1 / 21

Simple Aircraft Cost Functions

Simple Aircraft Cost Functions. Prof Nicole Adler University of Jerusalem Dr William Swan Boeing 2 July 2004 ATRS Symposium, Istanbul. Overview. Cost vs.. Distance is Linear Illustration Explanation Calibration Why we care Cost vs.. Airplane Size is Linear Illustration Explanation

ronda
Télécharger la présentation

Simple Aircraft Cost Functions

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Simple Aircraft Cost Functions Prof Nicole Adler University of Jerusalem Dr William Swan Boeing 2 July 2004 ATRS Symposium, Istanbul

  2. Overview • Cost vs.. Distance is Linear • Illustration • Explanation • Calibration • Why we care • Cost vs.. Airplane Size is Linear • Illustration • Explanation • Calibration • Why we care • Cost vs.. Distance and Size is Planar • Why we care

  3. 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 • 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

  4. 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

  5. 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 • 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

  6. Cost is Linear With Distance737-700 Example

  7. 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.

  8. Cost Formulae are Linear

  9. Observations • 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

  10. 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

  11. Costs Are Linear with Airplane Size(Example at 1500 km)

  12. 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

  13. 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

  14. Why We Care • 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

  15. Calibration Techniques • Calibrate each airplane vs.. distance • Two variables, k and b • Calibrate a for least error • Unbiased • Least squared • Compare to least % error (log form) • Compare to size-first process • Results very similar • Results also similar to 4-variable values

  16. 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.

  17. One try at “Fair” Relative Seat Counts

  18. Another Try at “Fair” Relative Seat Counts

  19. Cost is Linear With Distance777-200 Example

  20. Costs Are Linear with Airplane Size(Example at 6000 km)

  21. 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.

More Related