TAIL ASSIGNMENT WITH MULTIPLE TAIL ASSIGNMENT WITH MULTIPLE MAINTENANCE LOCATIONS USING MAINTENANCE LOCATIONS USING NETWORK MODEL NETWORK MODEL Ajyuk J. Raj*, Ajyuk J. Raj*, Vinay V. Panicker, Vinay V. Panicker, R. Sridharan, V. R. Sridharan, V. Madhusudanan Madhusudanan Pillai Pillai
Tail Assignment with Multiple Maintenance Locations Using Network Model
Jan 18, 2016
Only a very few practical discrete optimization problems could be solved to optimality in the available time. A pragmatic
proposition to these problems is use of heuristic algorithms, which do not guarantee the optimality of the solution. But, it
is possible to find nearly optimal solutions within a reasonable amount of computational time for many problems. Tail
assignment, which comes in np-hard class of problems, is the allocation of individual aircraft to different flight legs with
the consideration of maintenance schedule for each aircraft. The primary aim of tail assignment is making assignments
in such way that all maintenance constraints are satisfied. The tail assignment is traditionally solved manually with the
manager's intuitive skills and thus the solution will vary from person to person, providing sub-optimal solution. This
paper indents to provide a graphical model for solving practical cases of tail assignment with multiple maintenance hub.
The model is tested with instances extracted from real-world timetables of an airlines company in India. It is found that
the model can be solved using standard type of computers in 3-4 seconds for single fleet airlines with 18 aircraft and
1050 flights.
proposition to these problems is use of heuristic algorithms, which do not guarantee the optimality of the solution. But, it
is possible to find nearly optimal solutions within a reasonable amount of computational time for many problems. Tail
assignment, which comes in np-hard class of problems, is the allocation of individual aircraft to different flight legs with
the consideration of maintenance schedule for each aircraft. The primary aim of tail assignment is making assignments
in such way that all maintenance constraints are satisfied. The tail assignment is traditionally solved manually with the
manager's intuitive skills and thus the solution will vary from person to person, providing sub-optimal solution. This
paper indents to provide a graphical model for solving practical cases of tail assignment with multiple maintenance hub.
The model is tested with instances extracted from real-world timetables of an airlines company in India. It is found that
the model can be solved using standard type of computers in 3-4 seconds for single fleet airlines with 18 aircraft and
1050 flights.
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TAIL ASSIGNMENT WITH TAIL ASSIGNMENT WITH MULTIPLE MAINTENANCE MULTIPLE MAINTENANCE
LOCATIONS USING NETWORK LOCATIONS USING NETWORK MODELMODEL
Ajyuk J. Raj*, Vinay Ajyuk J. Raj*, Vinay V. Panicker, R. V. Panicker, R. Sridharan, V. Sridharan, V.
Madhusudanan PillaiMadhusudanan Pillai
o Airline Scheduling OverviewAirline Scheduling Overviewo Tail Assignment ProcessTail Assignment Process
o Problem DefinedProblem Definedo Generic ModelGeneric Model
o Data UsedData Usedo System AnalyzedSystem Analyzed
PPresentation resentation AAgendagenda
o Illustrationo Results & Conclusions
Terminologies Terminologies FamiliarizedFamiliarized
Airline Scheduling Airline Scheduling Modules Modules
Tail AssignmentTail Assignment
•Tail Assignment : Tail Assignment : Construction of routes for individual aircraft in order to cover the legs of a flight schedule and satisfy maintenance constraints.
•Ground Check : Ground Check : Currently done manually with the manager's intuitive skills, consuming considerable amount of time and energy.
•Target : Target : Automated system which provides a holistic solution for tail assignment module.
