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Stochastic Control of Turnarounds at HUB-Airports

Authors:

Abstract

A new approach is proposed to stochastically model parallel turnaround operations. Based on a microscopic process model, this paper introduces analytical and simulative methods to determine a presumable target off-block time and presents a scheduling approach to find optimal process alterations. An exemplary implementation at a HUB-airport provides extensive insights on the potential working procedure of the system, which will ultimately yield network costs for various disruption scenarios and give decision support for robust schedule recovery actions.
Stochastic Control of Turnarounds at HUB-Airports
A microscopic optimization model supporting recovery decisions in day-to-day airline
ground operations
Jan Evler, Ehsan Asadi, Henning Preis, Hartmut Fricke
Technische Universität Dresden
Institute of Logistics and Aviation
01062 Dresden, Germany
Email: jan.evler@tu-dresden.de
Abstract A new approach is proposed to stochastically
model parallel turnaround operations. Based on a
microscopic process model, this paper introduces analytical
and simulative methods to determine a presumable target
off-block time and presents a scheduling approach to find
optimal process alterations. An exemplary implementation
at a HUB-airport provides extensive insights on the
potential working procedure of the system, which will
ultimately yield network costs for various disruption
scenarios and give decision support for robust schedule
recovery actions.
Keywords - Aircraft Turnaround, Recovery Management,
Scheduling, Simulation, Stochastic Control, Decision Support
I. MOTIVATION
The aircraft turnaround is commonly described as a network
of individual sub-processes which are carried out partly in
parallel and partly in succession. Whilst not all scholars agree on
the same number and sequence of sub-processes, the turnaround
is uniformly defined to start with the arrival of an aircraft on
position, commonly referred to as “In-Block” (IB), and ends
with removal of wheel chocks, “Off-Block” (OB), after all
servicing activities for the next flight have been completed [1]
[5]. The timespan in-between IB and OB, also known as
available ground time (AVGT), is the only part of an aircraft’s
operational schedule that can be autonomously controlled by an
airline and has been spotlighted in various research projects.
Most of these rely on the assumption that airline schedules and
their subsequent ground servicing contracts and recovery
policies are created in a deterministic way. Thus, the sum of the
individual sub-process durations, which are taken from aircraft
constructors’ handling manuals, determines the minimum
ground time (MGT) needed in order to service an aircraft in-
between two flight assignments, excluding taxi-in and out times.
If possible, schedule buffers are added strategically to avoid
delay propagation and relax the AVGT. In combination with the
stochastic nature of aviation processes and the ever-increasing
traffic density in the international air space, these scheduling
procedures are observed to cause frequent and large-scale
disruptions to the entire Air Traffic Management (ATM) system,
which consequently turn into a loss of welfare for all related
stakeholders, especially for airlines and passengers [6].
In order to deal with the occurring schedule deviations in
day-to-day operations, a series of automated decision support
tools was implemented by EUROCONTROL over the course of
the last two decades in the context of Airport Collaborative
Decision Making (A-CDM). At the moment, the most advanced
procedures cover the arguably tightest bottleneck in aviation
operations the runway capacity. Arrival Manager (AMAN)
and Departure Manager (DMAN) calculate optimal pre-
sequences for Air Traffic Control (ATC) according to the
specific characteristics of the queued aircraft. The Surface
Manager (SMAN) extends this concept to the parking positions.
Once an aircraft has reached its assigned position, ground
operations proceed individually for each aircraft at the airport
until ATC issues an engine start-up time and the new flight is
scheduled for Departure Sequencing. In-between, the complex
interaction among the involved stakeholders of one turnaround
(see Fig. 1) is currently supervised by a Ramp Agent and
monitored by an Airline Operations Controller (AOC) of the
respective airline. Prior work of the Research Chair in Aviation
