A MODEL FOR PROJECTING FLIGHT DELAYS
DURING IRREGULAR OPERATION CONDITIONS
Khaled F. Abdelghany*
[email protected]
Tel: (847) 700-1425
Sharmila S. Shah
[email protected]
Tel: (847) 700-1423
Sidhartha Raina
[email protected]
Tel: (847) 700-6305
Fax: 847-700-5033
&
Ahmed F. Abdelghany
[email protected]
Tel: (847) 700-9272
Information Services Division, R&D
United Airlines
1200 East Algonquin Rd.
Elk Groove, IL 60007
A paper prepared for publication in the Journal of Air Transport Management
April, 2004
A MODEL FOR PROJECTING FLIGHT DELAYS
DURING IRREGULAR OPERATION CONDITIONS
ABSTRACT
On-time performance of airlines schedule is key factor in maintaining
satisfaction of current customers and attracting new ones. This requires clever
management of the different operation resources (crew/aircraft) to ensure their ontime readiness for each flight in the planned schedule. However, flight schedules are
often subjected to numerous sources of irregularity. In particular, weather accounts
for nearly 75% of system delays. Due to the tight connection among airlines
resources, these delays could dramatically propagate over time and space unless the
proper recovery actions are taken. This paper presents a model which projects flight
delays and alerts for possible future breaks during irregular operation conditions. The
results of applying the model at the operation control center of a major airlines
company in the United States are presented.
KEYWORDS: Airlines Schedule, Shortest Path Algorithm, Irregular Operations, and
Proactive Recovery.
2
A MODEL FOR PROJECTING FLIGHT DELAYS
DURING IRREGULAR OPERATION CONDITIONS
BACKGROUND
On-time performance of airlines schedule is key factor in maintaining
satisfaction of current customers and attracting new ones. Also, maintaining
economical operations during irregular conditions is essential to achieve expected
revenues. These require clever management of the different operation resources
(aircraft, pilots, and flight attendants) to ensure their on-time readiness for each flight
in the planned schedule. However, flight schedules are often subjected to numerous
sources of irregularity. In particular, weather accounts for nearly 75% of system
delays (Rosenberger et al., 2000). If adverse weather conditions are anticipated at one
airport, the Federal Aviation Administration (FAA) issues a Ground Delay Program
(GDP) at this airport, which increases the gap between successive flight arrivals to
ensure safe operations. In most cases, the available slots for flight arrivals are less
than what is required for the original planned schedule (Ball et al., 2000). Thus, a
scheduled flight could be held at its origin, diverted to another airport, or in the worst
case it could be canceled. These disruptions in the planned flight schedule impact
availability of crews and aircrafts for future flights. For instance, if a flight is delayed,
its crewmembers may misconnect their next scheduled flight(s). They may also
3
exceed the maximum allowed (legal) duty period length resulting in not completing
remaining flight(s) in their planned schedule (Yu et al., 2003). Figure 1 illustrates an
example of the possible cascading impact of GDP on the airline schedule over the
course of one day.
During the last decade, a considerable attention has seen been given to
proactive schedule recovery models as a possible approach to limit flight delays
associated with GDPs (Abdelghany et al., 2004a and Clarke, 1997). In these models,
the impact of any reported flight delays, due to GDP or any other reason, is
propagated in the network to determine any possible downline disruptions. Then, an
efficient plan is generated to recover these disruptions ahead of their occurrence. For
a small airlines network, tracking the downline impact of few delayed flights could be
an easy task. However, for a major airlines company with more that 2,000 daily
flights, if a GDP program is issued at one or more of its hubs, determining the
downline impact of this GDP could be extremely challenging and time consuming
(Monroe and Chu, 1995).
