________that yields the highest expected terminal value. Of the three expected values, choose 12.85, the branch associated with the __________ strategy. 2 This decision is indicated in the TreePlan by the number 2 in the decision node.

17. DECISION ANALYSIS Before implementing the Basic strategy, the Board of Directors insists that a market ________ study first be performed. The corporate marketing research group at Sonorola headquarters in Tokyo will perform the research study and will report on whether the study is ______________(E) or discouraging (D). The new information should be taken into account before making a__________. Sensitivity Analysis EXPECTED RETURN AS A FUNCTION OF THE PROBABILITY FOR A STRONG MARKET

18. OBTAINING REVISED PROBABILITIES BASED ON NEW INFORMATION Once the expected _______values are calculated, management must choose the alternative that yields the highest expected terminal value. Thus, ER(A) = 30P(S) – 8[1-P(S)] = -8 + 38P(S) This expected return is a ________function of the probability that the market response is________. ER(B) = 20P(S) + 7[1-P(S)] = 7 + 13P(S) For alternatives B and C, the expected returns are ER(C) = 5P(S) + 15[1-P(S)] = 15 - 10P(S)

19. Now, plot these functions in Excel using the Data Table____________. To do this, first change the probability in cell C1 to a formula (=1-B1).

20. Here is the resulting spreadsheet: Now, highlight these cells and click on Data - Table

21. In the resulting dialog, enter B1 as the _______ Input cell and click OK to calculate the expected _________from the three different strategies for P(S) values between 0 and 1. Now, use this data to create a ________of the expected return (ER) as a function of P(S):

22. For a given P(S), determine which __________is best. For example, let P(S) = 0.45, then the highest ER is given by alternative B. What about when P(S) = 0.8? Sonorola should select the Basic strategy if 0.348 < P(S) < 0.6

23. Conditional Probability: given Conditional Probability: For two events A and B, the _____________probability [P(A|B)], is the probability of event A given that event B will occur. DECISION ANALYSIS Lets expand on the previous example with new information concerning the ___________of the uncertain events. For example, P(E|S) is the conditional probability that marketing gives an encouraging report ____ that the market is in fact going to be strong. Decision Trees: Incorporating New Information A MARKET RESEARCH STUDY FOR CELLULAR PHONES

24. If marketing were perfectly reliable, P(E|S) = 1. However, marketing has the following “track record” in predicting the market: P(E|S) = 0.6 P(D|S) = 1 - P(E|S) = 0.4 P(D|W) = 0.7 P(E|W) = 1 - P(D|W) = 0.3

25. Calculating the Posterior Probabilities: Calculating the Posterior Probabilities: Suppose that marketing has come back with an _____________report. Knowing this, what is the probability that the market is in fact ________[P(S|E)]? Note that probabilities such as P(S) and P(W) are initial estimates called a___________________. probabilities Conditional probabilities such as P(S|E) are called ____________probabilities. The domestic tractor division has already estimated the _____probabilities as P(S) = 0.45 and P(W) = 0.55. Now, use _______Theorem to determine the posterior probabilities.

27. The previous spreadsheet makes it easy to calculate the ___________of the posterior probabilities to the reliabilities and the prior probabilities. The Data Table command can be used to _______ all posterior probabilities of a strong market [P(S|E) and P(S|D)] for values of the prior probability P(S) between 0 and 1 in _________of 0.1.

28. To do this, in cell I3, enter an _______value of 0, then use the Fill – Series option to fill the remaining cells.

29. Next, enter the formulas for the quantities that we want to track [P(S|E) and P(S|D)] for each of the values of P(S).

30. Finally, highlight the area below and click Data – Table: In the resulting table, enter B8 as the Column input cell and click OK.

31. Here is the resulting table: As the prior prob. of a strong market ________, so does the posterior prob. of a strong market given either an encouraging or a discouraging test ______. Given an encouraging test result, the __________prob. of a strong market is > the prior probability. Given a discouraging test result, the posterior prob. is < the _____(except when P(S) = 0 or 1.

32. Now, represent the model with a decision tree: INCORORATING POSTERIOR PROBABILITIES IN THE DECISION TREE I II IV V VI III VII VIII IX E D A B C A B C S W S W S W S W S W S W P(E) P(D) P(W|E) P(S|E) P(S|D) P(W|E) P(W|D) P(S|D) 30 -8 20 7 5 15 30 -8 20 7 5 15 Note that the tree is built in the _____________ order in which information becomes available and decisions are required:

33. TreePlan is used to build the tree in Excel. Here is the first half of the tree:

34. Here is the second half of the tree:

35. From the previous results, the ________return of performing the market test and making optimal decisions after determining the ________is: THE EXPECTED VALUE OF SAMPLE INFORMATION ER = 15.586(0.435) + 11.814(0.565) = 13.455 Remember that if the ______test is not performed, the optimal decision is to select B, the basic _______with an expected return of 12.85. Performing the market test _________Sonorola’s expected return by 13.46 – 12.85 = $0.61 million. expected value of ______ information This value is called the expected value of ______ information (EVSI).