and Logistics at TU Dresden has expanded the tool chain of
AMAN, SMAN and DMAN for ground operations (Ground
Manager GMAN dashed box in Fig. 1) and introduced the
stochastic prediction of target off-block times (TOBT), resp.
target start-up approval times (TSAT), for single aircraft [7].
Figure 1. GMAN concept with involved actors and support tools in
EUROCONTROL perspective. Modified from [7].
However, given the complexity of involved resources and
their individual schedules, the concept of the GMAN should
Eighth SESAR Innovation Days, 3rd 7th December 2018
similar to A/D/SMAN possess a station-wide perspective in
order to be of better assistance to the AOC. In this way,
negatively interacting schedule recovery interventions of
parallel turnarounds could be avoided and AOCs get a better
overview on the consequences of their clearances.
With the aim of presenting a modelling approach under
simplified stochastic circumstances, this paper will start in
Chapter 2 with an overview on the most recent research
undertaken on the topic of turnaround operations. Chapter 3
and 4 will present the two fundamental functions of the new
stochastic turnaround model stochastic target time prediction
and deterministic process scheduling. An implementation
approach of the working procedure at a HUB-airport is outlined
and analyzed in Chapter 5, while Chapter 6 provides
conclusions and describes the scope of further research.
II. RESEARCH ON TURNAROUND OPERATIONS
The precise prediction of the total turnaround time (TTT)
and the modelling of the involved processes and disruption
causes, also described as aircraft turnaround problem (ATP), has
been approached from different methodological viewpoints [8].
Schlegel [9] used linear regression in order to describe the
finishing times of individual turnaround processes for different
aircraft types operated by the Lufthansa Group based on
ALLEGRO-data. Building on the underlying principle of the
Critical Path Method (CPM), some authors tried to implement
the stochastic nature of ground handling processes by using the
Project Evaluation and Review Technique (PERT) [2], [10]. As
introduced above, Oreschko et al. [7] developed a stochastic
simulation tool, called GMAN, for the prediction of the TOBT
based on variable process parameters (starting time as a function
of delay patterns) previously defined by Fricke & Schultz [11].
In a different piece of research, Rosenberger et al. [12] proposed
a stochastic model for airline operations using Semi-Markov
chains in combinations with Monte-Carlo Simulation, which
was later extended by Wu & Caves [5] for the detailed
simulation of turnaround activities. The peculiarity of the model
by Wu & Caves is the inclusion of process disruptions as
separate states, in which the network progress sojourns until the
matter is resolved, which is usually depending on parameters
drawn from delay code analyses.
There are some approaches addressing the problem of
resource availability. Kuster et al. [4] extended the Resource
Constraint Project Scheduling Problem (RCPSP) to include
turnaround control options in a variable network graph. From a
set of pre-defined task variations, a supervisor can choose which
turnaround procedures are likely to produce the best outcome,
given a certain schedule deviation. Conversely, a number of
articles describes solving heuristics for the optimal allocation of
ground servicing equipment (GSE), staff and deicing vehicles
[3], [13], [14], or the tactical gate assignment [15].
A third group of scholars [16], [17], [18] acknowledged the
ATP as a result of the multi-stage, deterministic airline
scheduling procedure and built optimization models for the ideal
implementation of buffer times as a pre-tactical control option to
design schedules more robust.
The general aim of all concepts might be summarised as to
provide a more accurate prediction of the flight-specific TOBT
to an AOC in the airline´s operations control center (OCC). The
TOBT is influenced by stochastic trigger parameters and acts as
a foundation for the selection of potential schedule recovery
decisions. However, the final decision on aircraft recovery
actions might significantly affect turnaround events running in
parallel at other aircraft and their respective downstream
networks. This is especially the case at large-scale HUB-airports
where process interdependencies can hardly be handled
manually based on operational experience. Furthermore, it needs
to be taken into account that recovery actions may fail to cut time