This paper presents a flight delay projection model, which projects flight
delays and alerts for downline operation breaks for large-scale airlines schedules. In
this model, the airlines daily schedule is represented in the form of a directed acyclic
graph with its nodes are the different scheduled events, and its arcs are the scheduled
activities between these events. Scheduled events include flight departures, flight
arrivals, crew duty starts, crew releases from duty, aircraft maintenance starts and
ends etc. The in-between activities include aircraft taxi-out and taxi-in, flying, crew
4
connections and layovers, etc. Using this graph representation, the model applies the
classical shortest path algorithm to determine the earliest possible time at which the
different events could occur while considering all operation constraints that govern
the operation including GDP issued by the FAA and crew legality rules.
The paper is organized as follows. The next section briefly describes the main
rules that govern the daily operation of crew and aircraft and how these rules might
be violated during irregular operation conditions. The concept of resource slack and
flight slack times are then defined. Next, the modeling approach used in this paper is
described. Results of the model application at the Operation Control Center (OCC) of
United Airlines are then presented. Summary and suggestions for extensions of this
research work are finally given.
LEGALITY RULES AND RESOURCE BREAKS DURING IRREGULAR
OPERATION
Crew schedules are typically designed as trippairs. A trippair is a workload
assignment for each pilot and flight attendant. The length of a trippair is usually in the
range of one to five days where each day represents a duty period. A trippair
originates from one base station and ends at the same base station (domicile). A
trippair that belongs to one domicile is assigned to crews who are based at this
domicile. Between two successive duty periods, crewmembers are given a rest period
known as layover. Similarly, for two successive segments in the same duty period,
5
crewmembers are given a reasonable connection time that is enough to connect from
the arrival gate to the next departure gate, if they are different. Figure 2 shows a
typical 2-day trippair that starts and ends at domicile “A” and has away-from-home
layover at station “H”.
The lengths of duty periods and in-between layovers are determined based on
a set of rules that are specified in the FAA regulations and labor agreements. The
FAA mandates a list of regulations, which are designed mainly to ensure safe
operations. Airlines companies that violate these regulations are subjected to severe
fines. In addition, since the airlines industry is heavily unionized, companies and
labor unions set agreements to regulate the relation between the two sides. From the
labor prospective, these contracts are set to ensure that crews are receiving the right
compensation, training and good quality of life. From the company prospective, these
contracts obligate each employee to fulfill the assigned workload as long as it is
scheduled according to the rules in the negotiated agreements. Two main rules affect
the day-to-day operations, which are:
- Legal Rest: Each crewmember must be given the adequate rest between any two
successive duties. The length of the rest depends on a combination of several factors,
which may include:
-
Flying time in the last 24-hours or length of the previous duty.
-
Rest location (crewmember’s are at their base or away from their
base).
-
Crewmember work status (reserve or lineholder).
6
-
Market of the trip (Domestic / international).
Rest periods increase as flying time in last 24 hours increases and/or the
length of previous duty increases. Layovers at the base station of a crewmember are
usually longer than away-from-base layovers. Also, reserve crewmembers get longer
layovers than lineholder crewmembers. Furthermore, crewmembers assigned to
international trips usually get longer layovers than if they were assigned to domestic
trips.
- Legal Duty: Each crewmember should not exceed a certain number of working
hours in one duty. Factors affecting the length of the duty are:
-
The scheduled departure time for the first flight in the duty.
-
The last time when the crewmember received a rest.
-
Existence of augmented crew on the flight.
A duty period that starts early in the morning (2 or 3 a.m.) is usually shorter
than a duty period that starts around 7 or 8 a.m. The last time when a crewmember
received a rest also affects the length of her/his next duty period. For example, the
FAA mandates a rule that any crewmember has to receive unbroken rest of eight
hours
in
any
consecutive
24
hours
period
for
any
domestic
trippair
(http://www.alpa.org). As such, any domestic duty period cannot exceed more than
16 hours. Finally, if a flight is scheduled to have augmented crew, on-board
crewmembers are expected to have longer duty periods.
During a state of irregular operations, different operation breaks could happen.
