Module 5 Modeling Decisions Sensitivity Analysis

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Module 5Modeling DecisionsSensitivity 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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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

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Eagle Airline

• President of Eagle Airline would like to expand
  his operation with the companys 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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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

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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
  Carotherss desires for expand rather than simply
  how to acquire more airplanes

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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

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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

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Problem Identification and Structure

• Paste figure 5.1 on page 178

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Problem Identification and Structure

• Paste table 5.1 on page 179

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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

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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

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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

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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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Dominance Consideration

• In case of Eagle Airline, the question is whether
  purchasing the option is a dominated alternative
• Lets 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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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

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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?
• Lets 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

• Paste figure 5.2 on page 180

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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

• Paste figure 5.4 on page 183

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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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Sensitivity to Probabilities

• Paste figure 5.5 on page 185

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Sensitivity to Probabilities

• Paste figure 5.6 on page 186

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Sensitivity to Probabilities

• Paste figure 5.7 on page 186

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Sensitivity to Probabilities

• EMV (Purchase)
  0.5 q-9725r-4225(1-r)
  18,275(1-0.8r) 0.5q675r
  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 to Probabilities

• Paste figure 5.8 on page 188

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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

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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