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Module 5 Modeling Decisions Sensitivity Analysis

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- 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

- Effect of sensitivity analysis to the overall decision-modeling strategy
- Problem identification and structure
- Solving the right problem
- Error of the third kind

Dominance among alternative

- Use of tornado diagram
- One and two-way sensitivity analysis
Probability assessment

Use of computer program TopRank for 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

- 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

- 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

- 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%

- 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

- 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

- 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

- 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

- 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

- Paste figure 5.1 on page 178

- Paste table 5.1 on page 179

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- Paste figure 5.2 on page 180

- Con….figure 5.2 on page 180

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

- Paste figure 5.3 from page 181

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

- Paste figure 5.4 on page 183

- 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

- Paste figure 5.5 on page 185

- Paste figure 5.6 on page 186

- Paste figure 5.7 on page 186

- 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

- Paste figure 5.8 on page 188

- 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

- 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