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Scheduling models for optimal aircraft traffic control at busy airports: tardiness, priorities,
equity and violations considerations
Dipartimento di Ingegneria
Andrea D’Ariano, ROMA TRE University, Rome, Italy124/11/2016
Junior ConsultingDipartimento di Ingegneria
� Introduction�Modeling a Terminal Control Area
�MILP formulations
Scheduling models for optimal aircraft traffic control at busy airports: tardiness, priorities, equity and violations considerations
�MILP formulations
�Computational experiments
�Conclusions
This work has been recently accepted for publication in the journal OMEGA : Reference DOI: 10.1016/j.omega.2016.04.003
2
Junior ConsultingDipartimento di Ingegneria
Air Traffic Control (ATC)Air Traffic Control (ATC)
An efficient control of air traffic must ensure safe, ordered and rapid transit of aircraft on the ground and in the air resources.
With the increase in air traffic [*], aviation authorities are seeking methods (i) to better use the
[*] Source: IATA 2014
methods (i) to better use the existing airport infrastructure, and (ii) to better manage aircraftmovements in the vicinity of airports during operations.
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Junior ConsultingDipartimento di Ingegneria
Status Status ofof the the currentcurrent ATC ATC practisepractise• Airports are becoming a major bottleneck in ATC operations. • The optimization of take-off/landing operations is a key factor to improve the performance of the entire ATC system.
• ATC operations are still mainly performed by human controllers whose computer support is most often limited to a graphical representation of the current aircraft position and speed. • Intelligent decision support is under investigation in order to reduce the controller workload (see e.g. recent ATM Seminars).
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Junior ConsultingDipartimento di Ingegneria
Literature: Aircraft Scheduling Problem (ASP)Literature: Aircraft Scheduling Problem (ASP)Terminal Control Area (TCA) Terminal Control Area (TCA)
Detailed
BasicExisting Approaches Dynamic
Static
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Junior ConsultingDipartimento di Ingegneria
Literature: Research needsLiterature: Research needs
Aircraft Scheduling Problem in Terminal Control Areas:
Most aircraft scheduling models in literature represent the TCA as a single resource, typically the runway. These models are not realistic since the other TCA resources are ignored.
We present a new approach that includes both accurate modelling of traffic regulations at runways and airways.
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This approach has already been applied to successully control railway traffic for metro lines and railway networks.
Junior ConsultingDipartimento di Ingegneria
Our approach for TCAsOur approach for TCAs
Implementation and testing of:
• Detailed ASP-TCA models:incorporating safety rules at air segments, runways and holding circlesair segments, runways and holding circles
• Alternative objective functions:maximum versus average delays, delayed aircraft (violations), aircraft equity, throughput (completion time), priority tardiness
• Real-time traffic management instances:Roma Fiumicino (FCO) and Milano Malpensa (MXP) airports
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Junior ConsultingDipartimento di Ingegneria
� Introduction
�Modeling a Terminal Control Area �MILP formulations
Scheduling models for optimal aircraft traffic control at busy airports: tardiness, priorities, equity and violations considerations
�MILP formulations
�Computational experiments
�Conclusions
8
This work has been recently accepted for publication in the journal OMEGA : Reference DOI: 10.1016/j.omega.2016.04.003
Junior ConsultingDipartimento di Ingegneria
3 HOLDING
CIRCLES
SEVERAL AIR
SEGMENTS
1 COMMON GLIDE
PATH
3 RUNWAYS3 RUNWAYS
Junior ConsultingDipartimento di Ingegneria
ASP ASP ModelModel::AlternativeAlternativeGraphGraph (AG)(AG)
Air Segments
CommonGlide Path
RunwaysHolding Circles
8
16
173
SRN
1
TOR
MBR
2 6
4 10
11
12
15
7
513
14
RWY 16R
RWY 16L
9
A
[Pacciarelli
EJOR 2002]
RWY 25
A1
tA1
10
release date αA
(w0, A1 = αA = expected aircraft entry time)Fixed constraints
tA1 = t0 + w0, A1
A1
0
αA
t0
Junior ConsultingDipartimento di Ingegneria
AG AG ModelModelAir Segments
CommonGlide Path
RunwaysHolding Circles
8
16
173
SRN
1
TOR
MBR
2 6
4 10
11
12
15
7
513
14
RWY 16R
RWY 16L
9
A
A1
RWY 25
tA1
entry due date βA
(wA1,n = βA = - αA )
A1
0 n
αA
βA
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tn = tA1 + wA1,n
tn
Junior ConsultingDipartimento di Ingegneria
AG AG ModelModelAir Segments
CommonGlide Path
RunwaysHolding Circles
8
16
173
SRN
1
TOR
MBR
2 6
4 10
11
12
15
7
513
14
RWY 16R
RWY 16L
9
A
A1 A4
δ
0
-δ
RWY 25
dotted arc (A4, A1)No holding circle
dotted arc (A1, A4)Yes holding circle(δ = holding time)
A1 A4
0 n
αA
βA
-δ
0
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Alternative constraints
Junior ConsultingDipartimento di Ingegneria
AG AG ModelModel
A1 A4 A10min
Air Segments
CommonGlide Path
RunwaysHolding Circles
8
16
173
SRN
1
TOR
MBR
2 6
4 10
11
12
15
7
513
14
RWY 16R
RWY 16L
9
A
RWY 25
A1 A4 A10
0 n
αA
βA
- max
Time window for the travel time in each air segment[min travel time; max travel time]
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Junior ConsultingDipartimento di Ingegneria
CommonGlide Path
RunwaysHolding Circles Air Segments
8
16
173
SRN
1
TOR
MBR
2 6
4 10
11
12
15
7
513
14
RWY 16R
RWY 16L
9
AAAG AG ModelModel
A1 A4 A15A10 A13 AOUTA16
RWY 25Aircraft routing:A1-A4-A10-A13-A15-A16
A1 A4 A15A10 A13 AOUTA16
0 n
αA
βA
γA
exit due date γA
(γA = - planned landing time)
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Junior ConsultingDipartimento di Ingegneria
CommonGlide Path
RunwaysHolding Circles Air Segments
8
16
173
SRN
1
TOR
MBR
2 6
4 10
11
12
15
7
513
14
RWY 16R
RWY 16L
9
AA
BB
AG AG ModelModel
A1 A4 A15A10 A13 AOUTA16
Potential conflictbetween A and B on
the common glide path (resource 15) !
