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Module 5 Modeling Decisions Sensitivity Analysis

Module 5 Modeling Decisions Sensitivity Analysis. Module 5 Sensitivity Analysis. Topics -sensitivity analysis issues on decision modeling -identifying and structuring problems -dominance consideration in sensitivity analysis -sensitivity analysis and probabilities

candice-hebert
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Module 5 Modeling Decisions Sensitivity Analysis

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  1. Module 5Modeling DecisionsSensitivity Analysis

  2. Module 5Sensitivity 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. Sensitivity AnalysisLearning 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. Sensitivity AnalysisLearning 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. 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. “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. “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. “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. 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. 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. 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. 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. 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. Problem Identification and Structure • Paste figure 5.1 on page 178

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

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

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

  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. Tornado Diagram • Paste figure 5.3 from page 181

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

  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. Sensitivity to Probabilities • Paste figure 5.5 on page 185

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

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

  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. Sensitivity to Probabilities • Paste figure 5.8 on page 188

  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. 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

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