from the projected duration and underlie the same probabilistic
distributions as ground handling processes do. Concluding from
this overview, a decision support system at this stage should use
(1st) the probability prediction for a milestone in order to detect
schedule deviations and (2nd) suggest tactical as well as
proactive turnaround interventions so that overall network delay
costs can be kept as low as possible. These two fundamental
steps will be outlined in the next two chapters.
III. PREDICTION OF THE TARGET OFF-BLOCK TIME
In order to predict the TOBT of a flight, one needs to predict
the total processing time of the respective network chain. In a
deterministic graph there is usually only one critical path, which
is characterized by zero slack (highlighted in red in Fig. 2).
However, in a stochastic model, more than a unique critical path
might be expected due to variable individual process times. A
standard turnaround comprises several core processes
(highlighted in solid boxes in Fig. 2) and some optional
processes, which are executed only occasionally, depending on
e.g. weather (De-Icing) or crew schedules (Crew Exchange).
Others have a relatively short duration and appear almost never
on the critical path (Water and Toilet Servicing) or cause
exceptional big disruptions, such as maintenance and repair,
which are so far still out of the scope of this research.
Sometimes and depending on the airline´s business model, even
some of the traditional core processes are left out to guarantee
short turnaround times, e.g. Catering or Cleaning for Low-Cost
Carriers or Fuelling at out-stations (Tankering). For the
remainder of this paper, only the processes highlighted in solid
boxes in Fig. 2 will be considered for stochastic modelling.
Dashed gray processes might be taken up in future research.
Figure 2. MPM Network Graph of a Standard Turnaround (dashed gray
processes will not be further considered in this paper).
Eighth SESAR Innovation Days, 3rd 7th December 2018
For the introduction of stochastic process times, normally
distributed process durations were assumed with a mean which
corresponds to deterministic values taken from an Airbus 320
ground operations manual (GOM) and an assumed standard
deviation of one fifth of the mean (see Table I). This was done
with the primary purpose of simplifying the mathematical
expression of stochastic parameters in the analytical validation
process, rather than respecting results of previous operational
analyses, which found a good fit for Weibull-, Beta- and
Gamma-distributed process durations [5], [11], [19].
TABLE I. STOCHASTIC TURNAROUND PROCESS DURATIONS
Process
Mean Duration
in min
St.Dev. in min
= (0.2Mean)
Abbrev.
Name
IB*
In-Block
-
-
ACC
Aircraft Acceptance
2
0.4
DEB
Deboarding
7
1.4
FUE
Fuelling
12
2.4
CAT
Catering
10
2.0
CLE
Cleaning
10
2.0
BOA
Boarding
21
4.2
UNL
Unloading
14
2.8
LOA
Loading
19
3.8
PAX
Passenger Transfer
30
6.0
FIN
Aircraft Finalization
4
0.8
OB*
Off-Block
-
-
All processes are normally distributed. *IB and OB as start and end events have no duration.
Starting from the defined distributions of the individual
process durations, there are basically two ways to predict the
joint network distribution for OB times analytical convolution
and Monte Carlo (MC) Simulation.
A) Analytical Convolution
To the best of our knowledge, no analytical solution
deriving the joint network distribution of the TOBT was found
so far. However, using step-wise analytical convolution and
assuming the independence of the single processes, it is possible
to determine the integral of a cumulative density function
(CDF). This is done from inside out as shown in (1) to (9) based
on the parameters of the individual distributions where
is the probability density function (PDF) for the duration  
of process and is the corresponding CDF. In the first
step, the distribution of the maximum of three parallel processes
fuelling, catering, cleaning is determined by (1) to (3). Since
these processes are assumed to be independent, it is worth
mentioning that the CDF of the maximum can be written as
multiples of the single CDFs (2), which, however, is no longer
normally distributed [20], [21]. In the next step (4), the joint
distribution of de-boarding and boarding is convoluted with
the extreme-value distribution from (3). Let and be
independent random variables having the respective probability
density functions and . Then, the cumulative
distribution function of a random variable  
can be given as in (5). Further steps follow the same principle.
 
