M I T I n t e r n a t i o n a l C e n t e r f o r A i r T r a n s p o r t a t i o n

1. MIT MIT ICAT ICAT M I T I n t e r n a t i o n a l C e n t e r f o r A i r T r a n s p o r t a t i o n • Virtual Hubs: • A Case Study • Michelle Karow • karow@mit.edu • John-Paul Clarke • johnpaul@mit.edu

2. Presentation Overview: • Motivation • Definition • Characteristics • Problem formulation • Application at a major US carrier • Limitations and future considerations

3. Irregular operations at a hub airport can be crippling to an airline schedule • Reduction in capacity typically necessitates cancellations and delays • Effects resonate network-wide and on all levels of operation (fleet, maintenance, crew and passengers) • Majority of irregularities caused by weather Could airlines reduce the number of delays and cancellations by re-routing entire connecting banks to an airport with excess capacity?

4. Re-directing flights through a virtual hub can provide relief to the original hub with minimal disruption • Definition: • A virtual hub is a predetermined alternative airport that during irregular operations at the original hub, hosts connection complexes to maximize passenger flow through the network. • Shift connecting demand over two hubs, decreasing strain on the original hub • Continuity of passenger flow, insuring a reduction in total passenger delay • Capitalize on under-utilized airports

5. Destination Original Hub Origin Passengers destined for the hub Destination Origin Destination Passengers connecting to destinations not served by the virtual hub Origin Destination Origin Destination Origin Destination Virtual Hub Origin Destination Origin Sample virtual hub network

6. Average Delays Geographical location Virtual Hub Candidates Excess Capacity Virtual Hub Virtual hubs can be identified by the following characteristics: • Low average daily delays • Check FAA’s Airport Capacity Benchmark report for delay rankings of US airports • Geographically equivalent location to the original hub • Check relative location to existing hub • Excess capacity • Track airline gate utilization throughout the day, given low delays indicate excess airport capacity

7. Virtual Hub Model Accommodated Passengers Disrupted Passengers Add to the next time window Passenger Re-accommodation Module (PRM) Passengers that can be re-accommodated (and itineraries) Passengers that cannot be accommodated Implementing a virtual hub network consists of two phases: The Virtual Hub Model and The PRM

8. Anticipated Weather/ Ground Delay Program Airport Capacities Passenger Itineraries Aircraft Capacities Original Flight Schedule Time Window tn Time Window t1 Time Window t2 Update Variables for Next Time Window …. Maximize Passenger Flow Maximize Passenger Flow Maximize Passenger Flow Virtual Hub Flights Delayed/ Cancelled Flights Adjusted Itineraries Original Hub Flights Phase I: Implementing a virtual hub network • Implemented in the hours before the weather is predicted to impact the operations at the original hub • Maximizes passenger flow, in turn minimizing total passenger delay • Solved iteratively over connecting bank time-windows until weather has cleared

9. Key Assumptions: • Ground resource availability • Crew and maintenance flexibility • Passenger connections within a time window • Passenger consent

10. The virtual hub model is formulated as a mixed integer network flow problem. Input data: • Size of the time windows • Passenger itineraries • Original flight schedules • Airport capacities • Aircraft capacities

11. Objective function: Maximize passenger flow Where: O set of origins D set of destinations H set of hub airports {OH, VH, VHs} dij demand from origin i to destination j zijk positive variable representing the fraction of demand traveling on the network from origin i to destination j through hub k

12. Subject to: Definition of zijk: A path exists from origin to destination through a hub Where: wijk binary decision variable that the network exists from origin i to destination j through hub k xik binary decision variable that the network exists from origin i to hub k ykj binary decision variable that the network exists from hub k to destination j

13. Subject to: Airport capacity: Upper bounds on aircraft sent to a hub Where: xik binary decision variable that the network exists from origin i to hub ck capacity of hub k

14. Subject to: Aircraft Capacity: Upper bounds on the number of passengers on an aircraft Where: dij demand from origin i to destination j zijk binary decision variable that the network exists from origin i to destination j through hub k pi, qj aircraft capacity to and from the hub, respectively fi,, gj excess aircraft capacity on scheduled flights to and from the virtual hub, respectively

15. Subject to: Hub choice: A flight is served either by the virtual hub or the original hub Conservation of Flow: Upper bounds on aircraft departures from hubs Where: xik binary decision variable that the network exists from origin i to hub k ykj binary decision variable that the network exists from hub k to destination j bk number of aircraft on the ground from the previous time window at hub k

16. Phase II: Re-accommodating disrupted passengers After the scheduling decisions are made for a time window, some passengers will be disrupted and require re-accommodation. Disrupted passengers for the virtual hub network include the following: • A connecting passenger with their original flight from their origin serviced by the virtual hub and their original flight to their destination serviced by the original hub. • A connecting passenger with their original flight from their origin serviced by the original hub and their original flight to their destination serviced by the virtual hub. • A non-stop passenger with their original flight either to or from the original hub serviced by the virtual hub.