RWY 25
A1 A4 A15A10 A13 AOUTA16
0 n
B3 B8 B15B12 B14 BOUTB17
αA
αB
βA
γA
βBγB
Aircraft ordering problem between A and B for the common glide path (resource 15) : longitudinal and diagonal distances must be respected
15
Junior ConsultingDipartimento di Ingegneria
CommonGlide Path
RunwaysHolding Circles Air Segments
8
16
173
SRN
1
TOR
MBR
2 6
4 10
11
12
15
7
513
14
RWY 16R
RWY 16L
9
AA
BB
CC
AG AG ModelModel
A1 A4 A15A10 A13 AOUTA16α γ
Potential conflict between C and B on a runway (resource 17) !
RWY 25
0 n
B3 B8 B15B12 B14 BOUTB17
αA
αB
βA
γA
βBγB
COUTC17
γC
αC
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Junior ConsultingDipartimento di Ingegneria
� Introduction
�Modeling a Terminal Control Area
�MILP formulations
Scheduling models for optimal aircraft traffic control at busy airports: tardiness, priorities, equity and violations considerations
�MILP formulations �Computational experiments
�Conclusions
17
This work has been recently accepted for publication in the journal OMEGA : Reference DOI: 10.1016/j.omega.2016.04.003
Junior ConsultingDipartimento di Ingegneria
AG AG viewedviewed asas a MILP (a MILP (MixedMixed--IntegerInteger Linear Linear ProgramProgram))
∈∀−+≥
−−+≥∈∀+≥
AkhjiMxwtt
xMwttFmlwtt
xtf
hkijhkhk
hkijijij
lmlm
),(),,(()1(
),(
),(min
,
,C =
with m ≠ n
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• Fixed constraintsin F model feasible timing for each aircraft on its specific route, plus α, β, γ constraints on the entrance and exit times.
• Alternative constraintsin A represent the ordering decision between aircraft at air segments and runways, plus holding circle decisions.
=
−+≥
selectediskhif
selectedisjiifx
Mxwtt
hkij
hkijhkhk
),(0
),(1,
,
Junior ConsultingDipartimento di Ingegneria
InvestigatedInvestigated objectiveobjective functionsfunctionsAverage Tardiness
Priority TardinessPriority Equity
Maximum Tardiness
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Max Completion
Avg Completion
Tardy Jobs P
Junior ConsultingDipartimento di Ingegneria
� Introduction
�Modeling a Terminal Control Area
�MILP formulations
PresentationPresentation outlineoutline
�MILP formulations
�Computational experiments�Conclusions
20
This work has been recently accepted for publication in the journal OMEGA : Reference DOI: 10.1016/j.omega.2016.04.003
Junior ConsultingDipartimento di Ingegneria
DescriptionDescription ofof the test the test casescases
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� Each row presents 20 disturbed scenarios (ASP instances);
� Entrance delays are randomly generated with various distributions;
� Unavoidable delays cannot be recovered by aircraft rescheduling;
� ASP solutions are computed by means of CPLEX MIP solver 12.0.
Junior ConsultingDipartimento di Ingegneria
A A practicalpracticalschedulingscheduling rulerule
Optimizing an objective and Optimizing an objective and looking at the other objectiveslooking at the other objectives
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Junior ConsultingDipartimento di Ingegneria
Optimizing an objective and Optimizing an objective and looking at the other objectiveslooking at the other objectives
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Junior ConsultingDipartimento di Ingegneria
A A combinedcombinedapproachapproach
Optimizing an objective and Optimizing an objective and looking at the other objectiveslooking at the other objectives
24
Junior ConsultingDipartimento di Ingegneria
� Introduction
�Modeling a Terminal Control Area
�MILP formulations
Scheduling models for optimal aircraft traffic control at busy airports: tardiness, priorities, equity and violations considerations
�MILP formulations
�Computational experiments
�Conclusions
25
This work has been recently accepted for publication in the journal OMEGA : Reference DOI: 10.1016/j.omega.2016.04.003
Junior ConsultingDipartimento di Ingegneria
AchievementsAchievements• Microscopic ASP-TCA optimization models are proposed.
• Various objective functions and approaches are investigated.
• Computational results for major Italian TCAs demonstrate the existence of relevant gaps between the objective functions.existence of relevant gaps between the objective functions.
• Combining the various objectivesoffers good trade-off solutions.
[email protected]@ing.uniroma3.it