Process at AirlineProcess at Airline
Release of Release of SSIM SSIM
file/Schedulfile/Schedule e
informationinformation
Correct Correct Overlaps Overlaps
and and constraint constraint violationsviolations
CorrectinCorrecting cross g cross
over over flightsflights
Build Build Lines of Lines of flying flying (LOF)(LOF)
Segregate Segregate based on based on seating seating
requiremenrequirementsts
Segregate Segregate the flights the flights based on based on aircraft aircraft typestypes
Schedule Schedule GeneratioGeneratio
nn
Cross Cross validating validating completion completion
of of maintenancmaintenanc
e planse plans
Identify the Identify the line of flying line of flying
based on based on onward flight onward flight informationinformation
Assign Assign LOF to LOF to
Aircraft Aircraft
Identify Identify Overlaps Overlaps
and and constraint constraint violationsviolations
TAIL TAIL ASSIGNMENTASSIGNMENT
Release of Release of SSIM SSIM
file/Schedulfile/Schedule e
informationinformation
Schedule Schedule GeneratioGeneratio
nn
CorrectinCorrecting cross g cross
over over flightsflights
Cross Cross validating validating completion completion
of of maintenancmaintenanc
e planse plans
Segregate Segregate the flights the flights based on based on aircraft aircraft typestypes
Segregate Segregate based on based on seating seating
requiremenrequirementsts
Identify the Identify the line of flying line of flying
based on based on onward flight onward flight informationinformation
Build Build Lines of Lines of flying flying (LOF)(LOF)
Assign Assign LOF to LOF to
Aircraft Aircraft
Identify Identify Overlaps Overlaps
and and constraint constraint violationsviolations
Correct Correct Overlaps Overlaps
and and constraint constraint violationsviolations
From LiteratureFrom Literature
Aircraft Maintenance as mandated by the FAA: A-CheckA-Check•Visual inspection of major systems. •Performed approximately every 60 flight hours.B-CheckB-Check•Thorough visual inspection and lubricating of all moving parts.•Performed every 300 to 600 hours of flightC-Check & D-CheckC-Check & D-Check•Involve taking the aircraft out of service Performed every one to four years
Aircraft Maintenance as mandated by the FAA: A-CheckA-Check•Visual inspection of major systems. •Performed approximately every 60 flight hours.B-CheckB-Check•Thorough visual inspection and lubricating of all moving parts.•Performed every 300 to 600 hours of flightC-Check & D-CheckC-Check & D-Check•Involve taking the aircraft out of service Performed every one to four years
Rules & ConstraintsRules & Constraints
• Aircraft Type matching• Geographical Continuity• Ground Time• Respect Maintenance Slot• Scheduling Preferences
• Scheduling Preferences• Maintain Connection Time• Onward Flight Adherence
Changes from Airline to AirlineChanges within an airline depending on the time of running the assignmentUsers switch on and off rules due to dynamicity of business environment
Interval GraphInterval Graph
I3 I6
I1 I4
I2 I7
I5 I8
I9
1
2
3
4
5
6
7
9
8
7
9
(a)
(b)
System InputsSystem Inputs
FLIGHT IDFLIGHT_DAT
EDEPARTU
RESTD ARRIVAL STA
MIN GND TIME
ONWARD FLIGHT
AIRCRAFT TYPE
TOTAL SEATS
XX3319 26-NOV-13 TLV26/11/2013
04:10XXS
26/11/2013 09:45
00:45XX3142/26-
NOV-1331B 141
XX3142 26-NOV-13 XXS26/11/2013
15:15DME
26/11/2013 20:10
00:50XX3143/27-
NOV-1331B 141
XX3143 27-NOV-13 DME27/11/2013
03:55XXS
27/11/2013 09:15
00:45XX3324/27-
NOV-1331B 141
XX3324 27-NOV-13 XXS27/11/2013
15:50SSG
27/11/2013 21:50
00:50XX3325/27-
NOV-1331B 141
XX3325 27-NOV-13 SSG27/11/2013
23:01XXS
28/11/2013 05:15
00:45XX3464/28-
NOV-1331B 141
PRE PROCESSING MODULEAirline Fleet
Assignment Data from Commercial Department
Airline Fleet Assignment Data from
