Air Transportation: Irregular Operations and Control
by
Michael Ball
Robert H Smith School and Institute for Systems Research
University of Maryland
College Park, MD 20742
mball@rhsmith.umd.edu
Cynthia Barnhart
Department of Civil and Environmental Engineering
Massachusetts Institute of Technology
Room 1-235
Cambridge, MA 02139
cbarnhart@mit.edu
George Nemhauser
School of Industrial and Systems Engineering
Georgia Institute of Technology
Atlanta, GA 30332
george.nemhauser@isye.gatech.edu
Amedeo Odoni
Massachusetts Institute of Technology
Room 33-219
Cambridge, MA 02139
odoni@mit.edu
January 27, 2006
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1. Introduction
Commercial aviation operations are supported by what is probably the most complex
transportation system and possibly the most complex man-made system in the world.
Airports make up the fixed “nodes” on which the system is built. Aircraft represent the
very valuable assets that provide the basic transportation service. Passengers demand
transportation between a multitude of origins and destinations, and request specific travel
dates and times. Crews of pilots and flight attendants operate the aircraft and provide
service to passengers. These disparate entities are coordinated through a flight schedule,
comprised of flight legs between airport locations. The flight schedule itself defines three
other layers of schedules, namely the aircraft schedule, the crew schedule and passenger
itineraries. The aircraft schedule is an assignment of the legs in the flight schedule, with
each aircraft assigned to a connected sequence of origin to destination flight legs. When
an aircraft carries out a flight between an origin and destination airport, it follows a flight
plan that defines a sequence of points in the airspace through which it proceeds. The
crew schedule is an assignment of the legs in the flight schedule to pilots and flight
attendants, ensuring that all crew movements and schedules satisfy collective bargaining
agreements and government regulations. Passenger schedules, which represent the endcustomer services, define the familiar itineraries consisting of lists of origin and
destination airports together with scheduled arrival and departure times. Typically, pilots
and flight attendants have distinct schedules. The itineraries of a specific crew and a
specific aircraft may coincide for several flight legs, but they, like passengers and
aircraft, often separate at some point during a typical day’s operations.
The fact that a single flight leg is a component of several different types of schedules
implies that a perturbation in the timing of one leg can have significant “downstream”
effects leading to delays on several other legs. This “fragility” is exacerbated by the fact
that most of the largest carriers rely heavily on hub-and-spoke network configurations
that tightly inter-connect flights to/from many different “spokes” at the network’s hubs.
Thus, any significant disturbance at a hub, rapidly leads to disruptions of extensive parts
of the carrier’s schedules. Notable categories of events leading to such disruptions
include:
1. Airline resource shortages stemming from aircraft mechanical problems,
disrupted crews due to sickness, earlier upstream disruptions, longer than
scheduled aircraft turn times caused by lack of ground resources to operate the
turn, longer than expected passenger embarking and disembarking times, or
delayed connecting crews or connecting passengers.
2. Airport and airspace capacity shortages due to weather or to excessive traffic.
Inclement weather is cited as the source of 75% of airline disruptions in the
United States (Dobbyn 2000).
In 2000, about 30% of the jet-operated flight legs of one major U.S. airline were delayed,
and about 3.5% of these flight legs were cancelled. Yu et al (2003) report for another
major U.S. airline that, on average, a dozen crews are disrupted every day. The effects of
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these disruptions are exacerbated when applied to optimized airline schedules, for which
cost minimization and intensive resource utilization tend to go hand-in-hand. Nonproductive resources, such as idle aircraft and crew on the ground, are costly. Hence,
optimized schedules have minimal non-productive, or slack, time between flight legs. In
these finely tuned, optimized schedules, delay often propagates with no slack to absorb it,
making it very difficult to contain disruptions and to recover from their effects. A
mechanical delay affecting a single aircraft can result in delays to passengers and crews
assigned to aircraft other than those delayed, due to the interconnectivity of passengers,
crews and aircraft. This network propagation phenomenon explains why weather delays
in one geographical area, delaying flights in and out of that area, can result in aircraft,
crew and passenger delays and cancellations in locations far removed from the weather
delay. In fact, such local delays can impact network operations globally.
The significance of the delay propagation effect is illustrated in Figure 1 (reprinted from
Beatty et al 1998). This graphic is based on an analysis of American Airlines passenger
and aircraft schedule information. The x-axis tracks time of day from early morning to
evening. The y-axis tracks increasing values of an initial flight delay. The color of each
box in the x-y plane corresponds to the multiplier that can be applied to an initial delay to
estimate the impact of delay propagation. For example, an initial delay of 1.5 hours at
8:00 is colored dark green indicating a delay multiplier of 2.5. This means that an
original delay of 1.5 hours on a particular flight induces 2.5*1.5 = 3.75 hours in total
flight delay. Note that the delay multiplier increases with the size of the original delay
and is greatest during the peak morning periods.
The economic impact of disruptions is great. According to Clarke and Smith (2000),
disruption costs of a major U.S. domestic carrier in one year exceeded $440 million in
lost revenue, crew overtime pay, and passenger hospitality costs. Moreover, the Air
Transport Association (http://www.airlines.org/econ/files/zzzeco32.htm) reported that
delays cost consumers and airlines about $6.5 billion in 2000. These costs are expected
to increase dramatically, with air traffic forecast to double in the next 10-15 years. The
MIT Global Airline Industry Program (http://web.mit.edu/airlines/industry.html) and
Schaefer et al (2005) indicate that, at current demand levels, each 1% increase in air
traffic will bring about a 5% increase in delays.
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Figure 1.1: Estimation of Delay Propagation Multiplier (from Betty et al 1998)
In this chapter we consider problems related to the management of air traffic and airline
operations for the purpose of minimizing the impact and cost of disruptions. The
considerable system complexity outlined above makes these problems challenging and
has motivated a vibrant and innovative body of research. We start in Section 2 by
providing background which is essential to understanding the fundamental issues and
motivating the subsequent material. We first review the “physics” and characteristics of
airspace system elements and airspace operations in order to explain why capacity
constraints are so unpredictable and variable from day to day. Of critical importance are
the arrival and departure capacities of airports, which depend on weather, winds, and the
number of active runways and their configuration.
Providers of air traffic control services, such as the Federal Aviation Administration
(FAA) and Eurocontrol, have responsibility for overall airspace management and as such
are interested in achieving high levels of system-wide performance. The two broad
classes of “tools” at their disposal include restricting schedules and air traffic flow
management (ATFM). The former tool, which is treated in Section 3, is strategic in
nature. It seeks to control or influence the airline schedule-planning process by ensuring
that the resultant schedules do not lead to excessive levels of system congestion and
delays. Restricting schedules is particularly challenging in that the competing economic
interests of multiple airlines must be balanced. In fact, recent research in this area has
been investigating the potential use of market-based mechanisms for this purpose,
including auctions and peak-period pricing. The second tool, ATFM, is tactical in nature
and is treated in Section 4. ATFM encompasses a broad range of techniques that seek to
maximize the performance of the airspace system on any given day of operations, while
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taking into account a possibly broad range of disruptive events. Many ATFM actions and
solutions involve an allocation of decision-making responsibilities between the air traffic
control service provider and an airline. This is most notably the case for solutions
employing the Collaborative decision making (CDM) paradigm, which has the explicit
goal of assigning decision making responsibility to the most appropriate stakeholder in
every case (Section 4.4).
A brief Section 5 describes some simulation models that can be useful support tools in
understanding and visualizing the impact of certain types of disruptive events on airport,
airspace and airline operations and on air traffic flows, as well as in testing the
effectiveness of potential responsive actions.
Sections 6 and 7 address schedule planning and operations problems from the airline
perspective. The introductory paragraphs of this section described several factors, which
lead to the high complexity of these problems. This complexity is compounded by two
additional important considerations:
1. The predominant concern with safety and the significant unionization of crews
that, in combination, have led to the imposition of a very large set of
complicated constraints defining feasibility of flight plans and of flight, aircraft
and crew schedules.
2. The size of airline networks and operations, including, in the United States
alone, over 5,000 public-use airports serving over 8000 (non-general aviation)
aircraft transporting approximately 600 million passengers on flights covering
more than 5 billion vehicle miles annually
(http://www.bts.gov/publications/pocket_guide_to_transportation/2004/pdf/entire.
pdf).
The aircraft- and crew-scheduling problem, also referred to as the airline schedule
planning problem, involves designing the flight schedule and assigning aircraft,
maintenance operations and crews to the schedule. The typical size of this problem is so
large that it is impossible to solve it directly for large airlines. Instead, airlines partition it
into four sub-problems, namely: i) schedule generation; ii) fleet assignment; iii)
maintenance routing; and iv) crew scheduling. The sub-problems are solved sequentially,
with the solutions to the earlier, higher-level sub-problems serving as the fixed inputs to
subsequent ones. The schedule generation problem is to determine the flight legs, with
specified departure times, comprising the flight schedule. These legs, which define the
origin-destination markets served and the frequency and timing of service, have
significant effects on the profitability of airlines. Given the flight schedule, the fleet
assignment problem is to find the profit maximizing assignment of aircraft types to flight
legs in the schedule. Where possible, the goal is to match as closely as possible seat
capacity with passenger demand for each flight leg. With the fleeted flight schedule and
the size and composition of the airline’s fleet as input, the maintenance routing problem
is to find for each aircraft, a set of maintenance-feasible rotations, or routes that begin
and end at the same place and satisfy government- and airline-mandated maintenance
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requirements. Finally, given all the schedule design and aircraft assignment decisions,
the crew scheduling problem is to find the cost minimizing assignment of cockpit and
cabin crews to flights. Crew costs, second only to fuel costs, represent a significant
operating expense. A detailed description of the airline schedule planning problem is
provided in Barnhart, Belobaba and Odoni (2003).
From the airline perspective, the focus of this chapter is motivated by the fact that,
despite advances in aircraft and crew schedule planning, optimized plans are rarely, if
ever, executed. Thus, we shall not provide broad coverage of airline schedule planning
but rather focus on the topics that address the development of schedules and operating
practices and policies that provide operational robustness. In Section 6, we cover the
theme of optimizing airline schedule recovery. The associated tools are designed for use
in a near real-time mode to adjust operations in response to a variety of disruptions. In
Section 7, we address, by contrast, the more strategic topic of developing schedules that
provide operational robustness. This more recent area of study builds upon the longstanding and well-known body of research on aircraft and crew scheduling described in
the previous paragraph. Finally, in Section 8, we conclude with a very general
assessment of the state of research and implementation in this subject area.
