Module 5 Modeling Decisions Sensitivity Analysis

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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 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 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 AnalysisLearning Objectives

Dominance among alternative

• One and two-way sensitivity analysis

Probability assessment

Use of computer program TopRank for 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”
• 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 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 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
• 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 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 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 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 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 Structure
• Paste figure 5.1 on page 178
Problem Identification and Structure
• Paste table 5.1 on page 179
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 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 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
• 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 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 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:
• Investing in the money market
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
• Paste figure 5.2 on page 180
One-Way Sensitivity Analysis
• 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
• 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 Analysis
• Paste figure 5.4 on page 183
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 Probabilities
• Paste figure 5.5 on page 185
Sensitivity to Probabilities
• Paste figure 5.6 on page 186
Sensitivity to Probabilities
• Paste figure 5.7 on page 186
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 Probabilities
• Paste figure 5.8 on page 188
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
• 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