These breaks are defined as follows:
7
- Misconnect break: It occurs when a connecting crewmember is projected to arrive
late such that she/he is unable to timely connect to the next flight. Figure 3 shows an
example of a typical misconnect break. When flight B-S is delayed, the
crewmember’s ready time is shifted beyond the scheduled departure time of the next
flight. Therefore, flight S-H cannot depart on time unless the delayed crewmember is
substituted at station S.
- Rest break: This break is similar to the misconnect break. It occurs when a
crewmember gets a rest period (layover) that is less than the minimum required
(legal) rest period because of late arrival at the end of the previous duty period. In this
case, the crewmember would be unable to fly the first flight segment in the next duty
period on time. Figure 4 shows an example of a typical rest break. When flight S-H is
delayed, the layover becomes less than the legal layover. The first flight of the next
duty period (flight H-L) cannot depart on time since the crewmember has to get
her/his legal rest.
- Duty break: It occurs when the actual duty period exceeds the duty period limit due
to delaying one or more flights in this duty period. In this case, the remaining flight(s)
in the duty period cannot be flown by their original crewmember. Figure 5 shows an
example of a typical duty break. Flight S-H is delayed and its new arrival time passes
the duty limit for the crewmember. Therefore, a substitute crewmember should be
found at station S to fly flight S-H as its originally assigned crewmember cannot work
beyond her/his duty period limit.
8
Similar to crew, aircraft routes are designed to cover a list of consecutive
flights (route). The time interval between two successive flights in the same route is
scheduled to finish the aircraft service/maintenance activities. Aircraft service
includes fueling, cleaning, baggage handling and catering. Aircraft maintenance is
usually done on cyclic basis, which could be scheduled based on time, number of
flown hours, number of landings/take-offs, etc. Aircraft routes are designed to ensure
that all maintenance activities are conducted at the designated stations in the required
dates. Under irregular operation conditions, a similar set of breaks that is described
for the crew could also occur for the aircraft. For example, a misconnect break (short
turn) occurs if an aircraft arrives late such that its projected ready time, after service
or maintenance, is beyond the scheduled departure time of the next flight.
Furthermore, in analogous to crew duty break, an aircraft cannot be used for the next
flight, if it is going to violate its due maintenance.
RESOURCE AND FLIGHT SLACK TIMES
The departure time of a flight is the latest of (1) its scheduled departure time,
(2) the latest ready time among all its operating resources, and (3) any issued GDP
departure time (FAA flow control departure time) for this flight, if any. An aircraft is
ready after its required service/maintenance activities are completed. Similarly, a
crewmember is ready after she/he connects from the arrival gate to the next departure
gate, or after she/he receives the required legal rest between two successive duties.
9
Figure 6 shows an example of a small airline network that consists of seven flights
(numbered from F1 to F7). As shown in the figure, flight F1 departs at 8:15 and
arrives at 11:30. Upon arrival of flight F1, resources R7 and R8 connect to flight F3,
and resources R9 and R10 connect to flight F4, respectively.
In the normal operation conditions, all resources are planned to be ready
before the scheduled departure time of their next assigned flights by some slack time
(S  0). A resource slack time is the difference between the departure time of the
resource’s next flight and the ready time of the resource after completing the current
flight. As shown in Figure 6, resources R7 has 15 minutes slack and R8 has 60
minutes slack. Also, resource R9 and R10 have 135 minutes slack. One can easily
notice that if a resource is delayed within its slack, down-line flights can still depart
on time.
In addition, as shown in the figure, flight F1 could be delayed 15 minutes (the
slack of resource R7) without affecting any down-line flights. This defines a flight
down-line slack, which is the longest time interval a flight can be delayed without
affecting any down-line flights. Computationally, a flight down-line slack is the
shortest slack among all its outbound resources.