2. Flow Constraints in the Infrastructure of Commercial Aviation
The airspace systems of developed nations and regions consist of a set of often extremely
expensive and scarce nodes, the airports, and of air traffic management (ATM) systems
that provide aircraft and pilots with the means needed to fly safely and expeditiously
from airport to airport. The essential components of ATM systems are: a skilled
workforce of human air traffic controllers; organization of the airspace around airports
(“terminal airspace”) and between airports (“en route airspace”) into a complex network
of airways, waypoints and sectors of responsibility; procedures and regulations according
to which the ATM system operates; automation systems, such as computers, displays,
and decision support software; and systems for carrying out the functions of
communications, navigation and surveillance (CNS) which are critical to ATM. Any
flow constraints encountered during a flight may result from an obvious cause (e.g., the
closing down of a runway) or from a set of complex interactions involving failure or
inadequacy of several of the components of the ATM system.
A controlled flight is one for which an approved flight plan has been filed with the air
traffic management (ATM) system. Airline and general aviation operators prepare and
file flight plans usually based on criteria that consider each flight in isolation. Air
carriers typically employ sophisticated software, including advanced route optimization
programs, for this purpose. Far from being just a “shortest path” problem, the selection of
an optimal route for a flight typically involves a combination of criteria, such as
minimum time, minimum fuel consumption, and best ride conditions for the passengers.
Midkiff, Hansman and Reynolds (2004) provide a thorough description of air carrier
flight planning. By accepting a flight plan, the ATM system agrees to take responsibility
for the safe separation of that aircraft from all other controlled aircraft in the airspace and
to provide many other types of assistance toward the goal of completing the flight safely
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and expeditiously. Practically all airline flights and a large number of general aviation
flights are controlled. The focus of this entire chapter is on flow constraints that such
flights often face and on how ATM service providers, airport operators and airlines
attempt to deal with them. Figure 2.1 illustrates schematically the fact that such
constraints or “bottlenecks” occur when flights are departing from and arriving at airports
and when they seek to access certain parts of the airspace.
airport
departure
rate
waypoint
waypoint
A2
airport
arrival
rate
A1
sector
Figure 2.1: Airspace Flow Constraints
This section will seek to review the “physics” of the constraints, with emphasis on
explaining the causes of two of their most distinctive characteristics – variability and
unpredictability. It is these characteristics that make the constraints so difficult to deal
with in practice, as well as so interesting for many researchers. Emphasis will be given to
the specific topic of capacity-related flow constraints at major commercial airports, due
to the enormous practical significance and cost consequences of these constraints.
2.1. The “Physics” of Airport Capacity
Airports consist of several subsystems, such as runways, taxiways, apron stands,
passenger and cargo terminals, and ground access complexes, each with its own capacity
limitations. At major airports, the capacity of the system of runways is the most
restricting element in the great majority of cases. This is particularly true from a long-run
perspective. While it is usually possible – albeit occasionally very expensive – to
increase the capacity of the other airport elements through an array of capital
investments, new runways and associated taxiways require great expanses of land and
have environmental and other impacts that necessitate long and complicated approval
processes, often taking a couple of decades or even longer, with uncertain outcomes.
The capacity of runway systems is also the principal cause, by far, of the most extreme
instances of delays that lead to widespread schedule disruptions, flight cancellations and
missed flight connections. There certainly have been instances when taxiway system
congestion or unavailability of gates and aircraft parking spaces have become constraints
at airports, but these are more predictable and stable. The associated constraints can
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typically be taken into consideration in an ad hoc way during long-range planning or in
the daily development of ATFM plans (Section 4). By contrast, the capacity of the
runway system can vary greatly from day to day and the changes are difficult to predict
even a few hours in advance. This may lead to an unstable operating environment for air
carriers: on days when an airport operates at its nominal, good-weather capacity, flights
will typically operate on time, with the exception of possible delays due to “upstream”
events; but, with the same level of demand at the same airport, schedule reliability may
easily fall apart on days when weather conditions are less than ideal.
The capacity of a runway, or of a set of simultaneously active runways at an airport is
defined as the expected number of movements (landings and takeoffs) that can be
performed per unit of time in the presence of continuous demand and without violating
air traffic control (ATC) separation requirements. This is often referred to as the
maximum throughput capacity, C. Note that this definition recognizes that the actual
number, N, of movements that can be performed per unit of time is a random variable.
The capacity C is simply defined as being equal to E[N], the expected value of N. The
unit of time used most often is one hour.
To understand better the multiple causes of capacity variability, especially its strong
dependence on weather and wind conditions, it is necessary to look at the “physics” of
the capacity of runway systems. It is convenient to consider first the case of a single
runway and then (Section 2.1.4) the case of a system of several runways.
2.1.1. Factors Affecting the Capacity of a Single Runway
The capacity of a single runway depends on many factors, the most important of which
are:
1. The mix of aircraft classes using the airport.
2. The separation requirements imposed by the ATM system.
3. The type (high speed or conventional) and location of exits from the runway.
4. The mix of movements on each runway (arrivals only, departures only, or mixed)
and the sequencing of the movements.
5. Weather conditions, namely visibility, cloud ceiling and precipitation.
6. The technological state and overall performance of the ATM system.
The impacts of 1-4 are summarized below, while 5 and 6 are discussed in the more
general context of multi-runway systems in the next subsection.
Mix of aircraft: The FAA and other Civil Aviation Authorities around the world classify
aircraft into a small number of classes for terminal area ATC purposes. For example, the
FAA defines four classes, based on maximum take-off weight (MTOW): “Heavy” (H),
“Large” (L), the Boeing 757 (a class by itself), and “Small” (S). Most other Civil
Aviation Authorities have adopted the same or very similar classifications. Roughly
speaking, the H class includes all wide-body jets, and the L class practically all narrow-
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body commercial jets – including many of the larger, new generation, regional jets – as
well as some of the larger commercial turbo-props. Most general aviation airplanes,
including most types of private jets, as well as the smaller commercial turboprops and
regional jets with about 35 seats or fewer comprise the S class. The aircraft mix indicates
the composition of the aircraft fleet that is using any particular runway (e.g., 20% S, 60%
L, 5% B757 and 15% H).
Separation requirements and high-speed exits: The single most important factor in
determining runway capacity is the separation requirements, which impose safety-related
separations between aircraft that limit the service rate of the runway, i.e., its maximum
throughput capacity. For every possible pair of aircraft using the same runway
consecutively, the FAA and other Civil Aviation Organizations specify a set of separation
requirements in units of distance or of time. These requirements depend on the classes to
which the two aircraft belong and on the types of operation involved: arrival followed by
Trailing aircraft
H
L + B757
S
H
4
5
6*
Leading
B757
4
4
5*
aircraft
L
2.5
2.5
4*
S
2.5
2.5
2.5
Table 2.1: FAA IFR separation requirements in nautical miles (nmi) for “an arrival
followed by an arrival”. Asterisks indicate separations that apply when the leading
aircraft is at the threshold of the runway.
arrival, “A-A”, arrival followed by departure, “A-D”, etc. Table 2.1 shows the separation
requirements that currently apply at most of the busiest airports in the United States for
the case in which a runway is used only for arrivals under instrument flight rules (IFR).
Pairs of consecutive landing aircraft must maintain a separation equal to or greater than
the distances indicated in Table 2.1 throughout their final approach to the runway, with
the exception of the cases marked with an asterisk, where the required separation must
exist at the instant when the leading aircraft reaches the runway. The 4, 5 and 6 nautical
mile separations shown in Table 2.2 are intended to protect the lighter trailing aircraft in
the pair from the hazards posed by the wake vortices generated by the heavier leading
aircraft. These are therefore often referred to as “wake vortex separations.” In addition
to the “airborne separation” requirements of Table 2.2, a further restriction is applied: the
trailing aircraft of any pair cannot touch down on the runway before the leading aircraft
is clear of the runway. In other words, the runway can be occupied by only one arriving
aircraft at any time.
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The more restrictive of the two requirements – “airborne separation” and “single
occupancy” – is the one that applies for each pair of aircraft. When arrivals take place in
instrument meteorological conditions (IMC), “airborne separation” is almost always the
most restrictive. However, “single occupancy” may become the constraint when visual
airborne separations on final approach are allowed (instead of the distance requirements
of Table 2.1), as is often done in the United States under visual meteorological conditions
(VMC). In this case, high-speed runway exits and well-placed runway exits (the third of
the factors identified above), which reduce runway occupancy times for arriving aircraft,
can be helpful in increasing runway capacity. High-speed exits can also be useful when
the runway is used for both arrivals and departures: if landing aircraft can exit a runway
quickly, air traffic controllers may be able to “release” a following takeoff sooner.
Departures/hour
4
3
Feasible
region
45
0
o
2
1
Arrivals/hour
Figure 2.2: A capacity envelope for a single runway
Mix of movements: Separation requirements, analogous to those in Table 2.1, are also
specified for the other three combinations of consecutive operations, A-D, D-A and D-D.
Because the separation requirements for each combination are different – see, e.g.,
Chapter 10 of de Neufville and Odoni (2003) for details – the capacity of a runway
during any given time period depends on the mix of arrivals and departures during that
period, as well as on how exactly arrivals and departures are sequenced on the runway.
This also suggests that there is an important tradeoff between the maximum arrival and
departure rates that an airport can achieve.
2.1.2. Capacity envelope and its computation
The runway capacity envelope (Figure 2.2) is convenient for displaying the arrival and
departure capacities and associated tradeoffs. The capacity envelope of a single runway
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is typically approximated by a piecewise linear boundary that connects four points
(Gilbo, 1993). Points 1 and 4 indicate the capacity of the runway, when it is used only
for arrivals and only for departures, respectively. Point 2 is known as the “freedepartures” point because it has the same capacity for arrivals as Point 1 and a departures
capacity equal to the number of departures that can be inserted into the arrivals stream
without increasing the separations between successive arrivals – and, thus, without
reducing the number of arrivals from what can be achieved in the all-arrivals case. These
“free” departures are obtained by exploiting large inter-arrival gaps such as the ones that
arise between a “H-followed-by-S” pair of landing aircraft. Point 3 can be attained, in
principle, by alternating arrivals and departures, i.e., by performing an equal number of
departures and arrivals through an A-D-A-D-A... sequence. This sequencing strategy can
be implemented by “stretching,” when necessary, inter-arrival (inter-departure) gaps by
an amount of time just sufficient to insert a departure (arrival) between two successive
arrivals (departures). Because it is difficult for air traffic controllers to sustain this type
of operation for extended periods of time, Point 3 can be viewed as somewhat theoretical.
