From Bookings to Demand The Process of Unconstraining

1. From Bookings to DemandThe Process of Unconstraining • Stefan Pölt, Lufthansa • Presentation to the AGIFORS • Reservations and Yield Management Study Group • New York, 22.-24. March 2000

2. Agenda • Unconstraining • What is it ? • Why is it done ? • How is it done ? • What are the problems ? • Are there solutions ?

3. „Unconstraining“ „Detruncation“ „Spill Analysis“ „Censored Data Analysis“ What Is It ? • The process of estimating how much demand could have been accepted without any capacity or booking control limit

4. - Now You Don’t Now You See It

5. Example

6. What Is Demand ? • It is a ‘philosophical’ question how demand on a specific flight in a specific booking class should be defined • The choice of passengers depends on the availability of different alternatives • Not every booking represents ‘first choice’ demand • Concentrating on first choice demand makes the difference between demand and observed bookings even worse

7. Forecasting Optimization Unconstraining Booking Control Observed Bookings Passenger Choice Accept / Reject Why Is It Done ? • To fill the gap between what is needed and what can be observed Demand Bookings

8. Why Should We Look At It ? • In PODS we have seen that good unconstraining is as important as good forecasting and as the step from leg to O&D • That does not make the latter two less important !

9. Historical Bookings Historical Demand Historical Availabilities Unconstraining Parameter How Is It Done ? • Look for similar historical flights that have not been restricted • Take average booking change of these flights and apply it to restricted ones

10. Unconstraining Forecasting Historical Bookings Historical Demand Forecasting Parameter Forecast Demand Historical Availabilities Unconstraining Parameter Actual Bookings Unconstraining & Forecasting • Is the separation of unconstraining and forecasting necessary ? • Unconstraining is a special case of forecasting • Unconstraining parameters could be used to forecast future flights

11. Example

12. How Is It Done ? • Additive • Multiplicative • Expectation Maximization • Others

13. Possible Problems • Not enough unrestricted historical events • Sponsoring with similar markets ? • Outlier (e.g. group bookings / cancellations) • Outlier detection before unconstraining • No quality measurement possible • Simulations

14. Systematic Errors • Unconstraining is too low because: • Sampling bias: historical unrestricted off-peak flights are used to unconstrain restricted peak flights • Even if a class is not restricted at the fixed snapshots it might be restricted in between two snapshots • Even if a class is not restricted some connections might be restricted (holds for leg-based unconstraining only)

15. Systematic Errors • Unconstraining is too high because: • Double counting: if only one of two alternatives is available there might appear a booking on the open one and an additional (unconstrained) booking at the closed one • If the total demand flickers around the booking limit - e.g small numbers in O&D unconstraining (mainly affects unconstraining from snapshot to snapshot)

16. Sampling Bias

17. The higher the demand the greater the sampling bias Sampling Bias • Higher probability of being constrained in case of • high demand • low booking limit wish

18. Results

19. Results

20. Results • EM lowers the systematic error but does not solve the sampling bias problem.