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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 nM 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 [email protected]
John-Paul [email protected]
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ICATICAT
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Presentation Overview:
• Motivation
• Definition
• Characteristics
• Problem formulation
• Application at a major US carrier
• Limitations and future considerations
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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?
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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
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Origin
Original Hub
Virtual Hub
Destination
Passengers destined for the hub
Origin
Origin
Origin
Origin
Origin
Origin
Destination
Destination
Destination
Destination
Destination
Destination
Passengers connecting to destinations not
served by the virtual hub
Sample virtual hub network
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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
Virtual Hub Candidates
Virtual Hub
Excess Capacity
Average Delays
Geographical location
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Implementing a virtual hub network consists of two phases:The Virtual Hub Model and The PRM
Disrupted Passengers
Virtual Hub Model
Passenger Re-accommodation Module (PRM)
Passengers that cannot be accommodated
Passengers that can be re-accommodated (and
itineraries)
Add to the next time window
Accommodated Passengers
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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
Maximize Passenger Flow
Time Window t1
….
Airport Capacities
Passenger Itineraries
Original Flight Schedule
Aircraft Capacities
Original Hub Flights
Virtual Hub Flights
Adjusted Itineraries
Delayed/ Cancelled Flights
Anticipated Weather/ Ground Delay Program
Upd
ate
Var
iabl
es f
or
Nex
t Tim
e W
indo
w
Maximize Passenger Flow
Time Window t2
Maximize Passenger Flow
Time Window tn
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Key Assumptions:
• Ground resource availability
• Crew and maintenance flexibility
• Passenger connections within a time window
• Passenger consent
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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
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Objective function: Maximize passenger flow
Where:O set of originsD set of destinationsH 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
Maximize ij ijki O j D k H
d z
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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 kxik 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
ijk ijkz w i O, j D,k H , ,ijk ikw x i O j D k H
, ,ijk ikw y i O j D k H 1 , ,ijk ik kjw x y i O j D k H
1 ,ijkk H
z i O j D
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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
ik ki O
x c k H
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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, respectivelyfi,, gj excess aircraft capacity on scheduled flights to and from the virtual hub, respectively
,
ij ijk ij D k OH VH
d z p i O
,
ij ijk ji O k OH VH
d z q j D
, ij ijk j si O
d z g j D k VH
, ij ijk i sj D
d z f i O k VH
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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 kykj binary decision variable that the network exists from hub k to
destination jbk number of aircraft on the ground from the previous time window
at hub k
,
1 ikk OH VH
x i O
,
1 kjk OH VH
y j D
0 ik kj ki O j D
x y b k
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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.
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An overview of the Passenger Re-accommodation Module (PRM)
Disrupted Passengers
from Virtual Hub Model
Re-
acco
mm
odat
ed P
asse
nge
rs
2-leg itinerary
1-leg itinerary
1st Leg diverted to VH
2nd Leg rescheduled
from VH
Originating at OH
Destined for OH
Accommodated on a later flight
from OH
Accommodated on a later flight
to OH
Accommodated on a later flights
through OH
Accommodated on a later flight
from VH
Accommodated on a later flights
through OH
Accommodated on a later flight
to VH1st Leg on VHs + 2nd leg rescheduled from VH
1st Leg diverted to VH + 2nd leg on VHs
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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:
Domestic and International Flights 4,000
Number of Passengers 99,000
Distinct Itineraries 38,000
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Major delays plague the original hub while relatively minor effects are felt at the virtual hub
Delayed Flights per Hub on March 9, 2002
0
20
40
60
80
100
120
140
160
180
OH Departures OH Arrivals VH Departures VH Arrivals
Nu
mb
er
of
Flig
hts
Flightsdelayed >15minutes
Flightsdelayed >30minutes
Flightsdelayed >45minutes
Flightsdelayed >60minutes
Cancelledflights
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Input data: Size of the Time Window
Average Connection Time 151 minutes
Highest Frequency Markets1 flight per 60 minutes
Size of the Time Window 120 minutes
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.
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Input data: Passenger Itineraries
Itineraries Passengers
Traveling through the original hub during the period of irregular operations
4,342 19,291
• 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
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Input data: Original Flight Schedules
Domestic International
Flights between 8am and 6pm at the original hub
548 46
• 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.
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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
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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
0
5
10
15
20
25
30
35
40
45
400
500
600
700
800
900
1000
1100
1200
1300
1400
1500
1600
1700
1800
1900
2000
2100
2200
2300
2400
Time in Hours
Nu
mb
er
of
Air
cra
ft
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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
0
5
10
15
20
25
30
35
40
45
50
400
500
600
700
800
900
1000
1100
1200
1300
1400
1500
1600
1700
1800
1900
2000
2100
2200
2300
2400
Time in Windows
Nu
mb
er
of
Air
cra
ft
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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
0
10
20
30
40
50
60
70
80
90
100
800 -1000 1001-1200 1201-1400 1401-1600 1601-1800
Time Windows
Nu
mb
er o
f A
ircr
aft
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Input data: Virtual and Original Hub Airport Capacities
Time WindowScheduled Domestic Arrivals
Scheduled Domestic
Departures
cOH:
Original Hub Capacity
cvh:
Virtual Hub Capacity
800 to 1000 35 57 21 19
1001 to 1200 41 58 28 19
1201 to 1400 47 42 32 19
1401 to 1600 59 53 40 19
1601 to 1800 33 37 22 19
• 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.
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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).
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Phase I Implementation: The Virtual Hub Model
Time WindowNumber of Passengers
Constraints VariablesPassengers Served
(Objective Function)
800 to 1000 4,436 26,304 12,247 4,037
1001 to 1200 6,191 31,311 14,566 5,747
1201 to 1400 5,139 26,019 12,112 4,753
1401 to 1600 6,298 41,100 19,099 5,852
1601 to 1800 3,122 16,639 7,762 2,978
• 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.
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Phase II Implementation: PRM
Time Window
Passengers Not Accommodated by Virtual Hub Model
Re-accommodated Passengers
Disrupted International Passengers
Un-accommodated Passengers
800 to 1000 399 340 53 6
1001 to 1200 444 321 107 16
1201 to 1400 386 361 21 4
1401 to 1600 446 356 58 32
1601 to 1800 144 131 9 4
• 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.
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Comparing Actual Recovery to the Virtual Hub Network
Actual RecoveryVirtual Hub
Network
Total Passengers 19,291 19,291
Number of Cancelled Flights 123 0
Passengers Requiring Re-Accommodation
774 1,665
Disrupted International Passengers
237 248
Un-Accommodated Domestic Passengers
207 67
Passengers Delayed Over Two Hours
14,123 838
94% reduction
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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.