(1)
 
(2)
 
 
 
(3)
       
(4)
  

   

 

(5)
   
 
(6)
 
(7)
       
(8)
  

   

 

(9)
Having a convoluted CDF for the TOBT has the great
advantage that the probability of turnaround completion within
duration a can be directly calculated, e.g.  .
B) Monte Carlo Simulation
A MC simulation is usually run with several thousand
iterations, which means that for each of the ten listed processes
in Table I, 10,000 random durations are generated with the
according mean and standard deviation. The simulation process
was done in MATHEMATICA and led to the slightly right-
skewed distribution depicted in Fig. 3 with a mean
µ = 47.19 min and standard deviation σ = 4.52 min. Among the
simulation results in Table II and Fig. 3, it needs to be
highlighted that the joint distribution of all possible network
paths shows a higher mean duration and a lower standard
deviation than each of the four individual paths. This effect can
be explained by two network mergers before BOA and FIN (see
Fig. 2) which result in extreme-value distributions as previously
described in the convolution procedure.
TABLE II. NUMERICAL RESULTS OF THE MC SIMULATION
Network Path
Mean in min
St.Dev. in min
1
ACC-DEB-FUE-BOA-FIN-OB
46.00
5.12
2
ACC-DEB-CAT-BOA-FIN-OB
44.00
4.94
3
ACC-DEB-CLE-BOA-FIN-OB
44.00
4.94
4
ACC-UNL-LOA-FIN-OB
39.00
4.80
JP
Joint Path Distribution
47.19
4.52
Figure 3. Graphical Result of MC Simulation in MATHEMATICA
Eighth SESAR Innovation Days, 3rd 7th December 2018
For the validation of the new analytical convolution
function, a chi-square goodness-of-fit test was performed with
the results of the MC simulation. The 10,000 simulated network
processing times were clustered into 20 homogeneous classes
and the expected values per class were calculated in
MATHEMATICA using the convoluted network equation (9).
The resulting chi-square value χ² = 14.29 is smaller than the
corresponding test value χ² (95%, 17) = 27.59, which indicates
a good fit between the results of both methods and that the
simulation results can be obtained directly by applying (9).
Once the distribution of the TOBT is estimated and the
prediction exceeds airline internal delay criteria, e.g. OB is
20 minutes behind schedule with 90% probability, certain
recovery actions need to be considered in order to minimize the
resulting overall network costs. The approach to model this
optimization problem is the core of the next chapter.
IV. MODELLING TURNAROUND CONTROL WITH RCPSP
An optimization model based on RCPSP was chosen to
include multi-dimensional time dependencies as well as
resource-availability constraints. In order to meet the
requirements of practical implementation, the scope of the
model is expanded from single turnarounds, see Kuster et al.
[4], to multiple parallel turnaround operations. Therefore, this
paper introduces free-scalable process durations, variable
network dependencies and airport-wide resource constraints.
The final concept of a stochastic turnaround model aims at
providing a cost-benefit-comparison of various schedule
recovery actions under the influence of uncertainty.
In the model, set A comprises all activities over all parallel
aircraft turnarounds. Set A is divided into subsets for the
individual activities presented in Table I, defined with the
respective abbreviation, e.g. all “Acceptance” processes are set
  , etc. The predecessor-successor-relationships are
defined within the precedence matrix     Overall
objective function OF (10) is the minimization of delay costs
DC and costs RCk incurred by all applied recovery actions RA.
The elements that constitute each of the two blocks are outlined
in detail below. Standard operating costs are not considered.
    
  
(10)
A) Delay Costs
With  
being the variable starting time of an activity i,
(11) assures that operations cannot start before the arrival of the
aircraft . The duration of activity i is  
, so that (12)
ensures that succeeding processes j in the network can only
begin after process i has been finished. Since OB is fixed as a
milestone and has no duration, a delayed network processing
time is induced into variable  
as shown in (13) once the
scheduled off-block time LSj is surpassed. For the time being,
delay costs per minute are assumed to be constant and are
included in the OF by (14).

  
(11)
   
(12)

  
(13)

  
(14)
B) Schedule Recovery Costs
In the following, a not exhaustive sample of potential
turnaround control methods is presented to outline the basic
principle of the stochastic model. For each core process, one
methodological control example is given although it might be
possible to apply various methods on the given process.
1) Parallelization of Activities
For the Parallelization of two serial processes, their network
dependency in the PM needs to be modified. This alteration
usually underlies a certain costs  and is only applied once
the saved delay costs are higher than the control costs (see (10)
and (17)). In practice, FUE and BOA are normally completed
sequentially. In order to perform a quicker turnaround, this
sequential dependency can be changed into a parallel design
after explicit confirmation of the aircraft captain and the local
fire brigade. Thus, the link that connects FUE to BOA is
relocated to go directly from FUE into FIN (see Fig. 4) and the
boarding process can start even without the finishing of FUE,
once CLE and CAT have been completed. In mathematical
terms, the link dependency of FUE and BOA needs to be
excluded from (12) and redefined as given in (12a).
Additionally, (15) and (16) introduce a new dependency by
forcing a binary variable   to become zero in case
FUE and BOA should run as scheduled in sequence and one
in case the parallel procedure would be more efficient. The
trade-off is made within the objective function through (17).
    