However, it provides a useful upper limit on the total achievable capacity (landings plus
takeoffs) when arrivals and departures share a runway in roughly equal numbers.
Several mathematical models have been developed over the years for computing the
capacity of a single runway under different sets of conditions, beginning with
Blumstein’s (1959) classical model of a single runway used for arrivals only. The
models have become increasingly sophisticated over the years and include treatment of
some of the input parameters as random variables. Barnhart, Belobaba and Odoni (2003)
provide a literature review. The most recent of these models ((Long et al 1999;
Stamatopoulos, Zografos and Odoni 2004; EUROCONTROL 2001) incorporate most of
the best features of earlier models and generate capacity envelopes, such as the one in
Figure 2.2.
2.1.3. The Sequencing Problem
As a result of the airborne separation requirements shown in Table 2.1, certain aircraft
pairs require longer separation distances than others and thus the total time needed for the
landing of any set of aircraft on a runway depends on the sequencing of the aircraft. For
example, the “H followed by S” sequence will consume much more time than “S
followed by H”. Given a number n of aircraft, all waiting to land on a runway, the
problem of “determining the sequence of landings such as to minimize the time when the
last aircraft lands” is a Hamiltonian path problem with n points (Psaraftis 1980;
Venkatakrishnan, Barnett and Odoni 1993). This is a problem entirely analogous to
several well-known job-sequencing problems in manufacturing.
However, the Hamiltonian path approach addresses only a static version of a problem. In
truth, the problem of sequencing aircraft on a runway is dynamic: over time, the pool of
aircraft available to land changes, as some aircraft reach the runway while new aircraft
join the arrivals queue. Moreover, minimizing the “latest landing time” (or maximizing
“throughput”) should not necessarily be the objective of optimal sequencing. Many
alternative objective functions, such as minimizing the average waiting time per
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passenger, are just as reasonable. A further complication is that the very idea of
“sequencing” runs counter to the traditional adherence of ATM systems to a first-come,
first-served (FCFS) discipline, which is perceived by most as “fair” (see also Section 4).
These observations have motivated a great deal of research on the runway sequencing
problem with the objective of increasing operating efficiency while ensuring that all
airport users are treated equitably. Dear (1991) developed the concept of constrained
position shifting (CPS), i.e., of a limit in the number of positions by which an aircraft can
deviate from its FCFS position in a queue. For instance, an aircraft in the 16th position in
an FCFS queue, would have to land in one of the positions 14 through 18, if the specified
maximum position shift (MPS) is 2. Through many numerical examples and for several
reasonable objective functions, Dear showed that, by setting MPS to a small number,
such as 2 or 3, one can obtain most (e.g., 60-80%) of the potential benefits offered by
unconstrained optimal sequences and, at the same time, ensure reasonable fairness in
accessing runways. Several researchers (e.g., Psaraftis 1980; Venkatakrishnan, Barnett
and Odoni 1993; Beasley, Sonander and Havelock 2001) have investigated a number of
increasingly complex and realistic versions of the sequencing problem. Two advanced
terminal airspace automation systems, CTAS and COMPAS, that have been implemented
in the US and in Germany, respectively, incorporate sequencing algorithms based on CPS
(Erzberger, 1995).
Gilbo (1993), Gilbo and Howard (2000) and Hall (1999) have gone beyond the
sequencing of arrivals only, by considering how available capacity can best be allocated
in a dynamic way between landings and take-offs to account for the distinct peaking
patterns in the arrival and departure streams at airports over the course of a day. They
propose the application of optimization algorithms that use capacity envelopes (Figure
2.2) within the context of ATFM to achieve an optimal trade-off between arrival and
departure rates and, by implication, between delays to arrivals and to departures.
2.1.4. Factors Affecting the Capacity of Multi-Runway Systems
Most (but certainly not all) major airports typically operate with two or more
simultaneously active runways. The term runway configuration refers to any set of one
or more runways, which can be active simultaneously at an airport. Multi-runway
airports may employ more than ten different runway configurations. Which one they will
operate on at any given time will depend on weather and wind conditions, on demand
levels at the time and, possibly, on noise considerations, as will be explained below.
The six factors listed in Section 2.1.1 clearly continue to affect the capacity of each
individual active runway in multi-runway cases. In addition, at least four other factors
may now play a major role:
7. The interactions between operations on different runways, as determined by the
geometric layout of the runway system and other considerations.
8. The allocation of aircraft classes and types of operations (arrivals, departures,
mixed) among the active runways.
9. The direction and strength of winds.
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10. Noise-related and other environmental considerations and constraints.
Interactions between operations on different runways: The influence of the geometric
layout on the interactions among runways can most simply be illustrated by looking at
situations involving two parallel runways. Depending on the distance between their
centerlines, operations on the two runways may have to be coordinated all the time, or
may be dependent in some cases and independent in others, or may be completely
independent. For example, in the United States, two parallel runways separated by less
than 2,500 ft. (762 m) must be operated with essentially single runway separations in
instrument meteorological conditions (IMC). This means, for instance, that, if two
arriving aircraft are landing, one on the left runway and the other on the right runway,
they are subject to the same set of airborne separation requirements as shown in Table 2.1
for a single runway. At the opposite extreme, if the centerlines are separated by more
than 4,300 ft (1,310 m) the two runways may be operated independently and can accept
simultaneous parallel approaches. (With special instrumentation, the FAA will consider
authorizing independent parallel approaches with centerline separations as small as 3,000
ft (915 m).) Finally, for intermediate cases, contemporaneous arrivals on the two
parallel runways are treated as “dependent”, i.e., must be coordinated, but an arrival on
one of the runways and a contemporaneous departure from the other can be handled
independently. It follows that the combined capacity of the two runways will be highest
in the case of independent operations, intermediate in the “partially dependent”
operations case, and lowest when every pair of operations on the two runways must be
coordinated. In a similar way, the combined capacity of pairs of intersecting runways or
of runways that do not intersect physically but intersect at the projections of their
centerlines depends on many geometry-related parameters such as: the location of the
intersection or of the projected intersection; the direction of operations on the two
runways; the types of operations and the mix of aircraft; and, obviously, the separation
requirements for the particular geometric configuration at hand. Systems of three or
more active, non-parallel runways typically involve even more complex interactions.
Allocation of aircraft and operations: With more than one active runway, there is some
opportunity to “optimize” operations by judiciously assigning operations and/or aircraft
classes to different runways. For example, in the case of intermediately spaced parallel
runways (centerline separations of 2,500 to 4,300 ft in the United States) it may be
advisable to use one runway primarily for arrivals and the other primarily for departures.
Since, in this case, arrivals on one runway can operate independently of departures on the
other, this allocation strategy minimizes interactions between runways and reduces
controller workload. Similarly, when two or more runways are used for arrivals, air
traffic managers often try to assign relatively homogeneous mixes of aircraft to each of
the runways, e.g., keep the “Small” aircraft on a separate runway from the “Heavy” and
“Large”, to the extent possible. In this way, air traffic controllers can avoid the extensive
use of the 5 and 6 nautical mile wake-vortex separations that are required when a Small
aircraft is landing behind a Large or a Heavy (Table 2.1).
Weather-related factors: It is easy to infer from what has been said so far that weatherrelated factors (numbers 5 and 9 in our list) are critical in determining the variability of
13
the capacity of any system of runways. First, for individual runways, the actual
separations between consecutive operations are strongly influenced by visibility, cloud
ceiling and precipitation. This is especially true in the United States where, in good
weather, pilots are usually requested to maintain visual separations during the final
approach phase from the aircraft landing ahead of them. This practice results in
somewhat closer spacing of landing aircraft than suggested by the IFR separations of
Table 2.1. It also means smaller deviations from the required minima, as pilots can adjust
spacing as they approach the runway. This second effect is also present at airports where
the practice of “visual separations on final” in VMC has not yet been adopted. The
overall effect is that, with the same aircraft mix and the same nominal (IFR) separation
requirements, the capacity of individual runways in VMC is typically greater than in
IMC, occasionally by a significant margin.
Second, when it comes to multi-runway configurations, good visibility conditions have a
similar effect. For example, in the case of two parallel runways, the FAA generally
authorizes simultaneous parallel approaches in IMC, when the separation between
runway centerlines is 4,300 ft or more, as noted earlier. But in VMC, simultaneous
parallel approaches can be performed to parallel runways separated by only 1200 ft (366
m) when Heavy aircraft are involved and by only 700 ft (214 m) when they are not. As a
consequence, San Francisco International (SFO), one of the most delay-prone airports in
the world, has an arrival capacity of about 54 per hour in VMC, when simultaneous
parallel approaches are performed to a pair of closely-spaced parallel runways, and of
only 34 per hour in IMC, when the same two runways are operated essentially as a single
runway, as described earlier. The impact of VMC is similar when it comes to operations
on a pair of intersecting runways, as illustrated by New York’s LaGuardia Airport
(LGA). In VMC, LGA has a nominal capacity of 81 movements per hour and, with the
same two runways, a capacity of 63 (or 22% less) in IMC.
Wind direction and wind strength are just as critical in determining which runways will
be active at a multi-runway airport at any given time. First, landings and takeoffs are
conducted into the wind – the maximum allowable tailwind is generally of the order of 5
knots. Thus, the direction of the wind determines the direction in which the active
runways are used. Equally important, there are limits on the strength of the crosswinds
that aircraft can tolerate on landing and on takeoff. For any runway, the crosswind is the
component of the wind vector whose direction is perpendicular to the direction of the
runway. The crosswind tolerance limits vary according to type of aircraft and to the state
of the runway’s surface (dry or wet, slippery due to icy spots, etc.). Thus, airports are
often forced by crosswinds and tailwinds to utilize configurations that offer reduced
capacity. For example, with strong westerly winds, Boston Logan (BOS) is forced to
operate with two main runways even in VMC, instead of the customary three. This
reduces capacity by about 30 movements per hour from the VMC norm!
