1. 1 Module 5 Modeling Decisions Sensitivity Analysis

2. 2 Module 5 Sensitivity Analysis Topics -sensitivity analysis issues on decision modeling -identifying and structuring problems -dominance consideration in sensitivity analysis -sensitivity analysis and probabilities -tornado diagram and one-and two-way sensitivity graphs -sensitivity analysis performance using TopRank and Precision Tree program

3. 3 Sensitivity Analysis Learning Objectives Effect of sensitivity analysis to the overall decision-modeling strategy Problem identification and structure –Solving the right problem –Error of the third kind

4. 4 Sensitivity Analysis Learning Objectives Dominance among alternative Use of tornado diagram One and two-way sensitivity analysis Probability assessment Use of computer program TopRank for sensitivity analysis

5. 5 Sensitivity Analysis The purpose of sensitivity analysis is to refine the decision model –what makes a difference in each decision –Provide guidance for the development of a requisite decision model Eagle Airlines example

6. 6 “Eagle Airline” President of Eagle Airline would like to expand his operation with the company’s extra cash The mixture of charter flights and short schedule flights are profitable, but this is impossible without more aircraft A piper Seneca is for sale at a price of $95,000 with five seats for passengers

7. 7 “Eagle Airline” Operating cost: –Approximately $245 per hour –Annual fixed costs including insurance is about $20,000 –The company need to borrow 40% of the money with 9.5% interest rate

8. 8 “Eagle Airline” Total revenue: –The Eagle Airline could charge $100 per person per hour on schedule flight –Approximate 800 hours flight per year –If Eagle Airline lease the airplane for year with the option to buy it would cost the company between $2500 to $4000 –The Eagle Airline CEO could invest the extra cash in the money market and expect to earn about 8%

9. 9 Problem Identification and Structure As we discussed in chapter one, sensitivity analysis can lead the decision maker to reconsider the very nature of the problem –Are we solving the right problem? Answering different question/addressing a different problem or satisfying different objective can lead to a very different decision

10. 10 Problem Identification and Structure Solving the wrong problem is called “error of the third kind” or type III error It implies that the wrong question was asked To avoid the type III error, keep asking whether the problem on the surface is the real problem

11. 11 Problem Identification and Structure Example: Eagle Airline In this case Carothers (CEO of Eagle Airline) eager to expand the operation by acquiring more aircraft The real question may be how to satisfy Carothers’s desires for expand rather than simply how to acquire more airplanes

12. 12 Problem Identification and Structure Decision situation can be represented in a variety of different ways Sensitivity Analysis can help to identify the appropriate perspective on the problem as well as by identifying the specific issues that matter to the decision maker In Eagle Airline case, the alternative to purchase the airplane is the option to buy or neither

13. 13 Problem Identification and Structure The main objective for Eagle Airline is to maximize the profit Using influence diagram to assess the probabilities associated with various unknown quantities such as operating costs, amount of business

14. 14 Problem Identification and Structure Paste figure 5.1 on page 178

15. 15 Problem Identification and Structure Paste table 5.1 on page 179

16. 16 Problem Identification and Structure By using the estimated variable in table 5.1 we can calculate the annual profit The annual profit would be the total annual revenue minus the total annual cost: Total Revenue = Revenue from charters + Revenue from schedule flights = (charter proportion x Hours flown x charter price)+[(1-charter proportion) x hours flown x ticket price x number of passenger seats x capacity of schedule flight] = (0.5 x 800 x $325) + (0.5 x 800 x $100 x 5 x 0.5) = $230,000

17. 17 Problem Identification and Structure Total Cost = (hours flown x operation cost) + insurance + finance cost = (hours flown x operation cost) + insurance + (price x proportion financed x interest rate) = (800 x $245) + $20,000 + ($87,500 x 0.4 x 11.5%) = $220,025

18. 18 Problem Identification and Structure By using the base values, Eagle Airline annual profit is estimated to be $230,000 - $220,025 = $9975 This represents a return of approximately 19% on his investment of $52,500 (60% of the purchase price) He could place the $ 52,500 in money market account with the 8% interest and earn $4200

19. 19 Dominance Consideration In chapter 4 we learned that alternative can be screened on the basis of Dominance Dominance means that one alternative, called the dominating alternative, is always preferred over another alternative Identifying dominant alternative can be viewed as a version of sensitivity analysis

20. 20 Dominance Consideration In case of Eagle Airline, the question is whether purchasing the option is a dominated alternative Let’s look at the option to purchase the new airplane within a year: –It would let the Eagle Airline lock in a favorable price –Wait and see if the economic climate change for expansion becomes more favorable

21. 21 Dominance Consideration It is clear that, unless an inexpensive information- gathering strategy presents itself, purchasing the option probably is a dominated alternative For the purpose of the further analysis, we will assume that no such a information-gathering strategy exists, and that purchasing the option is unattractive Two alternative will be consider: –Buying the airplane –Investing in the money market

22. 22 Sensitivity Analysis Graphical Techniques One-Way Sensitivity Analysis (one variable analysis) In Eagle Airline case, what variables really make a difference in terms of the decision at hand? Let’s consider Hours Flown in Eagle Airline case Flown hours from table 5.1 can be between 500 to 1000 hours

23. 23 One-Way Sensitivity Analysis Paste figure 5.2 on page 180

24. 24 One-Way Sensitivity Analysis Con….figure 5.2 on page 180

25. 25 Tornado Diagram A tornado diagram allows us to compare one-way sensitivity analysis for many input variable at once Tornado diagram for Eagle Airline

26. 26 Tornado Diagram Paste figure 5.3 from page 181

27. 27 Two-Way Sensitivity Analysis Two-Way Sensitivity Analysis ( Impact of several variables at one time) Two-Way Sensitivity Graph for Eagle Airline: –Operating Cost –Capacity of Schedule Flight

28. 28 Two-Way Sensitivity Analysis Paste figure 5.4 on page 183

29. 29 Sensitivity to Probabilities In this section we will see how the two-way sensitivity analysis can be used in conjunction with probabilities The three uncertain Critical Variables for Eagle Airline –Capacity of Schedule Flights –Operation Cost –Hours Flown

30. 30 Sensitivity to Probabilities Paste figure 5.5 on page 185

31. 31 Sensitivity to Probabilities Paste figure 5.6 on page 186

32. 32 Sensitivity to Probabilities Paste figure 5.7 on page 186

33. 33 Sensitivity to Probabilities EMV (Purchase) = 0.5 {q[-9725r-4225(1-r)] + 18,275(1-0.8r)]} + 0.5{q[675r + 10,175(1-r]+(1-q)[16,925(0.8r) + 32,675(1-0.8r)]} After algebraic simplification the equation become: EMV (Purchase) = q(3500r-22,500) – 11,000r + 25,475 Solve the inequality for q and r, If EMV (purchase) > 4200 then purchase the airplane 21,275-11,000r/22,500-3500r > q

34. 34 Sensitivity to Probabilities Paste figure 5.8 on page 188

35. 35 Sensitivity Analysis Sensitivity Analysis using Computer programs: –Sensitivity Analysis using TopRank –Sensitivity Analysis using Precision Tree Eagle Airline example using TopRank Eagle Airline example using Precision Tree

36. 36 Chapter 5 Summary Sensitivity Analysis and decision modeling Problem identification and structure Dominance consideration in sensitivity analysis Graphical sensitivity analysis such as tornado diagrams, one-and two-way sensitivity graphs We also discuss ways to perform sensitivity analysis using computer software such as TopRank and precision Tree