Transcript Simple Aircraft Cost Functions

Biography for William Swan
Chief Economist, Seabury-Airline
Planning Group. AGIFORS Senior
Fellow. ATRG Senior Fellow.
Retired Chief Economist for Boeing
Commercial Aircraft 1996-2005
Previous to Boeing, worked at
American Airlines in Operations
Research and Strategic Planning
and United Airlines in Research and
Development. Areas of work
included Yield Management, Fleet
Planning, Aircraft Routing, and
Crew Scheduling. Also worked for
Hull Trading, a major market maker
in stock index options, and on the
staff at MIT’s Flight Transportation
Lab. Education: Master’s,
Engineer’s Degree, and Ph. D. at
MIT. Bachelor of Science in
Aeronautical Engineering at
Princeton. Likes dogs and dark
beer. ([email protected])
© Scott Adams
Simple Aircraft Cost Functions
Prof Nicole Adler
University of Jerusalem
Dr William Swan
Boeing
2 July 2004
ATRS Symposium, Istanbul
Overview
1.
Cost vs.. Distance is Linear
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2.
Cost vs.. Airplane Size is Linear
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3.
Illustration
Explanation
Calibration
Why we care
Illustration
Explanation
Calibration
Why we care
Cost vs.. Distance and Size is Planar
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Why we care
Cost vs. Distance is Linear
• Cost for a single airplane design
– Example 737-700
• Cost based on Engineering cost functions
– Data from 25-year Boeing OpCost “program”
– Divides cost into engineering components
• Fuel, crew, maintenance, ownership
• Calibrates components from airline data
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Records of fuel burn
Knowledge of crew pay and work rules
Schedule of recurring maintenance and history of failures
Market Ownership Rents allocated to trips
Engineering Approach is Different
• Not a “black box”
– We made what is inside the box
• Not a statistical calibration
– Although components are calibrated against data
• Less an overall average
– OpCost calibrations based on detail records
• OpCost estimates costs
– For standard input cost factors: fuel, labor, capital
– Ongoing function recalibration
• This report from 2001 version
• 2004 version now in use
We Generate “Perfect” Data Points
• Cost for exactly the same airplane
– At different distances
• Each point with identical input costs
– Fuel, labor, capital
• Superb spread of data points
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Costs at 1000, 1500, 2000, 3000, 4000, 5000km distances
Much larger than spreads of averages for airlines
Comparable overall average distance
Much greater sensitivity to slope
• Objective is to learn the shape of the relationship
– Find appropriate algebraic form
• For ratios of costs at different distances
Cost is Linear With Distance
737-700 Example
30
Trip Cost (index)
25
20
15
10
Cost Data
Linear (Cost Data)
5
0
0
1000
2000
3000
Distance (km)
4000
5000
Explanation:
Why is Cost Linear With Distance?
• Most costs are per hour or per cycle
• Time vs. distance is linear: speed is constant
– (roughly ½ hour plus 500 mph)
• Departure/arrival cycle time is about ½ hour
• Some costs are allocated
– Allocation is per hour and per cycle
– Ownership, for example
• Very small rise in fuel/hour for longer hours
• Beyond 8 hours, crew gains 1 or 2 pilots
– Does not apply to regional distances.
Cost Formulae are Linear
Airplane cost/seat-km km/departure
a318
0.039
691
737-600
0.038
700
737-700
0.035
692
a319
0.036
705
A320-200
0.033
727
737-800
0.031
701
737-900
0.030
715
A321-200
0.030
725
757-200
0.029
782
757-300
0.027
815
seats
107
110
126
126
150
162
177
183
200
243
R-Squared
0.9998
0.9997
0.9997
0.9997
0.9998
0.9997
0.9997
0.9998
0.9999
0.9999
Observations
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All airplanes’ cost vs.. distance was linear
Calibration using 6 “perfect” data points
Least squares
Slopes per seat-km similar
Intercept in equivalent km cost similar
757s designed for longer hauls
Otherwise comparable capabilities
Why we Care
• Costs Linear with distance means
– Average cost is cost at average stage length
• We generally know these data
• We can adjust and compare airlines at standard
distance
– Cost of an extra stop are separable
• Stop cost independent of where in total distance
• Simplifies Network Costs
– Costs are depend on total miles and departures
Costs Are Linear with Airplane Size
(Example at 1500 km)
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trip cost at 1500 km (index)
14
12
10
8
6
Data
Linear (Data)
4
2
0
100
120
140
160
180
200
220
seats for comparable single-aisle designs
240
Why we Care
• Costs Linear with Seats means
– Average cost is cost at average size
• We generally know these data
• We can adjust and compare airlines at a standard size
– Cost of Frequency and Capacity are Separable
• Frequency cost is independent of capacity
• Powerful Independence in Network Design
– Costs and values of Frequencies
– Cost and need for capacity
Calibration for Planar Formula
• NOT
Cost = a + b*Seats + c*Dist + d*Seats*Dist
• Yes:
Cost = k * (Seats + a) * (Dist + b)
= k*a*b + k*b*seats + k*a*Dist
+ k*Seats*Dist
NOTE: only 3 degrees of freedom
Why We Care
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Planar function is VERY easy to work with
Decouples frequency, size, distance
Vastly simplifies network design issues
Allows comparison of airline costs after
adjustment for size and stage length
• Calibration with broad ranges of size and
distance means slopes are very significant
Calibration Techniques
• Calibrate each airplane vs.. distance
– Two variables, k and b
• Calibrate a for least error
– Unbiased
– Least squared
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Compare to least % error (log form)
Compare to size-first process
Results very similar
Results also similar to 4-variable values
Calibration Formula
Cost = $0.019 * (Seats + 104) * (Dist + 722)
Where
Cost means total cost 2001US $ per airplane trip,
non-US cost functions.
Seats means seat count in standard 2-class regional
density.
Dist means airport-pair great circle distance in
kilometers.
One try at “Fair” Relative Seat Counts
Regional Configurations
Airplane
Nominal (all Y)
2-class (as used)
A318
117
107
737-600
122
110
737-700
140
126
A319
138
126
A320
160
150
737-800
175
162
737-900
189
177
A321
202
183
757-200
217
200
757-300
258
243
Another Try at “Fair” Relative Seat Counts
Long-haul Configurations
Airplane
Nominal (all Y) 2-class (long)
767-200
238
163
767-300
280
200
767-400
315
229
A330-2
355
233
A330-3
379
268
777-200
415
308
777-300
510
385
747-400
553
429
Cost is Linear With Distance
777-200 Example
120
Trip Cost Index
100
80
60
40
Data
20
0
3000
Linear (Data)
4000
5000
6000
Distance (km)
7000
8000
9000
Costs Are Linear with Airplane Size
(Example at 6000 km)
100
Trip Cost at 6000 km (index)
90
80
70
60
50
40
30
20
10
0
100
150
200
250
300
Long-haul seat count
350
400
Calibration Formula
Cost = $0.0115 * (Seats + 211) * (Dist + 2200)
Where
Cost means total cost 2001US $ per airplane trip,
non-US International trip cost functions.
Seats means seat count in standard 2-class long haul
density.
Dist means airport-pair great circle distance in
kilometers.