1. 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. (bill.swan@cyberswans.com)bill.swan@cyberswans.com © Scott Adams

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

3. Overview 1.Cost vs.. Distance is Linear Illustration Explanation Calibration Why we care 2.Cost vs.. Airplane Size is Linear Illustration Explanation Calibration Why we care 3.Cost vs.. Distance and Size is Planar Why we care

4. 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

5. 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

6. 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

7. Cost is Linear With Distance 737-700 Example

8. 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.

9. Cost Formulae are Linear

10. 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

11. 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

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

13. 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

14. 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

15. 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

16. 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

17. 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.

18. One try at “Fair” Relative Seat Counts Regional Configurations AirplaneNominal (all Y)2-class (as used) A318117107 737-600122110 737-700140126 A319138126 A320160150 737-800175162 737-900189177 A321202183 757-200217200 757-300258243

19. Another Try at “Fair” Relative Seat Counts Long-haul Configurations AirplaneNominal (all Y)2-class (long) 767-200238163 767-300280200 767-400315229 A330-2355233 A330-3379268 777-200415308 777-300510385 747-400553429

20. Cost is Linear With Distance 777-200 Example

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

22. 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.