Slack times play an important rule in generating recovering schemes during
irregular operations. For instance, if a flight is missing one of its crewmembers,
another crewmember could be used to substitute the missing one. If no substitute
crewmember with ready time less than the flight’s scheduled departure time is found,
the search could be extended to find a substitute crewmember with ready time less
10
than the flight’s scheduled departure time plus its down-line slack interval. If such
crewmember is found, the flight would be delayed within its slack interval while all
its outbound resources would make it on time for their next flights.
MODELING APPROACH
Assume a horizon of length h, which includes F flights. Each flight f in the
horizon is defined using a unique identification number and its latest quoted
(published) departure and arrival times ( D f , Af ). Resources scheduled to operate
each flight are also assumed known. This includes information on aircraft routes and
crew trippairs that cover the horizon under consideration. An aircraft route is defined
as a chain of scheduled flights and maintenance visits. Similarly, a crew trippair is
defined through a sequence of flights and layovers at the end of each duty in this
trippair. All mandatory rules that govern the operation are assumed given, which
include crew legality rules and required maintenance checks for the aircraft.
Historical data on expected taxi times, flying times and aircraft service and
maintenance durations at the different stations are also given. Furthermore, if a GDP
is issued at one or more airports, and a decision is made to delay some flights in the
horizon h, the new issued departure and arrival times for these flights are given. In
addition, if any flight that arrives before the start of the horizon h got delayed and a
resource is connecting out of this flight to a flight in the horizon h, the new expected
ready time for this resource is assumed given.
11
The objective is to project the departure and arrival times ( m f , n f ) and the
wheels-off and wheels-on times ( off f , on f ) for all flights in the horizon h and to alert
for any operation break that might occur due to any projected delays. As described
earlier, these alerts include crew misconnects, aircraft short turns, crew rest violation
and duty violations. If a flight is delayed, the reason (the inbound resource) for this
delay should also be identified. The objective also is to calculate the projected
downline slack S f for each resource and flight in the horizon h.
Figure 7 illustrates a graph representation for the hypothetical airline schedule
given in Figure 6. Four nodes and three arcs are used to represent each flight in the
horizon. The nodes represent the four main events associated with each flight, which
are departure, wheels-off, wheels-on, and arrival, respectively. The arcs represent
taxiing-out, flying and taxiing-in, respectively. Each resource is represented using a
set of nodes and arcs representing the different events and activities scheduled for this
resource. The number of nodes and arcs used to represent one resource depends on
the activities performed by the resource in the horizon under consideration. For
example, one node and two arcs are used to represent the resource connection
between two flights in the horizon. Each connection node (shown in gray color)
represents the event when the connecting resource is ready for its next flight. One of
the two arcs is inbound to the connection node (shown as solid arc), while the other
arc is outbound of the connection node (shown as dashed arc). The solid inbound arc
represents the activity required by this resource to get ready for the next flight. For
crewmembers, this activity could be a connection from the arrival gate of one flight to
12
the departure gate of the next flight. It could also be the required rest between the last
flight in the previous duty and the first flight in the current duty. For aircrafts, this
activity could be either a service or maintenance. Each solid arc is associated with a
cost that represents the time period required to perform the activity represented by
this arc. The dashed outbound arc is dummy arc with zero cost. The dummy arc
represents the slack time for the resource at the corresponding connection. As
mentioned earlier, this slack time is the difference between the projected departure
time of the next flight and the time at which the resource is ready for this flight.
Similarly, if a resource is connecting from one flight that arrives before the
start of the horizon under consideration, one node and two arcs are used to represent
this connecting resource. The node represents the event when the resource is ready for
its next flight. The inbound arc is connected out of a common source node, which
represents all events happening before the start of the horizon under consideration.
The outbound arc is a dummy arc and represents the slack time for the connecting
resource.
If a resource is scheduled to be released within the horizon (the resource has
no other assignments in the horizon), one node and one arc are used to represent the
release of this resource. The node represents the event when the resource is released.