Commercial Department
Maintenance Data from Operations DepartmentMaintenance Data from Operations Department
Data RetrievalData Retrieval Data WarehouseData Warehouse
FORMULATION MODULE
LOF-Aircraft Assignment
LOF-Aircraft Assignment
Flight CouplingFlight Coupling
Flight-Couple Timeline Formation
Flight-Couple Timeline Formation
Flight ReallocationFlight Reallocation
Rule EngineRule Engine
Data WarehouseData Warehouse
Data ConversionData Conversion
Re-allocated Flight-Aircraft Pair OutputRe-allocated Flight-Aircraft Pair Output
SOLUTION MODULE
Data WarehouseData Warehouse
SystemSystem
InputsInputs
LOF DetailsLOF DetailsAircraft ParametersAircraft ParametersMaintenance Parameters
Maintenance Parameters
Check Location of LOF and AircraftCheck Location of LOF and Aircraft
Check the Aircraft Available Time and
LOF Start Flight Time
Check the Aircraft Available Time and
LOF Start Flight Time
Check the Overlap count of LOF Aircraft
Pair
Check the Overlap count of LOF Aircraft
Pair
Select the Pair with minimum Overlap Count
Select the Pair with minimum Overlap Count
Select the LOF-Aircraft Pair with full Assignment
& minimum Overlap Count
Select the LOF-Aircraft Pair with full Assignment
& minimum Overlap Count
Iter
atio
ns
If matched
If matched
LOF-Aircraft AssignmentLOF-Aircraft Assignment
InputsInputs
LOF DetailsLOF DetailsMaintenance Parameters
Maintenance Parameters
LOF Timeline Formation
LOF Timeline Formation
Flight SortingFlight Sorting
Flight CouplingFlight Coupling
Coupled Flight Timeline Formation
Coupled Flight Timeline Formation
Final TimelineFinal Timeline
Iter
atio
ns
Flight Coupling & Timeline Flight Coupling & Timeline FormationFormation
Rule EngineRule EngineInputsInputs
LOF DetailsLOF DetailsAircraft ParametersAircraft ParametersMaintenance ParametersMaintenance Parameters
Check for Maintenance
Check for Maintenance
Check for Flight
Overlap
Check for Flight
Overlap
Check for free slots in the
remaining LOF
Check for free slots in the
remaining LOF
Re-assign flightRe-assign flight
Iter
atio
ns
Yes
Yes
Primary Mutual Swap
Primary Mutual Swap
Re-assign flightRe-assign flight
Yes
Secondary SwapSecondary Swap
Re-assign flightRe-assign flight
Yes
Final AssignmentFinal Assignment
Update Flight MatrixUpdate Flight Matrix
08:00 09:00 10:00 11:00 12:00 13:00 16:0015:0014:00 17:00Saturday, November 29, 2014
808
3316
851
3257
3314
3256
654
682 787
899
32583258
693 734
893
3318331
7
AIRCRAFTAIRCRAFT321321
HUHHUH56000095600009
ITNITN56000085600008
JGSJGS56000065600006
JMRJMR56000035600003
673
813
3315
867 895
686
3260
xxs xxs xxs
xxs xxs xxs
xxs xxs xxs
xxs xxsxxs FCO
LIN
FCOLIN
TFS
TFS
VCE
LHR
PRG
PRG
VCE
An Illustrative CaseAn Illustrative Case
MAINTENANCE
08:00 09:00 10:00 11:00 12:00 13:00 16:0015:0014:00 17:00Saturday, November 29, 2014
808
3316
851
3314
654
787
899
32583258
693 734
893
33183317
AIRCRAFTAIRCRAFT321321
HUHHUH56000095600009
ITNITN56000085600008
JGSJGS56000065600006
JMRJMR56000035600003
673
813
3315
867 895
3260
xxs xxs xxs
xxs xxs xxs
xxs xxs xxs
xxs xxsxxs FCO
LIN
FCOLIN
TFS
VCE
LHR
PRG
PRG
An Illustrative CaseAn Illustrative Case
MAINTENANCE
32573256 VCE
682 686TFS
INPUT SUMMARY INPUT SUMMARY PERIOD 26th November, 2013 - 14
December, 2013TOTAL NUMBER OF FLIGHT 314314TOTAL NUMBER OF AIRCRAFT 6 6
TOTAL NUMBER OF MAINTENANCE 33TOTAL NUMBER OF CONSTRAINTS 55
INPUT SUMMARY INPUT SUMMARY PERIOD 26th November, 2013 - 14
December, 2013TOTAL NUMBER OF FLIGHT 314314TOTAL NUMBER OF AIRCRAFT 6 6
TOTAL NUMBER OF MAINTENANCE 33TOTAL NUMBER OF CONSTRAINTS 55
OUTPUT SUMMARY - OUTPUT SUMMARY - EXPECTED EXPECTED
TOTAL TIME TAKEN <45 Seconds45 SecondsTOTAL NUMBER OF FLIGHTS ASSIGNED 314 314TOTAL NUMBER OF ONWARD FLIGHT RULES BROKEN <2020
