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

MIT MIT ICATICATMIT MIT ICATICAT

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]

MIT MIT

ICATICAT

MITMIT

ICATICAT


Presentation Overview:

• Motivation

• Definition

• Characteristics

• Problem formulation

• Application at a major US carrier

• Limitations and future considerations


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?


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


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


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


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


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


Time Window t2


Time Window tn


Key Assumptions:

• Ground resource availability

• Crew and maintenance flexibility

• Passenger connections within a time window

• Passenger consent


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


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


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


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


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


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


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.


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


to OH

Accommodated on a later flights

through OH


from VH

Accommodated on a later flights

through OH


to VH1st Leg on VHs + 2nd leg rescheduled from VH

1st Leg diverted to VH + 2nd leg on VHs


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


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




Cancelledflights


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.


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


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.


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


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


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


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


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.


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).


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.


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.


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


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.

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

Documents

hub ckcapacity of hub

virtual hub networkimplemented

origin i

passenger flowwhere

total passenger delay

aircraft capacity

ykjbinary decision variable

low delays