The arc is inbound to the resource release node and represents the debrief interval for
the crew or the interval required to taxi the aircraft to the parking facility. Also, if the
resource is connecting to a flight outside the horizon, one node and one arc are used
to represent this connection. The node represents the event when the resource is ready
13
for the next flight. The arc is inbound to the node and represents the activity required
by this resource to get ready as described earlier.
Each node is associated with a label representing the time at which the event
represented by this node is projected to occur. The label of the source node is taken as
zero. Except for the dummy arcs, the cost associated with an arc is the activity
duration represented by this arc. For example, the cost associated with an arc
connecting between the flight departure node and flight wheels-off node is the taxiout interval at the flight’s origin airport. Similarly, if the connecting resource is a
crewmember, the cost associated with an arc connecting between the flight arrival
node and the resource ready node is the required connection time to the departure gate
of the next flight or the required rest time at the end of the duty. The cost of all arcs
out of the common source node is the latest quoted ready time for the resource
represented by this arc.
In the defined graph, arc costs are not necessarily fixed. In some cases, the arc
cost (duration) depends on the value of the label of its upstream node. For example,
as mentioned earlier, the required rest duration for a crewmember is function of
her/his flying time in the last 24 hours. As such, the cost to be considered for an arc
that represents a crew layover is function of the arrival time of the previous flight in
the schedule (the label of the upstream node). Similarly, the expected
service/maintenance time for an aircraft may depend on the time at which the aircraft
arrives at the service/maintenance station. If a flight is delayed such that it arrives
during a busy period for the ground service/maintenance crew, the expected
14
service/maintenance interval could be longer than what is originally scheduled.
Furthermore, during peak periods, airports become crowded and flights are expected
to have longer taxi-in and taxi-out periods. Flights could also be held in the air until a
landing slot becomes available. As such, flying time for a flight could be longer than
what is originally scheduled.
THE DELAY MODEL
In the graph described above, arcs have a binary relation on nodes. Also, by
definition, the graph has no cycles (no resource can be used on the same flight twice).
This defines a directed acyclic graph. A special characteristic of a directed acyclic
graph is that its nodes can be sorted topologically in a linear time (Lawler, 1976). A
topological sort of a directed acyclic graph G, is a linear ordering of all nodes such
that if G contains an arc (x, y), then x appears before y in the ordering. The following
algorithm can be used to conduct the topological sorting of nodes in graph G, where
the list L returns the sorted nodes.
Linear Time Topological Sorting
list L = empty
while (G is not empty)
find a node v with no incoming arcs
delete v from G
add v to L
15
Now assume nodes in the graph are sorted topologically. Also, assume the
label of each node in the graph is initialized with the latest quoted time for the event
represented by this node. Running the shortest path algorithm to determine the
shortest path from the source node to all nodes in the network, the resulting label for
each node determines the earliest time at which the event represented by this node is
projected to occur. Lawler (1976) describes a linear time algorithm for shortest path
in directed acyclic graphs. The algorithm assumes all nodes in the graph are
topologically sorted. Adding one step to consider the time-dependent cost of the arcs,
the steps of the Delay Projection Algorithm are as follows:
Delay Prediction Algorithm
Sort nodes topologically
for each node x in a topological ordering of G
based on d(s,x), compute the lengths of all outgoing arcs of node x
for all outgoing arcs
if d(s,y) < d(s,x) + length(x,y)
d(s,y) = d(s,x) + length(x,y)
path(s,y) = path(s,x) + arc (x,y)
If a label of one node is changed from what is quoted for this node, it implies
that a delay is projected beyond what is currently quoted for the event presented by
this node. By tracking the path from the source node to the node at which delay is
projected, the delay reason (the inbound resource that is causing the delay) could be
identified. Once all labels are computed, slack times could then be determined. As
16
described earlier, a resource slack time at one connection is the length of the dummy
arc representing this resource at this connection. The length of the dummy arc is
calculated as the difference between the label of its downstream node and upstream
node, respectively (the dummy arcs are assumed to have a zero cost while running the
shortest path algorithm). A flight downline slack is the smallest slack time among all
its outbound resources.
