9 10 sensitivity analysis

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Outline14/11/14 www.debrina.lecture.ub.ac.id 2


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+9SENSITIVITY ANALYSISProblem Identification and Structure

One-Way Sensitivity Analysis

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Introduction! Purpose of sensitivity analysis:!

To analyze what really mattersin the decision problem

! To construct a requisite decision model

Examples of sensitivity analysis techniques in DA:

! Determine if deterministic dominance or stochasticdominance is present

! Identify the important variables through Tornado

Diagrams! Identify interaction effectsbetween important variables

! Identify the importance of probability assessments(which are also variables)

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+The Eagle Airline Case (2)

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Dick Carothers wants to expand his operation

! Finance charges:! Borrow 40% of the price at 2% above the prime rate (=9,5%, but subject

to change)

! Revenue data!

Chartered flights: $300 - $400 per hour! Scheduled flights: $100 per person per hours, plains are on average 50%

full! Expected number of hours flown with new plane 800-1000

!Variables in control! The price he is willing to pay

! The amount finance

!Variables not in control! Insurance cost

!

Operation cost

Carothers could always invest his cash $52,500.@8% yearly interest rate, yielding an annual

interest in the first year of $4,200

What should Dick Carothers do?14/11/14


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+ Influence Diagram Keputusan Eagle Airline

Gambar tersebut adalah Initial Influence Diagram yang hanya terdiri daridari decision node

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+Problem Identification Level


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+Problem Structure Level (1)


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Low Base High

Hours Flown 500 800 1000Charter Price per hour $300.00 $325.00 $350.00Ticket Price per hour 95 100 108Occupancy Rate on Scheduled Flights $0.40 $0.50 $0.60% of Charter Flights 0.45 0.5 0.7

Operating Cost per Hour $230.00 $245.00 $260.00Insurance 18000 20000 25000Proportion Financed $0.30 $0.40 $0.50Interest Rate 0.105 0.115 0.13Purchase Price $85,000.00 $87,500.00 $90,000.00

Revenue From Charters $67,500.00 $130,000.00 $245,000.00Revenue From Scheduled Flight $52,250.00 $100,000.00 $97,200.00Fixed Cost $20,677.50 $24,025.00 $30,850.00Variable Cost $115,000.00 $196,000.00 $260,000.00

Using Low Values Using Base Values Using High Values

Total Revenue $119,750.00 $230,000.00 $342,200.00

Total Cost $135,677.50 $220,025.00 $290,850.00Total Profit -$15,927.50 $9,975.00 $51,350.00


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Is this a worst case best case analysis?


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+One-Way Sensitivity Analysis (1)


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Sensitivity of Profit on Hours Flown(Keeping Everything Else Fixed)

-$15,000.00

-$10,000.00

-$5,000.00

$0.00

$5,000.00

$10,000.00

$15,000.00

$20,000.00

$25,000.00

$30,000.00

$35,000.00

$500.00 $600.00 $700.00 $800.00 $900.00 $1,000.00

Hours Flown

Profit

Hours Flown Money Market

$4,200


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STEP 3:Perform a one-way sensitivity analysis for allvariables and plot results in a Spider Diagram

-$15,000

-$10,000

-$5,000

$0

$5,000

$10,000

$15,000

$20,000

$25,000

$30,000

$35,000

-50% -40% -30% -20% -10% 0% 10% 20% 30%

Hours

Flown

Occupancy

Rate

Operating

Cost

CharterPrice

MoneyMarket


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STEP 4:Calculated payoff range is a measure of uncertainty inpayoff due to uncertainty in the free variable. Plot the payoffranges in a Tornado Diagramand visually determine theimportant variables

0

1

2

3

4

5

-$15,0

00

-$10,0

00

-$5,0

00

$0

$5,0

00

$10,0

00

$15,0

00

$20,0

00

$25,0

00

$30,0

00

$35,0

00

Profit

Rank

Occupancy Rate

Operating Cost

Hours Flown

Charter Price


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Tornado Diagram


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+10SENSITIVITY ANALYSISTwo-Way Sensitivity Analysis

Sensitivity to Probabilities

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+Two-Way Sensitivity Analysis (1)


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+ Two-Way Sensitivity Analysis (4) The point labeled base value shows that when we plug in the base values for the

capacity and operating cost, we get an estimated profit that is grater than 4200$ so

the project looks promising.

However if we consider point C where operating cost is slightly more than base

(248) and capacity is slightly less than base (48%) they lead to a situation which

suggest not to buy the plane!www.debrina.lecture.ub.ac.id

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Base Value =


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+Sensitivity to Probability

! Bagaimana menganalisis ketidakpastian yang terdapat pada variabel-variabel

kritis yang diidentifikasi dalam Diagram Tornado?

1. Capacity of Scheduled Flights

2. Operating cost

3. Hours flown

4. Charter price (decision variabel yang ditentukan oleh Carothers)

! Asumsi:

Charothers menetapkan 2 nilai untuk masing-masing variabel yang

menjelaskan kondisi optimis dan pesimis


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Chance Nodes


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+ Changed Influence Diagramuntuk Analisis Sensitivitas terhadapProbabilitas


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constants

Chance Nodes

Dependancy


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+Uncertainties

!Now that the problem is simplified, we can includeconsideration about interdependencies of the

chance variables.

! For example probability distribution of Hours

flown depend on Capacity of scheduled flights.

Thus r is greater than s in Decision tree.

!

The next step is to asses values to p,q,r, and s.


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+Sensitivity graph

!

Now we can create a two way sensitivity graph for q and r.

! We write the expected value of purchasing airplane in terms

of q and r. We set p=0.5 and set s=0.8r.


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+ Decision Tree with 3 Uncertainty Variables


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+Two-Way Sensitivity Analysis

for 3 Alternatives (1)

!An investor has funds available to invest in one of three choices:a high-risk stock, a low-risk stock, or a savingsaccount that pays

a sure $500. If he invests in the stocks, he must pay a brokerage

fee of $200.

! His payoff for the two stocks depends in part on what happens to

the market as a whole. If the market goes up (as measured, say,by the Standard and Poors 500 Index increasing 8% over the

next 12 months), he can expect to earn $1700 from the high-risk

stock and $1200 from the low-risk stock. Finally, if the stockmarket goes down (as indicated by the index decreasing by 3%

or more), he will lose $800 with the high-risk stock but still gain$100 with the low-risk stock. If the market stay at roughly the

same level, his payoffs for the high- and low-risk stock will be

$300 and $400, respectively.


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t = P(market up)

v= P(market sama)

P(market down) = 1 t v


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0.2 0.4 0.6 0.8 1

0.2

0.4

0.6

0.8

1v

t

Daerah yang memenuhi

t+ v!1

Cari region dimana Saving Accountlebih prefer

dari Low-risk Stock :

EMV (Saving Account) EMV (Low-risk Stock)

500 t(1000) + v(200) + (1tv) (-100)

v


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+ Two-Way Sensitivity Analysis



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+ Two-Way Sensitivity Analysis



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T W S iti it A l i


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+ Two-Way Sensitivity Analysis:Texaco Penzoil


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Liedtke is unsure of court probabilities. If Liedtke thinks that p must bemore than 0.15 and q must be more than 0.35 can he make the

decision without further probability assessment?


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+Two-Way Sensitivity Analysis:

Texaco Penzoil


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Texaco Penzoil


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Texaco Penzoil


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Texaco Penzoil


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Texaco Penzoil


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Texaco Penzoil

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9 10 sensitivity analysis

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