State and performance of the ATM system: An obvious underlying premise to all of the
above is that a high-quality ATM system with well-trained and experienced personnel is
a prerequisite for achieving high runway capacities. To use a simple example, tight
separations between successive aircraft on final approach (i.e., separations which are as
14
close as possible to the minimum required in each case) cannot be achieved unless (a)
accurate and well-displayed information is available to air traffic controllers regarding
the positions of the leading and trailing aircraft, and (b) the controllers themselves are
skilled in the task of spacing aircraft accurately during final approach. Major differences
exist in this respect between ATM systems in different countries.
Environmental considerations: Finally, runway usage and, by extension, airport capacity
at some major airports may be strongly affected by noise-mitigation and other measures
motivated by environmental considerations. In the daily course of airport operations,
noise is one of the principal criteria used by air traffic controllers to decide which one
among several usable alternative runway configurations to activate. (A choice among
two or more alternative configurations may exist whenever weather and wind conditions
are sufficiently favorable.) Environmental considerations act, in general, as a constraint
on airport capacity since they tend to reduce the frequency with which certain highcapacity configurations may be used.
The capacity envelope for multi-runway systems and its computation: The complexity
of computing the capacity envelopes of multi-runway airports depends on the complexity
of the geometric layout of the runway system and the extent to which operations on
different runways are interdependent. The simplest cases, involving two parallel or
intersecting runways, can still be addressed through analytical models, because they are
reasonably straightforward extensions of single-runway models (Stamatopoulos,
Zografos and Odoni 2004). Analytical models also provide good approximate estimates
of true capacity in cases involving three or more active runways, as long as the runway
configurations can be “decomposed” into semi-independent parts, each consisting of one
or two runways. This is possible at the majority of existing major airports and at
practically every secondary airport.
When such decomposition is not possible or when a highly detailed representation of
runway and taxiway operations is necessary, simulation models can be used. Generalpurpose simulation models of airside operations first became viable in the early 1980s
and have been vested with increasingly sophisticated features since then. Two models
currently dominate this field internationally: SIMMOD and the Total Airport and
Airspace Modeler (TAAM). A report by Odoni et al (1997) contains detailed reviews of
these and several other airport and airspace simulation models and assesses the strengths
and weaknesses of each. At their current state of development and with adequate time
and personnel resources, they can be powerful tools not only in estimating the capacity of
runway systems, but also in studying detailed airside design issues, such as figuring out
the best way to remove an airside bottleneck or estimating the amount by which the
capacity of an airport is reduced due to the crossing of active runways by taxiing aircraft.
However, these simulation models still involve considerable expense, as well as require
significant time and effort and, most importantly, expert users.
2.1.5. The Variability and Unpredictability of the Capacity of Runway Systems
15
The variability of the capacity of runway systems at major airports can now be easily
explained with reference to the previous discussion. There are three main causes of
drastic reductions in airport capacity. Two are related to weather: severe events, like
thunderstorms or snowstorms; and more routine weather events, like fog or very strong
winds. The third major cause is technical or infrastructure problems, such as air traffic
control equipment outage or the temporary loss of one or more runways, due to an
incident or accident or to maintenance work. For this last case, it should be noted that
major airports schedule runway maintenance carefully, so as to minimize impact on
airport traffic.
Thunderstorms and snowstorms are events that pose hazards to aviation. Thus, they
impede severely the flow of air traffic into and out of airports and through major portions
of affected airspace. They carry the potential for even shutting down airports completely
for several hours and, occasionally for a few days at a time in the case of snowstorms.
The more routine events can be much more frequent, such as heavy fog at the San
Francisco, Milan and Amsterdam airports or strong winds in Boston. These typically
cause a severe reduction of capacity, from the best levels achievable in VMC to levels
associated either with IMC or with non-availability of some runways due to winds. The
FAA in a 2001 study compared the maximum throughput capacities of the 31 busiest
commercial airports in the United States under optimum weather conditions, with the
capacity of the most frequently used configuration in IMC (FAA, 2001). The study
found that, on average, the capacity was reduced by 22% in the latter case, with 8 of the
31 airports experiencing a capacity reduction of 30% or more! Note that other, less
frequently used IMC configurations at these airports often have even lower capacities.
The overall effect of weather on an airport’s capacity can be summarized conveniently
through the capacity coverage chart (CCC), which is essentially a plot of the probability
distribution of available capacity over an extended period of time such as a year. An
example for Boston’s Logan International Airport (BOS) is shown in Figure 2.3. (The
CCC is somewhat simplified to indicate only five principal levels of capacity.) It
indicates that the capacity varies from a high capacity of 115 movements or more per
hour, available for about 77% of the time – the leftmost two levels of capacity – and
associated with the most favorable VMC, to a low of about 55-60 movements per hour
for about 6% of the time and associated with low IMC. (The airport also has capacity of
zero, meaning it is closed down due to weather conditions, about 1.5% of the time.) One
of the two intermediate levels of capacity (third from left) of about 94 movements per
hour is associated with the presence of strong westerly winds in VMC. As mentioned in
the previous section, these force the airport to operate with only two active main
runways. To prepare the CCC, it is necessary to examine historical hourly weather
records (visibility, cloud ceiling, precipitation, winds) for a long period of time (e.g., five
years) and identify the capacity available at each of these hours.
The CCC is drawn under the simplifying assumptions that (a) the mix of arrivals and
departures is 50%-50% and (b) the airport is operated at all times with the highestcapacity configuration that can be used under the prevailing weather conditions. While
neither of these assumptions is exactly true in practice, the CCC nonetheless provides a
16
good indication of the overall availability of capacity during a year, as well as of the
variability of this capacity. Obviously a CCC that stays level for the overwhelming
majority of time – as one might expect to find at airports that enjoy consistently good
Capacity Coverage: BOS
140
120
ru
oh100
re
ps 80
tn
e 60
m
ev
o 40
M
20
0
0
20
40
60
% of time
80
100
Figure 2.3 The capacity coverage chart for Boston Logan International Airport.
weather – implies a more predictable operating environment than the “uneven” CCCs of
BOS, SFO, LGA and other airports where weather is highly variable.
Although the associated technology is improving, meteorological forecasts still have not
attained the level of accuracy and detail needed to eliminate uncertainty from predictions
of airport and airspace weather, even for a time-horizon as short as one or two hours.
When it comes to impact on the operations of any specific airport, the challenge is
twofold: predicting the severity of an anticipated weather event at a quite microscopic
level; and, equally important, determining narrow windows for the forecast starting and
ending times of the event. For example, a few hundred feet of difference in the cloud
ceiling or the presence or absence of “corridors” for the safe conduct of approaches and
departures in convective weather may make a great difference in the amount of capacity
available at an airport. Similarly, over- or under-predicting by just one hour the ending
time of a thunderstorm may have major implications on a Ground delay program (see
Section 4) and, as a result, on the costs and disruption caused by the associated delays
and flight cancellations.
2.2. The Capacity of Airspace Sectors
17
Within the airspace itself, safety concerns and the need to separate aircraft leads to yet
another set of constraints. The most prevalent of these is associated with a sector. A
sector is a volume of airspace for which a single air traffic control team of one or two
individuals has responsibility. The principal constraint on the number of aircraft that can
safely occupy a sector simultaneously is controller workload. Both in North American
and in European airspace, it is generally accepted that this number should not exceed the
8-15 range, depending on a number of factors. This limitation, in turn, translates to
typical upper limits of the order of 15-20 on the number of aircraft that can be scheduled
to traverse a sector during a 15-minute time interval in U.S. en route airspace. This
capacity may be reduced significantly in the presence of severe weather.
Because of its heavy dependence on controller workload, it is difficult to compute the
capacity of a sector, in terms of either the number of simultaneously present aircraft or
the number of aircraft traversing the sector per unit of time (Wyndemere, 1996; Sridhar,
Seth and Grabbe 1998). Numerous factors affect the complexity of the controller’s task.
Hinston et al (2001) classify these into three major categories:
(a) Airspace factors: sector dimensions (physical size and shape, area that the
controller must effectively oversee); spatial distribution of airways and of
navigational aids within the sector; number and location of standard ingress and
egress points for the sector; configuration of traffic flows (number and orientation
relative to the shape of the sector, complexity of aircraft trajectories, crossing
points and/or merging points of the flows); and complexity of required
coordination with controllers of neighboring sectors (e.g., for “hand-offs” of
aircraft from one sector to the next).
(b) Traffic factors: number and spatial density of aircraft; range of aircraft
performance (homogeneous traffic vs. many different types of aircraft with
diverse performance characteristics); complexity of resolving aircraft conflicts
(which depends on many variables); sector transit time.
(c) Operational constraints: restrictions on available airspace, e.g., due to the
presence of convective weather or of special use airspace; limitations of
communications systems; and procedural flow restrictions at certain waypoints
(see Section 4.1.2) or noise abatement procedures in place.
Several attempts have been made in recent years to develop quantitative relationships
between some of these factors and controller workload – see, e.g., Manning et al (2002).
To deal with this complexity and handle a large number of aircraft, controllers attempt to
introduce a “structure” to the traffic patterns they handle. Examples include (Hinston et
al, 2001): spatial standardization of the flows of aircraft within sectors along specific
paths; consideration of aircraft in groups, with members of each group linked by common
attributes; and concentration around a few “critical points” of the location of potential
aircraft encounters or of other occurrences requiring controller intervention.
In order to effect such structuring, flow may usually be directed through a few waypoints
or fixes, which have an associated maximum flow rate. These maximum flow rates can
be derived from minimum separation standards or alternatively the maximum rates can be
18
specified by the ATM system itself in order to limit the amount of flow passing
downstream. In this latter case, the maximum flow rate can be viewed as a control
variable.
Finally, it is noted that airspace constraints typically have a less severe effect on airline
operations than airport constraints. This is especially true in the more flexible ATM
environment of the United States. The reason, quite simply, is that a capacity-constrained
en route sector can often be bypassed at limited cost by selecting an alternative route,
whereas a flight has no choice but to eventually end up at its destination airport.