36. In general, EVSI = - maximum possible expected return with sample information maximum possible expected return without sample information The EVSI is an ____________of how much one would be willing to pay for this particular sample information.

37. EVPI = 30(0.45) + 15(0.55) – 12.85  8.90 The EVPI is the expected value of perfect information: Thus, perfect __________will bring an expected increase of $8.90 million over the previous expected_________. This is the ____________possible increase in the expected return that can be obtained from new information.

38. The expected value of sample information (_____ = $0.61 million) is the increase in the expected return that was obtained with the information produced by the____________. The expected value of perfect information (EVPI) is $8.9 million. Since EVPI = 8.9 and EVSI = 0.61, we see that the market test is _______effective. If it were, the value for EVSI would be much _____to EVPI. As the __________of correct sample information increase, EVSI _________EVPI. When P(E|S) = 1.00 and P(D|W) = 1.00, then EVSI = EVPI.

39. DECISION ANALYSIS Sequential Decisions: To Test or Not to Test The value in performing the market research test depends (in part) on how Sonorola uses the ___________generated by the test. The value of performing the test depends in part on how Sonorola uses the information generated by the test. sequential decision__________ The value of an initial _________depends on a __________of decisions and uncertain events that will follow the initial decision. This is called a sequential decision__________

40. ANALYZING SEQUENTIAL DECISIONS This is the type of situation that decision trees are designed to handle. Here is the upper half:

41. Here is the lower half: The ________strategy is to conduct the test, and if the result of the test is Encouraging, then choose an Aggressive_________. If the result is Discouraging, choose a Cautious campaign.

42. THE IMPACT OF UTILITIES It is simple to incorporate __________in a decision tree. Consider the following utilities of all possible payoffs: A graph of utility vs. payoff would show that Sonorola is_____________.

43. To incorporate the utilities into the decision tree, ______the payoffs with their respective utilities and _________the tree as before. Here is the upper half of the tree.

44. The optimal decision is still to________. However, if the test is encouraging, alternative B is _______ because it has a higher expected _______. Here is the lower half of the tree.

45. OTHER FEATURES OF TREEPLAN Clicking on the _______feature in TreePlan will result in the following dialog. TreePlan has a built-in ______________utility function (choose Use exponential Utility Function). Choosing this will cause Tree Plan to _______a risk- averse utility function and calculate the utilities for the given ___________already on the tree. Tree Plan defaults to a Maximize _______ approach to folding back the tree.

46. SENSITIVITY OF THE OPTIMAL DECISION TO PRIOR PROBABILITIES Often, we want to see how ________the optimal decision is to various parameter values. This spreadsheet reproduces the previous ________ analysis.

47. We can graph the expected utility of Test and No- Test by creating a table in Excel using the Data – Table option.

48. DECISION ANALYSIS Management Decision Theory A typical management decision has the following characteristics: 1. It is made ______and only once. 2. The return depends on an ________event that will occur in the ______and we have no historical information about this future event. We know about related events that may tell something about the _________of the outcomes, but we cannot perform an experiment to provide estimates of the_______________.

49. The following __________framework is recommended: 1. For each decision, determine the _____of each possible outcome. 2. Determine the _________of each possible outcome. 3. Calculate the expected utility of each _______. 4. Select the decision with the _________ expected utility. Probabilitiesutilities best judgment and ________of the manager Probabilities and utilities are not known but are _________and represent the best judgment and ________of the manager.

50. ASSESSING SUBJECTIVE PROBABILITIES consistent framework An ____________concept gives one a consistent framework for quantifying both probabilities and utilities. The values obtained through this process are _________and a matter of judgment, and thus by definition, will vary from person to_________. What do we gain from assessing probability and utility_____________? Separating the assessments of probabilities and utilities forces a manager to give appropriate and separate ___________to each before combining the two to determine the final decision.

51. DECISION ANALYSIS Notes on Implementation Decision analysis involves ________probabilities and utilities to possible outcomes and maximizing expected________. This approach is applied to highly complex models that are typically __________in nature. There are four parts: 1. _______________the model 2. Assessing the probability of the possible outcomes 3. Determining the ________of the possible outcomes 4. Evaluating alternatives and selecting a strategy

52. ROLE OF PERSONAL JUDGMENT Decision analysis does not provide a completely __________analysis of complicated models. However, experience has shown that the ___________provided by decision analysis has been useful. Many qualitative and nonobjective _________are involved in all decision making, but the important role of decision analysis is to make it__________, not just “objective” and devoid of any subjective __________.