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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 [email protected] John-Paul Clarke [email protected] Presentation Overview:. Motivation Definition Characteristics

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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


Presentation overview
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
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 airline schedulevirtual 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


Destination airline schedule

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


Average Delays airline schedule

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


Implementing a virtual hub network consists of two phases the virtual hub model and the prm

Virtual Hub Model airline schedule

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


Phase i implementing a virtual hub network

Anticipated Weather/ Ground Delay Program airline schedule

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


Key assumptions
Key Assumptions: airline schedule

  • 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
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
Objective function: Maximize passenger flow network flow problem.

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


Subject to
Subject to: network flow problem.

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


Subject to1
Subject to: network flow problem.

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


Subject to2
Subject to: network flow problem.

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


Subject to3
Subject to: network flow problem.

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


Phase ii re accommodating disrupted passengers
Phase II: Re-accommodating disrupted passengers network flow problem.

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

1 network flow problem.st 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


A closer look: network flow problem.

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:


Major delays plague the original hub while relatively minor effects are felt at the virtual hub

Delayed Flights per Hub on March 9, 2002


Input data: Size of the Time Window effects are felt at the virtual hub

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 effects are felt at the virtual hub

  • 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 effects are felt at the virtual hub

  • 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 effects are felt at the virtual hub

  • 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


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


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


Input data: Virtual and Original Hub Airport Capacities time windows to determine the VH excess capacity during irregular ops

  • 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 time windows to determine the VH excess capacity during irregular ops

  • 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 windows to determine the VH excess capacity during irregular ops

  • 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 windows to determine the VH excess capacity during irregular ops

  • 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.


94% reduction time windows to determine the VH excess capacity during irregular ops

Comparing Actual Recovery to the Virtual Hub Network


Limitations and future considerations
Limitations and Future Considerations: time windows to determine the VH excess capacity during irregular ops

  • 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.


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