MODEL APPLICATION
The model is deployed at United Airlines’ operation control center to monitor
the daily schedule (about 1800 daily flights to more than 130 destinations).
Synchronized with the real-time clock, the model runs on a cyclic basis (every three
minute) to project the state of the airline for a future horizon of twelve hours. The
model starts by receiving a snap shot of the current state of the airlines including the
latest published departure time for each flight in the horizon under consideration. It
also receives the latest ground delay program issued by the FAA, if any. The model
generates the list of delayed flights and reasons for their delays. It also reports all
projected resource breaks as described earlier. Based on these generated reports,
controllers in the OCC react proactively to recover these breaks.
Impact of GDP on Total System Delays
Figure 8 illustrates the impact of GDPs on the total system delays in a twelve
hours horizon. The total system delays projected by the model for more than twenty
17
GDPs issued for United Airlines’ flights in January 2004 are presented. As shown in
the figure, the total flight-minute delays generally increases with the increase in
number of flights in the issued GDP. For example, a total flight delay of 600 minutes
was projected when the GDP included 17 flights. This number jumped to more than
2000 minutes when 161 flights were listed in the GDP. It should be noticed that same
number of flights in the GDP could have different impact on the total system delays.
For instance, more system delays are expected if the resources of the impacted flights
are heavily utilized for other downline flights. On the contrary, if most of the
resources are ending their duties such that they are not utilized for any downline
flights in the horizon under consideration, the total system delays would be lesser.
Abdelghany et al. (2004b) compares the impact of hypothetical GDPs on airlines
schedules at different times of the day. Their experiments show that because crew
duties typically start in the morning and end some time between late afternoon and
midnight, morning GDPs are in general having more disrupting impact on the
schedule than afternoon or late night ones.
Flight Delay Reason
The model determines the inbound resource reason for the predicted flight
delays. A flight is delayed either because its inbound resource(s) is not ready before
the scheduled departure time, or because a departure control time is issued by the
FAA for this flight. For the twenty recorded GDP instances, Figure 9 classifies the
delayed flights based on their projected delay reason. As shown in the figure, on
average, about 42% of the delayed flights are delayed because their assigned aircrafts
18
are not timely ready. Furthermore, pilots and FAs contribute to 18% and 12% as a
reason of the projected delayed flights, respectively. As aircraft is the most limited
resource, airlines companies construct aircraft routes such that the utilization of the
available aircraft fleet is maximized. This reduces slack times along aircraft routes.
Thus, a flight delay could have a snowball effect along all downline flights in the
aircraft route and consequently along the schedule of other resources. Once aircraft
routes are built, pilots and FAs are assigned to cover all flights in the planning
horizon. Due to the different legality rules and other quality of life issues that govern
crew scheduling, slack times could exist between successive flights in the crew
trippairs. These slack times absorb downline flight delays which results in less
number of flight delays because of crew unavailability. This argument is confirmed
by the results given in Figure 10, which compares the average slack time for the
different resources during normal operation conditions (no ground delay program is
received) for January’s flight schedule. For each flight in the 12 hour horizon (starting
8 a.m.), the slack time for each inbound resource is computed as described earlier. An
inbound resource could be connecting from a flight in the considered horizon, or
connecting from a flight that arrives in the previous day. These slacks are then
averaged by resource type. As shown in the figure, an average of 28 minutes slack is
observed for the aircraft. Comparing with the aircraft slack, the pilots and FAs
average slack are more by about 33% and 92%, respectively.