3. Restricting Schedules
3.1. Options and Current Practice on Airport Scheduling
With the background of Section 2, we can now proceed to review how the two principal
types of airspace system stakeholders attempt to deal with unpredictable and variable
capacity constraints in daily operations. This and the next section will discuss strategies
associated primarily with ATM service providers (Civil Aviation Authorities and other
national and international organizations) while Sections 6 and 7 will present the strategic
and tactical options available to the airlines.
To ATM service providers (e.g., the FAA) two approaches are essentially available. One,
restricting schedules (RS), is of a static and “pro-active” nature as it places, in advance,
limits on the maximum number of aircraft movements that can be scheduled during a unit
of time at an airport or other airspace element. The second, ATFM, is dynamic and
reactive: its goal is to prevent airport and airspace overloading by adjusting in “real time”
the flows of aircraft on a national or a regional basis in response to actual conditions. In
essence, the focus of RS is on controlling the number of scheduled operations through
airspace elements and of ATFM on controlling the number of actual operations through
these elements, given a schedule. This section reviews briefly the RS approach, while the
next deals more extensively with ATFM.
A far more frequently used term for RS, especially among aviation policy-makers, is
“demand management”. It refers to any set of administrative and/or economic policies
and regulations aimed at constraining the demand for access to airspace elements during
certain times when congestion would otherwise be experienced. This term is avoided
here, because it may cause confusion with a major aspect of ATFM, which is also
concerned with “managing demand” in a dynamic way in order to match it with available
capacity.
RS is not used currently in the United States, with the exception of four airports (New
York LaGuardia and Kennedy, Chicago O’Hare and Washington Reagan) where limits
on the number of movements that can be scheduled per hour – the so-called “high-density
rules” (HDR) – have existed since 1968. The HDR will be phased out by 2007 according
to the so-called AIR-21 legislation of 2000 and, in fact, in some cases, e.g. Chicago, the
restrictions have already been relaxed. However, RS is widely practiced outside the US:
19
about 140 of the world’s busiest airports are “fully coordinated”, meaning that they place
strict limits on the number of movements that the airlines can schedule there. These
airports serve the great majority of air travelers outside the US every year.
The concept underlying RS is the declared capacity, i.e., a declared limit on the
maximum number of air traffic movements that can be scheduled at an airport per unit of
time. At a few airports, separate limits are specified for the number of landings, the
number of takeoffs and the total number of movements. The typical unit of time is one
hour, but some airports use finer subdivisions of time. At a few airports, the declared
capacity may also vary by time of day, e.g., more departures than arrivals may be allowed
during certain hours and vice versa for other hours.
The declared capacity is determined by the capacity of the most restricting element of the
airport – the so-called “bottleneck element”. In most cases, this is the runway system of
the airport. However, the bottleneck element can also be the passenger terminal, or the
apron area, or some other part of the airport. Even in such cases, the computed limit (e.g,
the number of passengers that can be scheduled per hour at the passenger terminal) is
converted to a declared limit on the number of air traffic movements.
The RS approach – and the concept of declared capacity – can be extended to air traffic
control sectors. The declared capacity in this environment is primarily determined by
workload considerations, as noted in Section 2.2, taking into consideration traffic
patterns, traffic mix, route configuration, etc. EUROCONTROL, the agency that
coordinates air traffic management systems over Europe, in effect uses such capacity
figures for en route sectors in its six-month advance planning of traffic loads in European
airspace.
3.2. Critical Issues Regarding Restricting Schedules
If traffic volumes at airports and airspace sectors are restricted to levels that can be
handled comfortably all the time, the RS approach can clearly be effective in reducing
major delays and important schedule disruptions. However, the approach is also
characterized by several fundamental problems, three of which are described here. First,
implicit in the approach is the need to make a tradeoff between delays, on the one hand,
and resource utilization, on the other, on the basis of only very aggregate information.
Consider, for example, the case of Boston’s Logan International Airport (BOS). As
suggested by Figure 2.3, the maximum achievable arrival rate at BOS under favorable
weather conditions (visibility, cloud ceiling, winds, precipitation) is around 60 per hour.
Such conditions prevail about 77% of the time. During the other 22%, the maximum
arrival rate is lower – and can be as low as 30 per hour for about 6% of the time. Were
BOS to declare an arrival capacity of 60 (and assuming that the airlines and general
aviation operators actually scheduled that many movements), delays at BOS would reach
high to unacceptable levels during about 22% of the peak traffic hours over any extended
span of time, such as a year. On the other hand, declaring an arrival capacity of 30 would
practically ensure the absence of serious delays, but would result in gross underutilization
of the airport’s resources most of the time. In general, one should note that any choice of
20
the value of the declared capacity must be made on the basis of very aggregate statistical
information: when an airport “declares a capacity” for the next six months (as is currently
done under the process organized by IATA – see below), all it has to go on is historical
statistics about weather conditions at the airport and the resulting available capacity. By
contrast, as described in Section 4, the ATFM approach uses real-time capacity forecasts
with a maximum time-horizon of about 12 hours. In this light, it is not surprising that no
single, internationally accepted methodology exists today for determining and setting the
declared capacity of airports and airspace sectors. Practices vary greatly from country to
country and, in some cases, from airport to airport within the same country. Some major
international airports in Europe and in Asia clearly opt for allowing for a considerable
margin of “comfort” by declaring very “conservative” capacities, i.e., capacities near the
low end of the available range. This results in wasting significant amounts of extremely
valuable capacity.
The second problem with RS is the way it is currently practiced. The declared capacities
of the major airports, as updated at six-month intervals, are communicated to
international aviation authorities and to the airlines and serve as the basis for scheduling
airline operations at busy airports during the international Schedule Coordination
Conferences (SCC) that are organized by the International Air Transport Association
(IATA) and take place in November and June every year. During the SCC, a “schedule
coordinator” allocates the available capacity (“slots”) among the airlines that have
requested access to each fully coordinated airport. If the number of available slots is
insufficient to satisfy demand, then some requests are simply denied. The criteria used to
allocate slots are described in detail in IATA (2000) and discussed in de Neufville and
Odoni (2003). For our purposes, it is sufficient to note that the dominant and overriding
criterion is historical precedent: an airline which was assigned a slot in the same previous
season (“summer” or “winter”) and utilized that slot for at least 80% of the time during
that previous season is automatically entitled to the continued use of that “historical slot.”
No economic criteria are used for slot allocation and, in fact, buying and selling of slots
is prohibited – at least, under the official rules. The net result is that some of the older,
traditional airlines maintain in this way a “lock” on most of the prime slots at the world’s
most economically desirable airports. Airlines that wish to compete in these markets and
may be willing to pay high fees for the right to operate at the airports in question are
effectively “frozen out”.
Third, and perhaps most important, the RS approach, as currently practiced, distorts the
functioning of the marketplace and suppresses potential demand by placing an arbitrary
cap on the number of operations at some of the world’s busiest airports. This, in turn,
creates an illusionary equilibrium, i.e., an artificial balance between demand and
capacity. Thus, current RS practices do not provide decision-makers with true
information about the economic value that airspace users and the traveling public may
attach to additional capacity at the schedule-coordinated airports or at other elements of
the airspace.
A great deal of research has been performed over the years on these and related issues,
focusing primarily on the second of the problems described above and, to a lesser extent,
21
on the third. Several classical and more recent papers have dealt with the application of
“market-based” mechanisms, typically in combination with administrative measures, to
improve the current capacity allocation process of IATA – see Vickrey (1969), Carlin and
Park (1970), Morrison (1987), Daniel (1995), DotEcon Ltd (2001) and Ball, Donohue
and Hoffman (2005), for a sample. Such papers examine the use of congestion pricing
and of slot auctioning at major airports. Interestingly, some ongoing research on realtime capacity allocation and slot-exchange mechanisms in connection with ATFM – see,
e.g., Vossen and Ball (2005b) and Ball, Donohue and Hoffman (2005) – has also focused
on market-based approaches (see also Section 4.4).
Other recent work has investigated less generic issues related to computational and
implementation issues associated with such approaches. For example, advances in the
application of queuing theory have facilitated greatly the estimation of external delay
costs (Andreatta and Odoni 2003). Fan and Odoni (2002) and Hansen (2002) report
applications of queuing methodologies to the detailed estimation of external delay costs
at New York/LaGuardia and Los Angeles International, respectively. These independent
studies come up with strikingly similar results: many flights at these airports impose
external delay costs which exceed by at least an order of magnitude the landing fees these
flights pay. For example, Fan and Odoni (2002) estimate that the external delay cost per
movement for much of the day at New York/LaGuardia was about $6000 in August
2001, whereas the average fee per movement amounted to about $300. The implication
is that access to many busy airports may be greatly under-priced, thus attracting excessive
demand, which exacerbates congestion. This is especially true in the United States where
landing fees are comparatively very low. A third area of recent research addresses some
difficult problems that set the application of market-based mechanisms at airports apart
from analogous applications in other contexts. For example, Bruckner (2003) and Fan
(2003) point out that each airline operates a (possibly large) number of flights at airports,
in contrast to highway traffic where each user operates a single vehicle. When any single
airline operates a large fraction of the total movements at an airport, it also automatically
absorbs (“internalizes”) a similarly large fraction of the external delay costs that its
flights generate. That airline should therefore be charged only that portion of the external
costs that it does not internalize. But a pricing system under which different airlines
would pay different landing fees for the same type of aircraft would be both controversial
and technically difficult to implement. This and other complications, along with the
presence of many social policy objectives (service to small communities, access to
airports by regional carriers and by general aviation, etc.) suggest that any future RS
schemes that incorporate market-based features, will be governed by a complex set of
rules that may include exemptions, subsidies for certain carriers, slots reserved for certain
types of flights, etc.
4. Air Traffic Flow Management
4.1. Background and ATFM Controls
4.1.1. Basic Premises
22
Air traffic management (ATM) is now viewed as consisting of a tactical component and
a strategic component. The tactical component, Air Traffic Control (ATC), is concerned
with controlling individual aircraft on a time horizon ranging from seconds to 30 minutes
for the purpose of ensuring safe separation from other aircraft and from terrain. The
strategic component, Air Traffic Flow Management (ATFM) works at a more aggregate
level and on a time horizon of up to about 12 hours in the United States and 48 hours in
Europe. Its objective is to ensure the overall unimpeded flow of aircraft through the
airspace, so as to avoid congestion and delays and, when delays are unavoidable, to
reduce as much as possible their impact on airspace users.
