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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 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