   
(12a)
 
     
(15)
  
     
(16)
 
  
(17)
2) Process Acceleration through Additional Resources
Since the duration of all manually supported aircraft
servicing activities is directly depended on the number of
allocated staff or equipment units, in some cases it might be
possible to accelerate the process through the assignment of
additional resources. In fact, during the catering process, front
and rear galleys of a narrow-body aircraft are restocked
sequentially by only one catering vehicle. In case enough
catering vehicles would be available, see (23), this procedure
could be speeded up by assigning two entities to perform the
changing process in parallel. In the model, the initial process
duration would be reduced by 50% as the number of available
units   doubles and cuts the duration in half (18).
Similarly, more loading agents can be assigned to hasten the
cargo activities. Here the standard procedure foresees three
agents   and each additional agent would diminish the
original duration but with decreasing marginal effect (20). For
Eighth SESAR Innovation Days, 3rd 7th December 2018
simplification purposes, the optimal assignment is determined
only once for UNL and LOA (21) and is limited to the total
number of available loading agents (24). Note that in case of
available slack, the number of loading agents might also be
reduced for one turnaround in order to free agents for parallel
processes at other aircraft, which would induce a process
deceleration (20) and result in negative recovery costs (22).
    
 
(12b)

     
(18)
    
  
(19)

     
(20)
 
     
(21)
   
  
(22)
 

(23)
  

(24)
3) Process Acceleration through Reduced Execution
Some activities might be quickened by eliminating certain
steps in their standard operating procedure. The proportional
time saved through reduced execution can be defined by a free-
scalable parameter    which is multiplied with the
original duration. Potential applications of this method are
Reduced Cleaning, where the airline might determine an
internal penalty or opportunity costs  for superficial cabin
cleaning, and the so-called Rapid Passenger Transfer (RPT),
where delayed connecting passengers might be assigned a
special transfer bus for the costs  in order to shorten their
way through the terminal transfer area. In both cases, the
standard time sequence needs to be eliminated for the links from
CLE/ PAX to BOA (12c) in favor for variable process
durations, which are selected according to binary variables
  as in (25) to (28).
    
     
(12c)
 

   
 
(25)

 
  
(26)
 

   
 
(27)

 
  
(28)
4) Acceleration through Link Elimination
If one network dependency causes a large overall delay,
sometimes it might be effective to just eliminate this specific
link from the network in order to save the rest of the schedule.
While some processes are mandatory and cannot be neglected
without prior scheduling, e.g. fuelling, most of the routing
dependencies (connecting passengers, crews or aircraft between
flights) have more room to maneuver. Once the link elimination
is done, all prior control options need to be reconsidered,
especially when they focus on the same process. In case of
passenger transfer, RPT and Cancelled Connection are
mutually exclusive actions, which is why (27) needs to be
reformulated into (27a). In fact, for connecting passengers, the
“pushback” of OB of the receiving flight to guarantee
connection [12] would result in delay costs which are only
acceptable as long as they remain less than the accumulating
expenditures arising from the re-scheduling and caretaking of
the affected passengers . Once this threshold is exceeded,
it would make sense to cancel the connection of these
passengers and release the aircraft as originally scheduled. In
reality, airlines usually define such trade-offs in their recovery
policies, however, in the present case, the model will
mathematically decide    when it is favorable to cut
off the network link between two flights based on costs for all
affected passengers  (30).
    
(12d)



 
  
  
(27a)
 
  
  
(29)
    
  
  
(30)
5) Consideration of Resource Sequencing
While the first four measures enable an acceleration of the
delayed network processing time, there is also a number of side
constraints, such as resource dependencies and equipment
schedules, that need to be respected [3], [15]. Especially,
resources which are renewable but cannot be used in parallel
need to be brought into the right sequence, e.g. one position can
only be occupied by one aircraft at a time or one fire truck can
only supervise one parallel FUE/BOA procedure at a time.
Following the latter example of parallelization, it doesn’t matter
in which sequence the FUE/BOA procedures are supervised as
long as they are all supplied once  if needed, see
(31), (32). The number of available fire trucks  is
determined in (33), while (34) creates the corresponding
routings from a fire brigade depot FB with transition times t
between the single stations (highlighted in magenta in Fig. 4).
  

  
(31)
  

  
(32)
  

(33)
 
  
    