The primary airports and primary airspace are dominated by the operations of scheduled
air carriers. Air carrier schedules generate airspace demand and also serve as the basis
for measuring the performance of ATFM systems. The fundamental premise of ATFM is
that, roughly speaking, if all operations occurred at their scheduled times and if all
airspace elements were in their “normal” operating states, then there would be little need
for any flow management. Under such ideal conditions – and with the possible exception
of some brief periods at a few of the busiest airports – demand on all airspace elements
would be less than capacity and operations would generally proceed as if there were no
constraints. But ATFM recognizes that the complexity of the airspace system, its
susceptibility to weather conditions and the large number of possible ways in which
equipment and/or operations can fail to operate as planned, all imply that the probability
that the entire system will operate exactly according to schedule on any given day is
essentially zero. ATFM procedures are therefore in greatest demand when there are
significant imbalances between capacity and demand on airspace elements, usually
caused by capacity reductions due to weather or equipment failures. Demand surges can
also cause capacity-demand imbalances. Such surges may occur, for example, when
problems early in the day cause the postponement of scheduled operations into a time
interval that already contained significant numbers of operations. Additionally, the
number of unscheduled flights is growing and is having a greater impact on overall
system performance. Finally, as the number of scheduled operations has increased, there
have been instances where scheduled demand actually exceeded the capacity of network
elements for extended time periods each day. Probably the most notable example along
these lines occurred at LaGuardia airport between May 2000 and February 2001, i.e.,
during the period between enactment of the so-called Air-21 legislation – which opened
access to LaGuardia for certain types of flights – and the imposition of slot lotteries
aimed at relieving the resulting congestion. In such cases, even the routine operation of
the air transportation system requires the use of ATFM procedures.
23
4.1.2 Controls
ATFM performance is measured primarily with reference to deviations from schedules.
That is, ATFM systems generally seek to minimize the amount of time by which actual
operations (most importantly, the arrivals of aircraft at their destination airports) deviate
from scheduled operations. Thus, the key performance indicators usually involve
measures of delay. The next fundamental question to consider in describing and
analyzing ATFM systems is what controls can be used to impact system performance.
Before directly addressing this question we discuss two basic characteristics of controls:
who makes and implements the control decisions and what are the timing constraints
associated with the control. The two critical entities involved in ATFM decisions are the
air traffic service providers and the airspace users. Airspace users could range from the
owner/operator of a general aviation aircraft to a large air carrier. Within a large air
carrier there can be multiple decision-makers: most central to this discussion are the
airline operational control centers (AOCC) and the pilots. On the air traffic service
provider side, the units involved are the regional air traffic control centers (Air Route
Traffic Control Centers -- ARTCC in the U.S.), as well as the central traffic flow
management units (Air Traffic Control System Command Center – ATCSCC in the
U.S.). Properly distributing decision-making among all these entities can be critical to
the success of ATFM systems and is at the heart of the recent emergence of the
Collaborative decision making (CDM) paradigm, which is described in Section 4.3. The
time constraints associated with control actions can greatly impact the manner in which
they can be applied and the manner in which multiple actions can be coordinated. The
key issue, in this respect, is the length of time that elapses between a control decision and
the implementation of that decision. A rough categorization is that strategic decisions are
typically made hours in advance of implementation, whereas tactical decisions involve
shorter time scales. Generally, the appropriateness and effectiveness of any particular
control action, strategic or tactical, depend on system dynamics and on the level of
uncertainty associated with future states of the airspace system.
We now describe the most important types of ATFM control actions.
Ground holding (including ground stops): Ground holding involves delaying the
departure of a flight in order to avoid overloading a capacitated system element. Ground
holding is most often implemented in the U.S. through a Ground delay program (GDP),
which is put into effect when the demand for arrivals into an airport is predicted to
exceed significantly the arrival capacity. In Europe, ground holding is commonly used to
avoid overloading of en route sectors. Ground holding is generally considered a strategic
decision. A “ground stop” is a more tactical and extreme form of ground holding,
whereby all departures of aircraft bound for a particular destination airport are
temporarily postponed. A ground stop typically applies only to a specified set of airports,
usually ones that are proximate to the affected destination airport. In the past, air traffic
service providers were the sole decision makers when it came to decisions regarding
ground holding. More recently, however, CDM procedures have led to shared decision
making with airspace users.
24
Airborne speed control and airborne holding: Airborne speed control and airborne
holding are tactical controls used to avoid overloading (en route or terminal) airspace
elements by adjusting the time at which flights arrive at those elements. Speed controls
can involve simply slowing down or speeding up aircraft or aircraft vectoring
implemented through minor directional detours. Airborne holding is usually
implemented by having aircraft fly in oval-shaped patterns. The providers of air traffic
services usually make these control decisions.
Route choice and route adjustments: Generally speaking airspace users control route
choice. As discussed at the beginning of Section 2, airline and general aviation operators
choose and file flight plans based on several criteria including winds and other weather
conditions, fuel usage, en route turbulence predictions, safety constraints, etc. Flight
plans may be filed several hours in advance of departure but in many cases are not filed
until shortly before departure (even within an hour of departure) in order to take
advantage of the most recent information on weather conditions and congestion. For
purposes of managing congestion, air space managers can reject flight plans leading to
new filings. In some cases, standard reroute strategies are specified, e.g. the air space
manager designates that all flights originally filed along one airspace path should re-file
along a second alternate path. A variety of more tactical route adjustments are possible.
For example, alternative “departure routes” might be specified by an airline; then,
immediately before departure, one would be chosen based on a negotiation process
between the airspace manager and user. Once airborne, major or minor route adjustments
might be made. These decisions generally involve some level of collaboration between
the regional air traffic service provider and the pilot or AOCC. A very extreme form of
route adjustment is the diversion of a flight, which involves altering its destination
airport.
Flight cancellations: The cancellation of a flight is another drastic, although not
particularly unusual, ATFM measure. Responsibility for flight cancellations always rests
with the airline or the general aviation operator.
Arrival sequencing: The sequencing of flights can be very important as the maximum
arrival rates into airports depend on the sequence and mix of aircraft types (Section
2.1.3). Due to the uncertainty of en route operations this should be considered a tactical
decision. Primary responsibility in this respect rests with the air traffic service provider,
although CDM concepts are now being applied to this setting, leading to some air carrier
participation in sequencing decisions.
Airport arrival or departure rate restrictions: As discussed in Section 2, there can be a
tradeoff between the maximum airport arrival and departure rates. Evaluating this
tradeoff and setting these rates should be considered a tactical decision that traditionally
is made by regional air traffic service providers (Gilbo 1993, 1997). Proposals to allow
air carrier participation in this decision have been made (Hall 1999).
Waypoint flow restrictions: An important and widely used control within the U.S.
airspace system is the so-called miles-in-trail (MIT) restriction. Regional air traffic
25
service providers impose such restrictions in order to ensure that the flow of aircraft into
a region of airspace is kept at a safe level. When such a restriction is put in place, the
adjacent “upstream” regional air traffic service provider has responsibility for
maintaining a traffic flow at or below the restricted level. This can be done in a variety
of ways, including the use of airborne holding, rerouting of some traffic and issuing
similar flow restrictions on flights further upstream. In this way, it is possible for a flow
restriction to propagate through much of the airspace system, possibly eventually leading
to ground holds at airports of origin.
4.2 Deterministic Models
Using as a starting point the capacity constraints described in Section 4.1, one can
formulate large-scale optimization models that map airspace demand onto the various
elements of the airspace in such a way that all capacity constraints are respected. Such
models trace flights through both space and time and seek to minimize some global
demand function. In Section 4.2.1 we describe a large-scale comprehensive modeling
approach and then, in Section 4.2.2, specialize this model to the ground holding problem.
4.2.1
Global Models
There are two broad classes of global air traffic flow models. The first assumes that the
trajectory (route) of each flight is fixed and optimizes the timing of the flight’s
operations. The second allows the route of each flight to vary, as well. Clearly, the
second type of model has a much larger decision space.
We start with models of the first type. The modeling approach chooses a time horizon of
interest and decomposes it into a discrete set of time intervals. A geographic scope is
also selected. This determines the set of capacitated elements under consideration,
including airports, sectors and waypoints. The combination of the model’s temporal and
geographic scope determines the set of flights to be considered. The basic decision
variable specifies the airspace element occupied by a flight at each time interval, i.e.,
xfte =
1
0
if flight f occupies airspace element e during time interval t;
otherwise.
For airports, the capacitated airspace element would be either the airport’s arrival or
departure component. For example, LaGuardia Airport (LGA) would be represented by
an arrival element LGA1 and a departure element LGA2, with xf1,t,LGA1 indicating the time
interval t of a flight f1’s arrival to LGA and xf2,t,LGA2 indicating the time interval t for
flight f2’s departure from LGA.
The capacity constraint associated with an element e and time interval t is of the form:
∑f xfte ≤ cap(t,e)
for all t and e,
26
where cap(t,e) is the capacity of element e during time interval t. For airport arrival and
departure capacities and for waypoints, cap(t,e) is equal to the maximum number of
flights that could flow through that element during time interval t. For a sector, it is equal
to the maximum number of flights that can occupy the sector simultaneously.
The remaining constraints define temporal restrictions on the manner in which each flight
can progress through the airspace. For example, they might specify that, once a flight
enters a sector, it must remain in the sector for 3, 4 or 5 time intervals. In this case, 3
time intervals would correspond to traversing the sector on a direct path at maximum
speed and 5 time intervals might correspond to a longer traversal time based on
application of some type of speed control. We note that since the flight’s route is an
input, the progression from departure airport through a specific sequence of sectors to a
destination airport is a fixed model input, as well.
Bertsimas and Stock Paterson (1998) have shown that models of this type can be solved
very efficiently. Of particular note is their use of an alternative set of decision variables.
Specifically, the xfte variables are replaced with a set, wfte, defined by:
wfte = 1
0
if flight f arrives at airspace element e by time interval t;
otherwise.
While the w variables can be obtained from the x variables through a simple linear
t
transformation (wfte = ∑ x fse ), the w variables are much easier to work with because they
s =1
produce very simple and natural temporal progression constraints. Further, the associated
linear programming relaxations are very “strong” in the sense that they lead to the fast
solution of the associated integer programs. Bertsimas and Stock Patterson show that a
variety of additional features can be included in the model, including the propagation of
delays that occurs when a delay in the arrival of a flight arrival causes the delay of an
outbound flight that uses the same aircraft. The model can also capture the dependence
between an airport’s arrival and departure capacities and choose the appropriate
combination of the two for each time interval.
