Incorporating Weather Uncertainty in Airport Arrival Rate Decisions

1. Incorporating Weather Uncertainty in Airport Arrival Rate Decisions FAA-NEXTOR-INFORMS Conference on Air Traffic Management and Control Joyce W. Yen Zelda B. Zabinsky Catherine A. Serve’ 5 June 2003

2. Objective • Investigate the trade-off between ground delay and air delay given uncertainties in the weather prediction • To examine, “How do inaccuracies in weather forecasts affect flow decisions?”

3. Agenda • Air Traffic Background • Stochastic Optimization Formulation • Sample Test Case • Sensitivity Analysis on Weather Forecast Accuracy • Next Steps

4. Flow Control Decisions • A collaborative decision is made between Air Traffic Control (ATC), the Airline Operational Control (AOC), and affected centers • Decisions result in some form of ground delay or air delay • Ground holding (delay on ground) • Miles-in-Trial (delay in air)

5. Decision Representation • Single airport with multiple arrivals • How to make delay decisions to minimize total delay or cost of delay?

6. Agenda • Air Traffic Background • Stochastic Optimization Formulation • Sample Test Case • Sensitivity Analysis on Weather Forecast Accuracy • Next Steps

7. Stochastic Optimization Formulation - Assumptions • Due to weather uncertainty, there is a probabilistic reduction of capacity, airport acceptance rate (AAR) • Modeled decisions as a stochastic optimization problem • Model Assumptions • Single airport • Flights aggregated by scheduled arrival • Previous work • Octavio Richetta and Amedeo Odoni (1993,1994) • Min E[Cost of ground delay] + E[Cost of air delay] • Dynamic formulation

8. Stochastic Optimization Formulation - Utility Function • New objective function included utility of flight as function of total delay

9. Stochastic Optimization Formulation - Utility Function • In addition to cost of ground delay and air delay, the value of the system should include the utility of the flights based on their total delay • This new objective would be a utilitarian point of view; good for both ATC and AOC • Max (Utility - Cost) • Delay Costs • Air delay cost = Ground delay cost • Air delay cost = 2* Ground delay cost • Air delay cost = 5* Ground delay cost

10. Deterministic Mathematical Formulation

11. Expansion into Stochastic Formulation Network component for q=1 Network component for q=2 Network component for q=Q

12. Stochastic Optimization Formulation • Two sets of decision variables determine rescheduled number of arrivals (RNA) for each time period • First stage decisions (Xij) reschedule the arrival time of flights from i to j • Recourse decisions ( ) assign actual arrival time k (which may differ from the original arrival time i or rescheduled arrival time j) • Probability of scenario q, (pq ) weather uncertainty

13. Agenda • Air Traffic Background • Stochastic Optimization Formulation • Sample Test Case • Sensitivity Analysis on Weather Forecast Accuracy • Next Steps

14. Experimental Design - Demand Vector • Sixteen time period model - 15 min intervals Based On Official Airline Guide Boston Logan Airport Arrival Data Demand for Monday 8AM to 12PM

15. Experimental Design – Scenario Setup • Forecast gives capacity for each time period • Five capacity cases (each with three possible forecasts) created to represent various weather conditions • Fair Weather • Late Storm • Intense Storm • Mid-time Storm • Unpredictable Weather • Four probability cases represent different distributions of capacity forecasts • Twenty scenarios

16. Experimental Design - Probability Cases • Each capacity case has three possible forecasts

17. Model Run Results – Makeup of Total Delay One Unit of Delay = 15 min

18. Model Run Results – Time & Length of Delays • As cost of air delay increases see more flights rescheduled in later time periods Averaged over all weather cases

19. Model Run Results – Summary of Insights • Decisions sensitive to value of total delay and relative costs of air delay and ground delay If only minimize cost of air and ground (and ignore total delay), assign more ground delay and not value opportunity to take advantage of clearing weather • When air delay cost > ground delay cost, schedules more ground delay • Unpredictable & Late Storm scheduling longer delays • As relative cost of air delay increases see more flights rescheduled in later time periods

20. Agenda • Air Traffic Background • Stochastic Optimization Formulation • Sample Test Case • Sensitivity Analysis on Weather Forecast Accuracy • Next Steps

21. Sensitivity Analysis - Objective • Currently attempting to understand effects of weather forecast accuracy on model • Constructed three new capacity cases each again with three possible forecasts • Late Storm • Early Storm • Intense Storm

22. Sensitivity Analysis - Objective • Created five probability profiles to reflect varying inaccuracies of forecasts each with three probability cases (distributions for forecasts) • Examining changes in scheduling decisions as confidence in timing of storm varies

23. Sensitivity Analysis - Experimental Setup • Created capacity cases representing a early, late, and intense storm

24. Sensitivity Analysis - Experimental Setup Created 5 probability profiles each reflecting a different % inaccuracy in forecast

25. 1x 2x 5x Sensitivity Analysis - Results Total Delay Make-up F1 .5 F2 .3 F3 .2 F1 .2 F2 .5 F3 .3 F1 .3 F2 .2 F3 .5

26. Sensitivity Analysis - ResultsTotal Delay Make-up F1 .75 F2 .2 F3 .05 F1 .85 F2 .10 F3 .05 F1 .5 F2 .3 F3 .2 F1 .6 F2 .2 F3 .2 F1 .65 F2 .25 F3 .10

27. Sensitivity Analysis - ResultsTotal Delay Make-up F1 .75 F2 .2 F3 .05 F1 .85 F2 .10 F3 .05 F1 .5 F2 .3 F3 .2 F1 .6 F2 .2 F3 .2 F1 .65 F2 .25 F3 .10

28. Sensitivity Analysis - ResultsTotal Delay Make-up F1 .85 F2 .10 F3 .05 F1 .65 F2 .25 F3 .10 F1 .75 F2 .2 F3 .05 F1 .5 F2 .3 F3 .2 F1 .6 F2 .2 F3 .2

29. Sensitivity Analysis - ResultsTiming Of Rescheduling • Decision variables Xij indicate when flights are being rescheduled

30. Sensitivity Analysis - Summary of Insights • When cost of air delay is same as cost of ground delay see insensitive ground delay decisions • More ground delay is taken as cost of air increases • As the forecast certainty increases better able to assign proper amount ground delay

31. Next Steps • More examination of demand effects especially when relative cost of air is greater than 5x ground • Investigate possible application to particular real weather scenarios, such as morning fog effects in San Francisco

32. Questions ?

33. Contact Information Joyce W. Yen joyceyen@u.washington.edu 206-543-4605 Zelda B. Zabinsky zelda@u.washington.edu 206-543-4607