17. 1st Leg diverted to VH + 2nd leg on VHs Accommodated on a later flight to OH Destined for OH 1-leg itinerary Accommodated on a later flight from OH Originating at OH 1st Leg diverted to VH Accommodated on a later flights through OH Accommodated on a later flight from VH 2-leg itinerary 2nd Leg rescheduled from VH Accommodated on a later flights through OH Accommodated on a later flight to VH 1st Leg on VHs + 2nd leg rescheduled from VH An overview of the Passenger Re-accommodation Module (PRM) Disrupted Passengers from Virtual Hub Model Re-accommodated Passengers

18. A closer look: Application of the Virtual Hub Network to a Major US Carrier A thunderstorm was present at the original hub airport on March 9, 2002 while the virtual hub remained relatively unaffected. For this day, throughout the network:

19. Major delays plague the original hub while relatively minor effects are felt at the virtual hub Delayed Flights per Hub on March 9, 2002

20. Input data: Size of the Time Window The two-hour time window was selected to accommodate both the need for high scheduling accuracy and a large percentage of passengers connecting in distinct time windows.

21. Input data: Passenger Itineraries • Only the flight legs originating or arriving at the original hub were considered. • Itineraries with international flight legs were treated as originating or arriving at the original hub • Itineraries with connections overlapping two time windows were separated into two itineraries, originating and arriving at the original hub

22. Input data: Original Flight Schedules • Only domestic flights are eligible for diversion to the virtual hub • International flights operated by the airline are assumed to depart or arrive within one time window of their schedule. • International flights operated by the airline’s code-share partners are also assumed to depart or arrive within one time window of their schedule.

23. Input data: Virtual Hub Airport Capacities • Track cumulative operations at the virtual hub airport throughout the day • Bias the data to produce positive aircraft totals at the airport throughout the day (account for aircraft kept overnight) • Subtract the number of operations at the airport from the number of gates to find the excess capacity per time window

24. Throughout the day, the virtual hub is does not reach it’s maximum gate capacity of 45 gates Cumulative Number of Aircraft for the Airline at the VH on March 9, 2002

25. Subtracting the cumulative number of aircraft from the total number of gates provides a measure of excess capacity Excess Capacity for the Airline at the VH on March 9, 2002

26. The excess capacity over the day is compressed into two hour time windows to determine the VH excess capacity during irregular ops Excess Capacity for the Airline at the VH on March 9, 2002

27. Input data: Virtual and Original Hub Airport Capacities • The capacity at the original hub was reduced by 1/3 to reflect the reduction in the airport arrival rate required by the ground delay program. • The capacity at the virtual hub was the minimum number of gates to accommodate all diverted flights.

28. Input data: Aircraft Capacities • Flights remain assigned to their originally schedule aircraft, regardless of which hub airport they are sent to. • Capacity for flights traveling through the original hub is the number of seats on the aircraft. • Capacity for scheduled flights through the virtual hub is the number of seats minus the number of passengers booked on the flight (i.e., excess capacity).

29. Phase I Implementation: The Virtual Hub Model • Solution times for the time windows range from 5 minutes to over an hour, depending on the sparsity of the data set. • In each time window, the maximum number of aircraft were sent to the original hub.

30. Phase II Implementation: PRM • Passengers (and itineraries) not accommodated by the virtual hub model were entered into the PRM after each time window. • International passengers were considered disrupted if their domestic leg was delayed by more than 4 hours (i.e., two time windows). • Un-accommodated passengers are passengers that could not be accommodated by the end of the day on flights traveling through either hub airport.

31. 94% reduction Comparing Actual Recovery to the Virtual Hub Network

32. Limitations and Future Considerations: • Number of airline gates is somewhat flexible; cannot ensure airports will maintain good virtual hub candidacy. • Crew constraints and contract conditions could limit feasibility and increase diversion costs. • Availability of ground resources may constrain the capacity of the virtual hub. • Iterating over time windows under-estimates abilities of weather forecasting while optimizing over multiple time windows adds complexity and non-linearity. • Consideration of re-accommodating passengers on scheduled non-stop flights will provide a better (or equivalent) solution.