module 5 modeling decisions sensitivity analysis

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Module 5Modeling Decisions

Sensitivity Analysis

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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

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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

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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

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• 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

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“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

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“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

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“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%

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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

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• 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

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• 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

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• 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

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• 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

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• Paste figure 5.1 on page 178

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• Paste table 5.1 on page 179

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• 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

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• 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

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• 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

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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

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• 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

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• 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

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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

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One-Way Sensitivity Analysis


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One-Way Sensitivity Analysis

• Con….figure 5.2 on page 180

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Tornado Diagram

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

• Tornado diagram for Eagle Airline

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Tornado Diagram

• Paste figure 5.3 from page 181

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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

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Two-Way Sensitivity Analysis


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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

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• 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

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• 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

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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

module 5 modeling decisions sensitivity analysis

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