Proactive Recovery Actions
19
In response to flight delay predictions and reason for these delays that are
generated by the model, controllers in the OCC take the appropriate recovery actions
to recover/avoid these delays. Main recovery actions include replacing the delayed
resources (aircraft and crewmembers) with other equivalent resources such that the
projected delays are completely avoided or reduced (a new departure time is issued
for the flight). Figure 11 illustrates the number of recovery actions taken by
controllers during the month of January, 2004 to recover flight delays projected by
the model. As shown in the figure, about 280 aircraft reassignments, 96 pilot
reassignments and 66 FA reassignments are made. In addition, a total of 425 flights
are issued a new departure time. One can observe the correlation between the delay
reason presented in Figure 9 and the type of taken recovery action presented in Figure
11. As the percentage of delayed flights because of a resource type increases, more
recovery actions are made for this resource type. United Airlines estimates that it
saves approximately $1.6 million by using the flight delay projection model presented
in this paper during the first quarter of 2004.
SUMMARY
This paper presents a flight delay model, which uses the classical shortest path
algorithm as its core. The model projects downline flight delays and alert for
crew/aircraft operation breaks that might occur due to any introduced operation
irregularity. In this model, the flight schedule is represented in the form of a directed
20
acyclic graph where the different scheduled events are considered as nodes and the
different activities required for these events to occur are considered as arcs. Events
include flight departure, flight wheels-off, flight wheels-on, flight arrival, etc.
Activities include taxiing-out, flying, taxiing in, resource connection, etc. The label
associated with each node is the earliest possible time at which the event represented
by this node could occur. The arc cost represents the duration required for each
activity. The results of applying the model to predict schedule disruption at United
Airlines’ OCC are presented. The results show that downline schedule disruptions
are proportional to the number of flights impacted by the GDP. Furthermore, in the
recorded GDP instances, aircraft appears to be the reason for most flight delays
predicted by the model. Also, recovery actions taken by controllers in the OCC to
recover the predicted flight delays are observed to be correlated with the projected
reason for these delays.
Several extensions are considered for this research work. For example, as this
model provides the capability of projecting possible system breaks ahead of their
occurrence, integrating this model with a recovery decision support tool to avoid
these breaks is one possible extension. In addition, the model can be used to answer a
wide variety of what-if scenarios that controllers are interested to investigate. Finally,
one possible extension is to study the stochastic version of the problem. For example,
activities such as taxi time and flying time are stochastic in nature and could be
affected by many variables. Using the probability distributions of the duration of
these activities, a stochastic version of the shortest path algorithm can be used to
21
provide the probability distribution that describes the occurrence time of each
scheduled event.
REFERENCES
- Abdelghany, A. F., Ekollu, G., Narasimhan R., and Abdelghany, K. F., 2004. A
Proactive Crew Recovery Decision Support Tool for Commercial Airlines during
Irregular Operations. Annals of Operations Research 127, 309-331.
- Abdelghany A. F., Abdelghany, K. F., Ekollu, G., 2004. A Genetic Algorithm
Approach for Ground Delay Programs Management: The Airlines’ Side of the
Problem. Air Traffic Control Quarterly 12(1), 53-74.
- Ball, M.O., Hoffman, R.L., Knorr, D., Wetherly, J., Wambsganss, M., 2000.
Assessing the Benefits of Collaborative Decision Making in Air Traffic Management.
3rd USA/Europe Air Traffic Management R&D Seminar, Napoli, Italy.
- Clarke, M., 1997. The Airline Schedule Recovery Problem. Working Paper, MIT
International Center for Air Transportation, Boston, MA.
- Yu, G., Argüello, M., Song, G., McCowan, S., and White A., 2003, A New Era for
Crew Recovery at Continental Airlines, Interfaces 33(1), 5-22.
- Lawler, L. E., 1976. Combinatorial Optimization: Networks and Matroids. Holt,
Rinehart, and Winston, Austin, Texas.
- Monroe, W., and Chu H., 1995. Real-Time Crew Rescheduling. Presented at
INFORMS meeting, New Orleans.
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- Rosenberger, J. et al., 2000. A Stochastic Model of Airline Operations, Georgia
Institute of Technology, TLI-00-06 working paper.
- Teodorovic, D. and Stojkovic, G., 1995. A Model to Reduce Airline Schedule
Disturbances”, Journal of Transportation Engineering 121, 324-331.