OUTPUT SUMMARY - OUTPUT SUMMARY - EXPECTED EXPECTED
TOTAL TIME TAKEN <45 Seconds45 SecondsTOTAL NUMBER OF FLIGHTS ASSIGNED 314 314TOTAL NUMBER OF ONWARD FLIGHT RULES BROKEN <2020
OUTPUT SUMMARY - OUTPUT SUMMARY - ACTUALACTUAL
TOTAL TIME TAKEN = 0.45 SecondsTOTAL NUMBER OF FLIGHTS ASSIGNED 314 TOTAL NUMBER OF ONWARD FLIGHT RULES BROKEN = 13
OUTPUT SUMMARY - OUTPUT SUMMARY - ACTUALACTUAL
TOTAL TIME TAKEN = 0.45 SecondsTOTAL NUMBER OF FLIGHTS ASSIGNED 314 TOTAL NUMBER OF ONWARD FLIGHT RULES BROKEN = 13
Results – Set 1Results – Set 1
INPUT SUMMARY INPUT SUMMARY PERIOD 26th November, 2013 - 14
November, 2013TOTAL NUMBER OF FLIGHT 10501050TOTAL NUMBER OF AIRCRAFT 18 18
TOTAL NUMBER OF MAINTENANCE 1919
TOTAL NUMBER OF CONSTRAINTS 55
INPUT SUMMARY INPUT SUMMARY PERIOD 26th November, 2013 - 14
November, 2013TOTAL NUMBER OF FLIGHT 10501050TOTAL NUMBER OF AIRCRAFT 18 18
TOTAL NUMBER OF MAINTENANCE 1919
TOTAL NUMBER OF CONSTRAINTS 55
OUTPUT SUMMARY - OUTPUT SUMMARY - EXPECTED EXPECTED
TOTAL TIME TAKEN <20 Seconds20 SecondsTOTAL NUMBER OF FLIGHTS ASSIGNED 10501050TOTAL NUMBER OF ONWARD FLIGHT RULES BROKEN <2020
OUTPUT SUMMARY - OUTPUT SUMMARY - EXPECTED EXPECTED
TOTAL TIME TAKEN <20 Seconds20 SecondsTOTAL NUMBER OF FLIGHTS ASSIGNED 10501050TOTAL NUMBER OF ONWARD FLIGHT RULES BROKEN <2020
OUTPUT SUMMARY - OUTPUT SUMMARY - ACTUALACTUAL
TOTAL TIME TAKEN = 3.34 Seconds= 3.34 SecondsTOTAL NUMBER OF FLIGHTS ASSIGNED 10501050 TOTAL NUMBER OF ONWARD FLIGHT RULES BROKEN = 17 = 17
OUTPUT SUMMARY - OUTPUT SUMMARY - ACTUALACTUAL
TOTAL TIME TAKEN = 3.34 Seconds= 3.34 SecondsTOTAL NUMBER OF FLIGHTS ASSIGNED 10501050 TOTAL NUMBER OF ONWARD FLIGHT RULES BROKEN = 17 = 17
Results – Set 2Results – Set 2
• New paradigm for tail assignment, where routes and pairings are generated based on the onward flight ruleonward flight rule rather than cost function.• Formulation based on a heuristic approachheuristic approach and solved
in MATLAB that results in a significant reduction in computation time.• Solution for large data set with 1050 flights1050 flights, 20 stations 20 stations
and 18 aircrafts18 aircrafts, and multiple maintenance hubs. • Model with alternate solutions for flexibility.
Conclusions & Future WorksConclusions & Future Works
[1] Nikolaos Papadakos, (2009) Integrated airline scheduling, Computers & Operations Research 36 (2009) 176 – 195.
[2] Karine Sinclair, Jean-François Cordeau, Gilbert Laporte, (2014) Improvements to a large neighborhood search heuristic for an integrated aircraft and passenger recovery problem, European Journal of Operational Research 233 (2014) 234–245.
[3] Sebastian Ruther, Natashia Boland, Faramroze Engineer, (2013) Integrated aircraft routing, crew pairing, and tail assignment: branch-and-price with many pricing problems, School of Mathematical and Physical Science, University of Newcastle.
[4] Yanina V. Ageeva, John-Paul Clarke, (2000) Approaches to Incorporating Robustness into Airline Scheduling, MIT International Center for Air Transportation.
[5] Mattias Grὸnkvist, (2005) The Tail Assignment Problem, Department of Computer Science and Engineering, Chalmers University of Technology.
[6] Lloyd Clarke, Ellis Johnson, George Nemhauser, Zhongxi Zhu, (1997) The aircraft rotation problem, Annals of Operations Research 69(1997)33 – 46.
[7] Ibrahim Muter, S Ilker Birbil, Kerem Bulbul, Guvenc Sahin, Husnu Yenigun, Duygu Tas, Dilek Tuzun (2013) Solving a robust airline crew pairing problem with column generation Computers & Operations Research 40 (2013) 815–830.
[8] www.enerjet.ca
[9] noukousoku.air-nifty.com
[10] commons.wikimedia.org
[11] www.airportimprovement.com
[12] hsimonis.wordpress.com
RReferenceseferences
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