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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

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Module 5 modeling decisions sensitivity analysis
Module 5Modeling DecisionsSensitivity Analysis

Module 5 sensitivity analysis
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

Sensitivity analysis learning objectives
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

Sensitivity analysis learning objectives1
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

Sensitivity analysis
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

Eagle airline
“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

Eagle airline1
“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

Eagle airline2
“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%

Problem identification and structure
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

Problem identification and structure1
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

Problem identification and structure2
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

Problem identification and structure3
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

Problem identification and structure4
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

Problem identification and structure5
Problem Identification and Structure

  • Paste figure 5.1 on page 178

Problem identification and structure6
Problem Identification and Structure

  • Paste table 5.1 on page 179

Problem identification and structure7
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

Problem identification and structure8
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

Problem identification and structure9
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

Dominance consideration
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

Dominance consideration1
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

Dominance consideration2
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

Sensitivity analysis graphical techniques
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

One way sensitivity analysis
One-Way Sensitivity Analysis

  • Paste figure 5.2 on page 180

One way sensitivity analysis1
One-Way Sensitivity Analysis

  • Con….figure 5.2 on page 180

Tornado diagram
Tornado Diagram

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

  • Tornado diagram for Eagle Airline

Tornado diagram1
Tornado Diagram

  • Paste figure 5.3 from page 181

Two way sensitivity analysis
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

Two way sensitivity analysis1
Two-Way Sensitivity Analysis

  • Paste figure 5.4 on page 183

Sensitivity to probabilities
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

Sensitivity to probabilities1
Sensitivity to Probabilities

  • Paste figure 5.5 on page 185

Sensitivity to probabilities2
Sensitivity to Probabilities

  • Paste figure 5.6 on page 186

Sensitivity to probabilities3
Sensitivity to Probabilities

  • Paste figure 5.7 on page 186

Sensitivity to probabilities4
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

Sensitivity to probabilities5
Sensitivity to Probabilities

  • Paste figure 5.8 on page 188

Sensitivity analysis1
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

Chapter 5 summary
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