23
UA 258
UA 1432
UA 2552
AC &
Pilots
UA 1180
UA 2015
UA 2718
UA 417
UA 1256
FA
UA 6973
GDP induced Delay
UA 1180
UA 2106
UA 7048
UA 6976
UA 0350
UA 6870
UA 670
UA 6936
Time
Figure 1: An example of delay amplification over the course of a day: one GDPinduced delay causing 16 downline delays
24
Time away from base
Duty #1
Duty #2
Layover
Connection time
A -> B
Sign in
B -> S
H -> L
S -> H
Sign out
L -> H
Sign in
H -> A
Sign out
Figure 2: A Typical Trippair in Normal Operation Conditions.
25
Time away from base
Duty #1
Duty #2
Layover
Delay
A -> B
B -> S
H -> L
S -> H
L -> H
H -> A
Minimum
connection time
Sign in
Ready time
Sign out
Sign in
Sign out
Figure 3: Example of Misconnect Break.
26
Time away from base
Duty #1
Duty #2
New layover
Delay
A -> B
Sign in
B -> S
S -> H
Old layover
Sign out
H -> L
L -> H
Ready time
H -> A
Sign out
Figure 4: Example of Rest Break.
27
Time away from base
Duty #1
Duty Limit
Duty #2
Delay
Layover
A -> B
Sign in
B -> S
S -> H
Sign out
H -> L
Sign in
L -> H
H -> A
Sign out
Figure 5: Example of Duty Break.
28
R1
Horizon Start
R16
13:15 13:30
R7
12:15
R2
D1
F1
8:15
F3
D3
15:30
A3
A1
11:30
R9
R11
D2
8:10
R6
F2
D4
F4
A4
11:10
R14
R13
13:40
D5
R15
R20
17:00
F5
F7
17:15
A5
R30
R29
R21
D7
15:00
R24
R25
R26
R27
R28
R19
R12
A2
A6
R18
12:15
R10
12:15
21:30
F6
D6
14:30
R5
18:30
R17
R8 12:30
R3
R4
Horizon End
R22
R31
A7
20:00
R33
R32
R23
8:00
Time
Figure 6: Resources Connectivity in the Normal Operation Conditions.
29
13:15
34:30
F3
16:30
34:30
13:15
13:30
F1
7:30
13:45 15:20 15:30
16:30
8:15 8:30 11:20 11:30
12:30
16:30
12:15
8:00
S
7:30
7:30
Flight Departure
Wheels-off
18:00
18:00
12:15
34:30
24:15
18:00
14:30 14:40 16:50 17:00
8:10
34:30
18:50 20:15 20:30
18:30
F4
7:30
34:30
F6
32:15
12:10
F2 10:50 11:10
8:30
21:10
12:10
21:10
F5
13:10
20:00
13:40 14:00 19:20 19:30
F7
32:15
21:30 23:50 24:00
21:15
24:15
20:00
Wheels-on
Flight Arrival
Resource
is Ready
Figure 7: Graph Representation of the Flights Schedule.
30
32:15
2000
1500
1000
500
0
0
20
40
60
80
100
120
140
160
180
Number of Flights in the GDP
Figure 8: Impact of GDP on Total System Delays.
0.45
0.4
% Delayed Flights
Total Flight Delays in Minutes
2500
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
Aircraft
Pilot
FA
Flow
Delay Reason
Figure 9: Flight Delay Reason by Type.
31
60
Average Resource
Slack in Minutes
50
40
30
20
10
0
AC slack
Pilot slack
FA slack
Resource Type
Figure 10: Average Resource Slack in Minutes during Normal Operation Conditions.
450
Number of Actions
400
350
300
250
200
150
100
50
0
AC
Reassignment
Pilot
Reassignemnt
FA
Reassignemnt
Requote
Action Type
Figure 11: Proactive Recovery Actions.
32