(34)
Eighth SESAR Innovation Days, 3rd 7th December 2018
V. IMPLEMENTATION APPROACH OF DETERMINISTIC
OPTIMIZATION IN A STOCHASTIC HUB-AIRPORT SETTING
For the merger of the two functionalities stochastic TOBT
prediction presented in chapter 3 and deterministic optimization
presented in chapter 4 an implementation setting at a HUB-
airport was configured. A scenario situation which requires
operational control is introduced and analyzed within this
chapter in order to showcase the operating principle that the
new stochastic turnaround model is supposed to work with.
A) Assumptions for the HUB-Airport
The example airport with three letter-code HUB provides five
walk-boarding positions directly adjacent to its terminal. The
terminal comprises five boarding gates and a connected transfer
area. The example network carrier “TU” operates a flight
schedule which includes four feeder flights from domestic out-
stations A, B, C and D as well as an intercontinental flight to
station E (see Table III). The long-haul flight from E carries 250
passengers, of which 40% are connecting equally-distributed to
four spoke-stations on flights 006 to 009 (. In
return, flights 002 to 005 each bring 125 passengers to the HUB,
of which 25 each are continuing their journey with flight 010
( . Thus, the schedule resembles a typical
wave of arriving and departing aircraft of a network carrier.
TABLE III. FILGHT SCHEDULE OF HUB AIRPORT
Flg.No.
Aircraft
Origin
Destination
Arrival
Departure
TU001
e
E
HUB
8:00
TU002
a
A
HUB
8:15
TU003
b
B
HUB
8:45
TU004
c
C
HUB
9:00
TU005
d
D
HUB
9:25
TU006
a
HUB
A
9:13
TU007
b
HUB
B
9:31
TU008
c
HUB
C
9:46
TU009
d
HUB
D
10:11
TU010
e
HUB
E
10:57
It needs to be mentioned at this point that the odd departure
times originate from the fact that no additional slack was put
into the turnaround network. Thus, the AVGT resembles the
MGT for each aircraft (based on the deterministic mean process
time values in Table I) with addition of potential network
dependencies through transfer passengers as depicted in Fig. 5.
Figure 5. GANTT Chart of Parallel Turnaround Activities at HUB-Airport
Delay costs are determined at 
  and  
per minute. Costs for schedule recovery actions are set at
  for parallel FUE/BOA,   as
operating costs per catering vehicle,   as wage
costs per loading agent,   as penalty costs for
Reduced-Cleaning,   for each rapid transfer
process, and   per passenger that misses the
scheduled transfer connection. Factors for process acceleration
are defined as    and   . Airport resources are
limited to   ,   and    The
transition time for the fire trucks is  .
Figure 4. Control Graph for Two Parallel Turnarounds
Eighth SESAR Innovation Days, 3rd 7th December 2018
B) Deterministic Optimization with Stochastic Processes
The exemplary scenario describes arrival delays in four
different dimensions (15, 30, 60, 90 minutes) for flight TU003.
All other arrivals in the described flight schedule (see Table III)
arrive on-time. For each of the five parallel aircraft turnarounds,
random durations are generated in 1,000 iterations for each
activity, according to the respective process parameters in Table
I. Per iteration, the generated set of process durations is then
used as deterministic input for a single optimization run within
the branch-and-cut solver SCIP. Solutions are retrieved from
the solver once without the application of recovery actions
(which basically corresponds to a prediction of the delayed
TOBT) and once when all control options are available, so that
the decision is left to the solver which combined actions might
result in an optimal solution. Since the optimization algorithm
is applied 1,000 per scenario dimension, probabilities can be
estimated as to which set of turnaround recovery actions might
be the best for which arrival delay situation.
C) Scenario Analysis
First of all, it needs to be emphasized that the analyzed off-
block times of flight TU007 (see Table IV and Fig. 6) clearly
prove a correct working procedure of the new simulation
model, as the average total turnaround time of roughly 47 min
with a standard deviation of 4.5 min corresponds to the one
calculated in Chapter 3 (see Table II). As process parameters
are not changing with the amount of arrival delay, which might
be the case in reality [11] but goes beyond the scope of this
paper, the distributions of the OB-time are similar for all four
arrival delay dimensions.
TABLE IV. ANALYSIS OF OFF-BLOCK TIMES (FLIGHT TU007) WITH AND
WITHOUT APPLIED RECOVERY ACTIONS AFTER ARRIVAL DELAY
Arr.Delay
TU003
15min
30min
60min
90min
OBT
TU007
w/o
with
w/o
with
w/o
with
w/o
with
Min
9:35
9:31
9:50
9:42
10:21
9:52
10:46
10:44
Median
9:47
9:40
10:02
9:55
10:32
10:26
11:02
10:55
75%-Q.
9:50
9:43
10:05
9:58
10:35
10:28
11:05
10:58
90%-Q.
9:53
9:46
10:08
10:01
10:38
10:31
11:08
11:01
Max
10:03
9:57
10:16
10:11
10:50
10:40
11:16
11:09
Mean
9:47
9:40
10:02
9:55
10:32
10:25
11:02
10:55
St.Dev.
4.5
4.3
4.4
4.4
4.5
4.5
4.5
4.4