A second type of model also allows for flight routes to vary. Bertsimas and Stock
Paterson (2000) extend the model described above to this case. Since the decision space
becomes much larger, aggregate variables and approximate methods must be employed in
order to solve problems of realistic size.
4.2.2
Deterministic Ground Holding Models
A simple, yet very important special case of the model just described is the deterministic
ground holding problem. For this problem, en route constraints and airport departure
constraints are ignored leaving only a constraint on arrival capacity. These assumptions
allow a large multi-airport problem to be decomposed into separate problems, one for
each arrival airport. This model is very important to the U.S. ATFM environment since it
underlies the Ground delay programs (GDP) as currently operated. Although the control
27
variable for a GDP is ground delay at the origination airport of each flight, the problem
can be modeled as one of assigning flights to arrival time intervals at the destination
airport. For each flight a (constant) en route time is then subtracted from the arrival time
to obtain a departure time, which in turn implies an amount of ground delay at the
origination airport.
Define the following inputs: for a set of time intervals t (t = 1, 2,…, T) and set of flights f
(f = 1, 2,…, F), let
bt
e(f)
cft
= the constrained airport’s arrival capacity at time interval t,
= the earliest time interval at which flight f can arrive at the constrained
airport,
= the cost of assigning flight f to arrive at time interval t,
and the variable:
xft =
1
0
if flight f is assigned to time interval t;
otherwise.
Then, the deterministic ground holding problem can be formulated as:
Min
s.t.
∑f ∑t cft xft
∑f xft
≤
bt
∑t≥e(f) xft
=
1
xft ≥ 0 and integer
for all t,
for all f,
for all f and t.
As can be seen, this is a simple transportation model that can be solved very efficiently.
This model was first described in Terrab and Odoni (1993). In Ball et al (1993), various
issues related to its practical use were investigated. In particular, it was suggested that
the definition cft = rf (t – e(f))1 + ε is attractive since flight delay costs tend to grow with
time at a greater than linear rate. In addition, solutions produced using this objective
function are attractive from the standpoint of equity or fairness – see Vossen and Ball
(2005a) for a detailed discussion of this issue. Hoffman and Ball (2003) investigate
generalizations of this model that preserve the proximity of banks of flights associated
with airline hubbing operations. Vranas, Bertsimas and Odoni (1994) describe a multiairport version of the problem where both airport arrival and departure rates are
constrained and flights are “connected” to each other, in the sense that the late arrival of a
flight f at an airport may also imply the late departure of one or more subsequent flights
from that airport. This can happen if the departing flight must use the same aircraft as
flight f or, less obviously, if flight f carries many transfer passengers who must board
subsequent departing flights.
4.3 Uncertainty and Stochastic Models
Uncertainty on multiple levels has led to the failure of many attempts at practical
implementation of various air traffic flow management models. This is particularly true
28
for models that attempt to optimize over a broad geographic area and/or extended periods
of time. To be effective, models must include stochastic components explicitly or they
must address problems restricted to limited geographic and time domains for which
available information is less subject to uncertainty. We use the term demand uncertainty
to describe the possibility that, due to random or unforeseen events, flights may deviate
from their planned departure or arrival times or from their planned trajectories.
Similarly, capacity uncertainty refers to the possibility that random or unforeseen events
will cause changes to the maximum achievable flow rates into and out of airports or
through airspace waypoints or to the maximum number of flights that can occupy
simultaneously a portion of the airspace. Examples of factors contributing to demand
uncertainty include problems in loading passengers onto an aircraft, mechanical
problems, queues on the departure airport’s surface or in the air and en route weather
problems. Examples of factors contributing to capacity uncertainty include weather
conditions at an airport or in the en route airspace, failures or degradation of air traffic
control equipment, unavailability of air traffic control personnel and random changes in
flight sequences and aircraft mix that require alterations of anticipated flight departure or
arrival spacing.
The largest body of work in this area has focused on ground holding models that
explicitly take into account uncertainty in airport arrival capacity. These models are
covered in Section 4.3.1. There is a less extensive body on work on capacity uncertainty
for GDPs, which is covered in Section 4.3.2.
The performance of a GDP planning and control system can be evaluated based on three
measures: the total assigned ground delay, the total airborne delay and the utilization of
the available arrival capacity. Figure 4.1 illustrates a generic model (Odoni, 1987) that is
convenient for evaluating the tradeoffs among these three performance criteria and for
understanding how they are impacted by demand and capacity uncertainty. The airport’s
arrival component (terminal airspace and runways) is viewed as a server subject to
demand uncertainty. The assigned ground delay (the control mechanism) and the random
events that perturb the planned arrival stream of flights determine the rate of arrivals at
the server. Thus, demand uncertainty impacts the rate of arrivals at the server and
capacity uncertainty impacts the service rate. The planning and control of a GDP must
balance the possibility of too low an arrival rate, which leads to underutilization of the
server, with too high an arrival rate, which leads to a large airborne queue and excessive
airborne delay. Generally speaking because of demand and capacity uncertainty, the
“best” policy calls for some degree of airborne delay in order to ensure an acceptably
intensive utilization of the available arrival capacity. The starting point for defining
airport arrival capacity is specifying the number of flights that can land within a time
interval (this quantity is referred to as the airport acceptance rate – AAR). A key
observation in light of this discussion is that the presence of demand and capacity
uncertainty makes it necessary to distinguish between the planned AAR (PAAR) and the
actual AAR. In the following two sections we discuss two types of models: those that
assign ground delay to individual flights and those only concerned with determining a
PAAR vector. The second objective (determining a PAAR vector) is appropriate in the
context of Collaborative Decision Making (CDM), where the assignment of ground
29
delays to individual flights results from a complex set of distributed decision making
procedures. Thus, the second set of models is the one more directly geared to the CDM
environment. Interestingly, some models in the first set can also generate the same
PAAR vectors through a simple “post-processing” step, as has been shown by Kotnyek
and Richetta (2004).
reduced
arrival
capacity
origin airports
airborne
queue
ground delay
airborne
delay
destination
airport
airport
throughput
Figure 4.1: Schematic representation of a single-airport GDP
4.3.1
Ground Holding Models with Stochastic Airport Capacity
As discussed in the previous section, optimization models for the ground holding
problem subdivide time into an arbitrary number of discrete intervals. Typical time
intervals might be 10 or 15 minutes or even as much as 1 hour for the most aggregate
models. One would then characterize the AAR over a period of time, e.g. four hours, as a
vector that provides the AAR in each of the constituent time intervals. In a typical GDP
caused by a weather disturbance that moves through a region, the AAR would start at its
normal level, e.g. 60 arrivals per hour, decrease to one or more degraded levels, e.g. 30
arrivals per hours, for several time intervals, e.g. 4 hours, and then return to its original
level. If it were known that such a scenario would occur with certainty, then a
deterministic ground holding model (Section 4.2.2) could obviously be used with this
scenario providing the capacity constraints input. By contrast, stochastic models treat the
AAR as a random variable and use as input several such scenarios together with
associated probabilities. For example, an “optimistic” scenario indicating no capacity
degradation would consist of a vector of hourly AARs of 60 throughout the period of
interest, whereas, a more pessimistic scenario might assume that the AAR will be 30
during every hour in the period. The input can thus be characterized as
Dtq
pq
= AAR for time interval t under scenario q, for t = 1,…, T and q = 1,…, Q.
= probability of the occurrence of scenario q, for q = 1, …, Q.
The xft variables are then defined as in the deterministic ground holding model, but the
capacity constraints are replaced with a new set of scenario-based constraints and
associated variables. The new variable set is defined by:
30
ytq
= the number of flights held in the air from time period t to t+1, under
scenario q, for q = 1,…, Q.
The new set of capacity constraints then is:
Σf=1,F xft + yt-1 q - ytq ≤ Dtq
for t = 1,…,T and q = 1,…,Q.
Thus, under these constraints, there is a separate capacity for each scenario. However,
the y variables allow for flow between time intervals, so the number of flights assigned to
land in an interval under a particular scenario can exceed the AAR by allowing excess
flights to “flow” to a future time interval. Note that this set of capacity constraints
defines a small network flow problem for each q, with flights “flowing” from earlier time
intervals to later ones. To be feasible, for each given q, the total arrival capacity for the
entire period of interest, Σt Dtq, must be at least as large as the total number of flights (F).
The objective function for the model minimizes the sum of the cost of ground delay plus
the expected cost of airborne delay. If we define ca as the cost of holding one flight in the
air for one time period then we can define the objective function as:
Min: Σf=1,F Σt=1,T cft xft + Σq=1,Q pq Σt=1,T ca yt-1 q.
This class of model was first described in Richetta and Odoni (1993) and a dynamic
version was given in Richetta and Odoni (1994). Ball et al (2003a) defines a simpler
version of this model that computes a PAAR vector (i.e., the total number of flights
assigned to arrive during each time interval in the period) rather than an assignment of
ground delay to individual flights or groups of flights. This model was created in order to
be compatible with CDM procedures, which will be discussed in Section 4.4. The
constraint matrix of the underlying integer program is the transpose of a network matrix,
allowing the integer program to be solved using linear programming or network flow
techniques. Inniss and Ball (2002) and Wilson (2004) describe recent work on estimating
arrival capacity distributions. Willemain (2002) develops simple GDP strategies in the
presence of capacity uncertainty and also takes into account the possibility of flight
cancellations. Inniss and Ball (2002) also presents a dynamic approach to this problem.
