D'ARIANO ATRS 2016

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, Italy
124/11/2016

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

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 aircraft
movements in the vicinity of
airports during operations.
3

StatusStatus ofof thethe currentcurrent ATCATC 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).
4

Literature: Aircraft Scheduling Problem (ASP)Literature: Aircraft Scheduling Problem (ASP)
Terminal Control Area (TCA)Terminal Control Area (TCA)
Detailed
BasicExisting
Approaches Dynamic
Static
5

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.
6
This approach has already been applied to successully
control railway traffic for metro lines and railway networks.

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
7

Introduction
MILP formulations
MILP formulations
Conclusions
8

3 HOLDING
CIRCLES
SEVERAL AIR
SEGMENTS
1 COMMON GLIDE
PATH
3 RUNWAYS3 RUNWAYS

ASPASP ModelModel::
AlternativeAlternative
GraphGraph (AG)(AG)
Air
Segments
Common
Glide Path
RunwaysHolding Circles
8
16
17
3
SRN
1
TOR
MBR
2 6
4 10
11
12
15
7
5
13
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

AGAG ModelModel
Air
Segments
Common
Glide Path
8
16
17
3
SRN
1
TOR
MBR
2 6
4 10
11
12
15
7
5
13
14
RWY 16R
RWY 16L
9
A
A1
RWY 25
tA1
entry due date βA
(wA1,n = βA = - αA )
A1
0 n
αA
βA
11
tn = tA1 + wA1,n
tn

AGAG ModelModel
Air
Segments
Common
Glide Path
8
16
17
3
SRN
1
TOR
MBR
2 6
4 10
11
12
15
7
5
13
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
12
Alternative constraints

AGAG ModelModel
A1 A4 A10
min
Air
Segments
Common
Glide Path
8
16
17
3
SRN
1
TOR
MBR
2 6
4 10
11
12
15
7
5
13
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]
13

Common
Glide Path
Air
Segments
8
16
17
3
SRN
1
TOR
MBR
2 6
4 10
11
12
15
7
5
13
14
RWY 16R
RWY 16L
9
A
A
AGAG ModelModel
A1 A4 A15A10 A13 AOUTA16
RWY 25Aircraft routing:
A1-A4-A10-A13-A15-A16
0 n
αA
βA
γA
exit due date γA
(γA = - planned landing time)
14

Common
Glide Path
Air
Segments
8
16
17
3
SRN
1
TOR
MBR
2 6
4 10
11
12
15
7
5
13
14
RWY 16R
RWY 16L
9
A
A
B
B
AGAG ModelModel
Potential conflict
between A and B on
the common glide path
(resource 15) !
RWY 25
0 n
B3 B8 B15B12 B14 BOUTB17
αA
αB
βA
γA
βB
γB
Aircraft ordering problem between A and B for the common glide path
(resource 15) : longitudinal and diagonal distances must be respected
15

Common
Glide Path
Air
Segments
8
16
17
3
SRN
1
TOR
MBR
2 6
4 10
11
12
15
7
5
13
14
RWY 16R
RWY 16L
9
A
A
B
B
CC
AGAG ModelModel
α 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
βB
γB
COUTC17
γC
αC
16

Introduction
MILP formulations
MILP formulations
Conclusions
17

AGAG viewedviewed asas a MILP (a MILP (MixedMixed--IntegerInteger LinearLinear ProgramProgram))





∈∀
−+≥
−−+≥
∈∀+≥
Akhji
Mxwtt
xMwtt
Fmlwtt
xtf
hkijhkhk
hkijijij
lmlm
),(),,((
)1(
),(
),(min
,
,C =
with m ≠ n
18
• Fixed constraints in F model feasible timing for each aircraft on its
specific route, plus α, β, γ constraints on the entrance and exit times.
• Alternative constraints in A represent the ordering decision between
aircraft at air segments and runways, plus holding circle decisions.



=
 −+≥
selectediskhif
selectedisjiif
x
Mxwtt
hkij
hkijhkhk
),(0
),(1
,
,

InvestigatedInvestigated objectiveobjective functionsfunctions
Average Tardiness
Priority TardinessPriority Equity
Maximum Tardiness
19
Max Completion
Avg Completion
Tardy Jobs P

Introduction
MILP formulations
PresentationPresentation outlineoutline
MILP formulations
Conclusions
20

DescriptionDescription ofof the testthe test casescases
21
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.

AA practicalpractical
schedulingscheduling rulerule
Optimizing an objective andOptimizing an objective and
looking at the other objectiveslooking at the other objectives
22

23

AA combinedcombined
approachapproach
24

Introduction
MILP formulations
MILP formulations
Conclusions
25

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 objectives
offers good trade-off solutions.
dariano@ing.uniroma3.itdariano@ing.uniroma3.it

D'ARIANO ATRS 2016

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