Figure 6. Distributions of OBT (Flight TU007) with and without applied
Recovery Actions after Arrival Delay (Flight TU003)
In the ideal case that for each of the 1,000 simulation runs
the optimal set of recovery actions would be applied, ceteris
paribus the TTT is reduced by up to 7 min at each level of
arrival delay (see Table IV). Solely, maximum and minimum
TTT values show high variances, while mean values, 75%- and
90%-quantiles reveal stable time reductions of 6 to 7 min and a
general left-shift of the controlled OBT distribution (see Fig. 6).
In terms of network costs, it was the objective to minimize
the sum of delay costs and schedule recovery costs over all
flights (10). As one might expect, the optimization potential
with only 15 min of arrival delay is very low (average reduction
by 200 MU from 3,245 to 3,045) in comparison to a 90 min
delay (average reduction by 4490 MU from 19,836 to 15,346
see Table V). This is largely depended on the fact that schedule
deviations at 15 min delay are smaller and result in lower delay
costs, while the costs for recovery actions constitute a larger
part of overall costs. Once delay increases, there is also an
increasing network effect, which explains that, while delay
triples from 30 min to 90 min, average network costs rise more
than fourfold. This effect, also defined as delay multiplier [22],
is likely to be even greater if more than one flight would receive
passengers or crew members from the delayed aircraft and is
therefore dependent on the individual interconnection of the
flight in the airline network. Another interesting observation in
Table V and Fig. 7 is that the application of recovery actions
significantly decreases the standard deviation in resulting
network costs and, hence, provides a higher certainty for the
overall cost prediction.
TABLE V. ANALYSIS OF NETWORK COSTS ARRIVAL DELAY LEVELS
WITH AND WITHOUT APPLIED RECOVERY ACTIONS
Arr.Delay
TU003
15 min
30 min
60 min
90 min
Network
Cost
w/o
with
w/o
with
w/o
with
w/o
with
10%-Q.
1,663
2,427
3,225
3,904
7,788
7,175
16,513
14,497
Mean
3,245
3,045
4,871
4,539
10,940
8,612
19,836
15,346
90%-Q.
5,258
3,669
7,104
5,206
13,957
10,710
23,032
16,203
St.Dev.
1,485
527
1,574
551
2,342
1,397
2,474
871
Figure 7. Network Cost Development with and without applied Recovery
Actions after Arrival Delay (Flight TU003)
Eighth SESAR Innovation Days, 3rd 7th December 2018
Regarding the individual recovery actions, Fig. 8 reveals that a
simultaneous application of Parallelization, Quick-Catering
and Reduced-Cleaning was the optimal strategy in more than
80% of all cases for each scenario dimension. This corresponds
to the fact that in 80-90% of all turnarounds the critical path
goes via path 1-3 (see Table II). In all other cases and also once
control options are applied for FUE/CLE/CAT, path 4 becomes
critical, so that in roughly 20-30% of all cases more loading
agents are needed to accelerate the cargo processes. Thus, a so-
called Quick-Turnaround with increased resources for CAT and
LOA, a shorter CLE procedure and parallel FUE/ BOA is
always the best solution for a delayed aircraft no matter how
big the arrival delay is. In case some of those four control
options are not available, results might be very different, so that
a sensitivity analysis of the individual impact of turnaround
recovery actions needs to be done in further research, as well as
a cost calibration between the different options and delay costs.
In contrast to the first four measures, the two network
control options RPT and Cancelled Connection show a very
heterogenetic development when the arrival delay grows larger.
Judging from Fig. 8, in about 15% of all cases the allocation of
a RPT for passengers connecting from flight TU003 to TU010
would result in optimal solutions when TU003 has 30 min
Arrival Delay. Once the Arrival Delay increases to 60 min, RPT
almost always yields the best network solution. However, at
90 min Arrival Delay, it is the most efficient solution in only
20% of all cases, while cancelling the connection has an 80%
probability of yielding the best overall outcome. Depending on
the airline´s recovery policy, an AOC in the OCC would decide
based on these numbers whether to push back the TOBT of
flight TU010 or to release the aircraft as scheduled without the
passengers from TU003. The first would only be efficient until
11:22 (see Fig. 9) and has an 80% probability of resulting in
higher network costs for the airline. The latter would ensure on-
time departure for flight TU010 with 20% risk of higher costs.
Figure 8. Frequency of Optimal Recovery Actions applied on the
Turnaround of Aircraft b after Arrival Delay (Flight TU003)
Figure 9. Distribution of OBT (Flights TU007/010) with and without
applied Recovery Actions after 90 min Arrival Delay (Flight TU003)
VI. CONCLUSIONS
An initial stochastic turnaround optimization model is
introduced in this paper with its two core elements stochastic
prediction of the TOBT and deterministic optimization of
parallel turnaround operations using RCPSP. The stochastic
TOBT prediction is taken up from previous research using
Monte Carlo Simulation of network processes, while, for the
first time, analytical convolution is presented to produce equal
prediction results with less calculation effort. Within the
optimization problem, various sequencing approaches are
extended from earlier studies into a microscopic, multi-
stakeholder model under the objective of minimizing network-
wide costs for ground operations. Both procedures are
combined into a simulation algorithm and are implemented at
an exemplary HUB-airport with assumed costs and process
parameters. The methodological showcase provides extensive
insights into the possibilities of the new model, which aims to
act as tactical decision support system for the selection of robust
schedule recovery actions by an AOC in the airline´s OCC. By
doing so, it calculates cost-benefit-comparisons between the
network consequences of uncontrolled and controlled schedule
disruptions. The effectiveness of the method is proven to work
especially once larger arrival delays propagate from one aircraft
to multiple parallel turnarounds and increase network costs in a
non-linear fashion. The non-existence of a standardized
turnaround control algorithm results in huge inefficiencies in
day-to-day ground operations, which is why this new approach
is deemed appropriate for the expansion of the literature in the
field of developing (semi-)automated tools for the future of
digital aviation.
Starting from the theoretical concept of this article, further
research will expand the model to include a broader variety of
control options which can be adapted to airline´s individual
recovery policies. Additional control options may comprise
flexible boarding strategies, gate dependencies among aircraft
and aircraft swaps between two flights (so-called tail swaps).
More network dimensions might be introduced by adding crew
dependencies and passengers connecting from all flights to one
another or by taking into consideration that some of the
recovery actions may be influenced by further restrictions
originating from the operating schedule of GSE or by the
turnaround of aircraft from other carriers. The expansion of the
basic flight schedule to multiple airports in the airline´s network
might further bring network control options which include
downstream effects in their cost consideration. Such options
may cover flight cancellations; passenger re-routings; the trade-
off between a quicker turnaround on ground and an in-flight
trajectory acceleration; or the trade-off between recovery
actions at the first or a later station in the aircraft´s daily routing.
Regarding the methodology, future steps will deepen the
approach of using analytical convolution as a substitute to time-
consuming simulation procedures and in order to describe the
fundamental mathematics of the controlled network processes.
Likewise, stochastic features will be tested directly inside the
optimization model through the application of chance
constraints. Furthermore, it will be an aim to substitute the
Eighth SESAR Innovation Days, 3rd 7th December 2018
normal-distributed dummy processes with fitted distributions
from operational analytics and calibrate the costs in order to
replicate a real-life operational environment. Once this
validation is done, it will be the ultimate goal to perform
sensitivity analyses for different disruption scenarios under the
objective of determining the ideal amount and lead time of
schedule interventions.
ACKNOWLEDGMENT
This research has been conducted in the framework of the
research project Ops-TIMAL, financed by the German Federal
Ministry of Economic Affairs and Energy (BMWI).
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Eighth SESAR Innovation Days, 3rd 7th December 2018
... The integrated turnaround monitoring and scheduling tool, "Ground Manager -GMAN 2.0" (Evler et al., 2018, Evler et al., 2021, models multiple parallel aircraft turnarounds and is applied with a rolling planning horizon within this article. Each aircraft turnaround a ∈ A is defined by a scheduled start and finishing time of the turnaround SIBT a and SOBT a which are retrieved from the flight plan. ...
... Fig. 2). Thus, contrarily to the description in ground operations manuals, the critical path is flexible and can contain different processes for different turnarounds, so that the estimated total turnaround time might deviate from official minimum ground times even in case of on-time arrivals (Evler et al., 2018). ...
... The highest impact is achieved when all mentioned subprocesses of one turnaround are prioritized simultaneouslywhich is called quick-turnaround. This was found to guarantee a reduction of the tobt a even under stochastic influences (Evler et al., 2018) (see Fig. 3b). ...
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