4.3.2
Modeling Demand Uncertainty
Recent experience with new decision support tools for planning and controlling GDPs
has strongly suggested that demand uncertainty is the reason that these tools have not
performed quite as strongly as expected. In this context, demand uncertainty refers to
differences between the planned and actual characteristics of the stream of flights arriving
at the destination airport. These differences can be attributed to three categories of
causes: (1) cancellations – flights in the planned arrival stream that are absent from the
actual arrival stream during the planning time period; (2) “pop-ups” – flights that arrive at
the destination airport during the planning time period, but were not in the planned arrival
stream; (3) “drift” – a discrepancy between the actual arrival time of a flight and the
31
flight’s planned arrival time. Ball, Vossen and Hoffman (2001b) present a demand
uncertainty model, where each flight can be cancelled with a known probability, pop-ups
arrive in each time interval according to a binomial distribution and flights drift within
predefined intervals according to a uniform distribution. Considering only cancellations
and pop-ups, the authors provide an optimization model that determines a PAAR that
minimizes airborne delay subject to a constraint on the minimum allowable airport
capacity utilization. This integer programming model contains embedded binomial
distributions. The authors also present simulation results covering all three forms of
demand uncertainty. The results not only provide new PAAR setting policies, but also
give an approach to estimating the benefits of reducing demand uncertainty. For
additional details see Bhogadi (2002) and for a related model Willemain (2002).
4.4 Collaborative Decision Making
The Collaborative decision making (CDM) effort (Ball et al, 2001; Ball et al, 2001a;
Chang et al, 2001; Wambsganss, 1996) grew out of a desire on the part of both the
airlines and the FAA for improvements in the manner in which GDPs were planned and
controlled. The FAA and, more specifically, the ATCSCC had realized the need for
more up-to-date information on the status of flights currently delayed due to mechanical
or other problems or even cancelled unbeknownst to the ATCSCC. Equally important,
the success of GDPs also depends vitally on timely information regarding airline
intentions vis-à-vis flight cancellations and delays over the next few hours. At the same
time, the airlines did not feel the allocation procedures used by the ATCSCC were always
fair and efficient. In addition, each airline wished to gain more control over how delays
were allocated among its own flights. Thus, both the airlines and the FAA had specific
(although different) objectives that motivated their participation in CDM.
The CDM “philosophy”, broadly speaking, represents an application of the principles of
information sharing and distributed decision making to ATFM. Specific goals are:
•
•
•
generating a better “knowledge base” by merging information provided by the
airspace users with the data that are routinely collected by monitoring directly the
airspace;
creating common situational awareness by distributing the same information to
both traffic managers and airspace users;
creating tools and procedures that allow airspace users to respond directly to
capacity/demand imbalances and to collaborate with traffic flow managers in the
formulation of flow management actions.
4.4.1 CDM Resource Allocation Procedures for Ground Delay Programs
CDM brings new modeling requirements to ATFM resource allocation problems
including: considering allocation at a more aggregate level, e.g. by allocating resources to
airlines rather than to individual flights; integrating equity criteria into model objectives
and/or constraints; ensuring that resource allocation mechanisms provide incentives for
information sharing; and developing inter-airline resource exchange mechanisms. These
32
concepts evolved in the process of developing new allocation methods for GDPs. We
describe the GDP procedures here, as well as related recent research and efforts to extend
these ideas to en route ATFM problems.
ration-by-schedule
(RBS)
cancellations
and
substitutions
compression
Figure 4.2: CDM Resource Allocation Procedures
As discussed in Section 4.2.2, the GDP planning problem can be viewed as one of
assigning each flight in the GDP to an arrival time interval (or time slot). Figure 4.2
illustrates the GDP resource allocation process under CDM. The FAA, using Ration-byschedule (RBS), provides an initial assignment of slots to flights. Each airline, using the
cancellations and substitution process, may then cancel flights and modify slot-to-flight
assignments for its own flights (intra-airline exchange). Thus, although RBS, in concept,
allocates slots to flights, the cancellation and substitution process effectively converts the
slot-to-flight assignment into a slot-to-airline assignment. The final step, compression,
which is carried out by the FAA, maximizes slot utilization by performing an inter-airline
slot exchange in order to ensure that no slot goes unused.
The assignment of time slots by RBS can be viewed as a simple priority rule. Using the
scheduled arrival order as a priority order, each flight is assigned the next available
arrival slot. If this rule were applied to all flights and there were no cancellations or
substitutions, then the flights would arrive in their original sequence, but generally later
in time. Two groups of flights are exempted from this basic allocation scheme: (1) flights
that are currently airborne (clearly these cannot be assigned any ground delay) and (2) a
set of flights selected according to the distance of their departure airports from the GDP
(arrival) airport (Ball and Lulli, 2004). The motivation for (2) is to include in the
allocation scheme flights originating from airports that are close to the GDP airport and
to exempt flights from airports further away from the GDP airport. The reasoning is that
flights a greater distance away must be assigned ground delays well in advance of their
actual arrival at the GDP airport, e.g. 4 or 5 hours in advance. At such a long time before
arrival, there tends to be a greater level of uncertainty regarding weather and, as a
consequence, airport arrival capacity. If these distant flights are assigned ground delay,
there is a significant likelihood that this ground delay might prove unnecessary. Thus,
distance-based exemptions constitute a mechanism for avoiding unrecoverable delay, as
well as for increasing expected airport throughput.
After the round of substitutions and cancellations, the utilization of slots can usually be
improved. The reason for this is that an airline's flight cancellations and delays may
create “holes” in the current schedule; that is, there will be arrival slots that have no
flights assigned to them. The purpose of the compression step is to move flights up in the
schedule to fill these slots. The basic premise behind the algorithm currently used to
33
perform compression is that airlines should be “paid back” for the slots they release, so as
to encourage airlines to report cancellations.
FLIGHTS
SLOTS
FLIGHTS
SLOTS
AA826: 1600
1600-1601
AA826: 1600
1600-1601
AA290: 1601
1602-1603
AA290: 1601
1602-1603
UA687: 1602
1604-1605
UA687: 1602
1604-1605
US322: 1602
1606-1607
US322: 1602
1606-1607
UA950: 1602
1608-1609
UA950: 1602
1608-1609
CO822: 1606
1610-1611
CO822: 1606
1610-1611
UA543: 1606
1612-1613
UA543: 1606
1612-1613
AA334: 1607
1614-1605
AA334: 1607
1614-1605
CNX
Figure 4.3: Execution of the CDM Compression Algorithm
To illustrate the compression algorithm, consider the example shown in Figure 4.3. The
left side of the figure represents the flight-slot assignment prior to the execution of the
compression algorithm. Associated with each flight is an earliest time of arrival, and each
slot has an associated slot time. Note that there is one cancelled flight. The right side of
the figure shows the flight schedule after execution of the compression algorithm: as a
first step, the algorithm attempts to fill AA's open slot at 16:02-16:03. Since, there is no
flight from AA that can use it, the slot is allocated to UA, and the process is repeated with
the next open slot, which, using the same logic, is assigned to US. The process is
repeated for the next open slot, which is now assigned to AA. AA thus receives the
earliest slot that it can use. The net result of compression in this case can be viewed as an
exchange among airlines of the slots distributed through the initial RBS allocation.
4.4.2
CDM Concepts, Philosophy and Research Directions
We now investigate the special properties of the CDM resource allocation procedures and
describe how these are being extended and enhanced.
RBS, Compression and Information Sharing: One of the principal initial motivations
for CDM was that the airlines should provide updated flight status information. It was
quickly discovered that the existing resource allocation procedures, which prioritized
flights based on the current estimated time of arrival, actually discouraged the provision
of up-to-date information. This was because, by updating flight status, the airlines would
34
change the current estimate of flight arrival (almost always to a later time), which in turn
changed their priority for resource allocation. On the other hand, the RBS priority, which
is based on the (fixed) schedule, does not vary with changes in flight status. Further, as
in the example of Figure 4.3, compression most often provides an airline with another
usable slot whenever an announced cancellation generates a slot that the airline cannot
fill via the substitution process.
Properties of RBS: We summarize some basic properties of RBS derived in Vossen and
Ball (2005a). RBS assigns to each flight, f, a controlled time of arrival, CTA(f). This is
equivalent to assigning a delay, d(f), to flight, f, given by d(f) = CTA(f) – OAG(f), where
OAG(f) is the scheduled arrival time for f. All time values are rounded to the nearest
minute under RBS, hence, each delay value d(f) is integer. If we let D equal the
maximum delay assigned to any flight and ai = |{f : d(f) = i}| for i = 0 , 1, 2, …, D, then
the important properties of unconstrained RBS (RBS with no flight exemptions) can be
defined by,
Property 1: RBS minimizes total delay = Σf d(f).
Property 2: RBS lexicographically minimizes (aD,…, a1, a0). That is, aD is minimized;
subject to aD being fixed at its lexicographically minimum value, aD-1 is minimized;
subject to (aD, aD-1) being fixed at its lexicographic minimum value, aD-2 is minimized;
and so on.
Property 3: For any flight f, the only way to decrease a delay value, d(f), set by RBS is
to increase the delay value of another flight g to a value greater than d(f).
CDM and Equity: Property 3, which follows directly from Property 2, expresses a very
fundamental notion of equity that has been applied in a number of contexts (Young,
1994). It is remarkable that procedures, such as RBS, which were developed in very
practical war-gaming and consensus-building exercises have such elegant and desirable
properties. On the other hand, this may not be surprising in that these properties
represented the basis for reaching consensus, in the first place. The properties show that
unconstrained RBS produces a fair allocation. However, one should consider whether the
exemption policies described earlier, in fact, introduce bias. Vossen et al (2003) show
that exemptions do introduce a bias and also describe procedures for mitigating these
biases. The approach taken initially computes the unconstrained RBS solution and
defines it as the “ideal” allocation. Optimization procedures are then described that
minimize the deviation of the actual allocation from the ideal. These procedures build
upon approaches developed in connection with just-in-time (JIT) manufacturing for
minimizing the deviation of an actual production schedule from an ideal schedule – see
for example, Balinski and Shihidi (1998). The resulting approaches maintain the
exemption policies, but take into account the “advantages” provided to an airline by its
exempted flights when allocating delays to its other flights.
Compression as Trading: Although the initial interpretation of compression is as a slot
reallocation procedure that maximizes slot utilization, there is also a natural interpretation
of compression as an inter-airline trading or bartering process (Vossen and Ball, 2005a).
For example, in Figure 4.3, American Airlines “traded” the 1602 – 1603 slot, which it
could not use for the 1606 – 1607 slot, which it could use, and United Airlines reduced its
35
delay by trading the 1604 – 1605 slot for the earlier 1602 – 1603 slot. Vossen and Ball
show that a bartering process can be structured so as to produce a result essentially
equivalent to compression. This view of compression suggests many possible extensions.
For example, Vossen and Ball (2005b) define a more complex 2-for-2 bartering
mechanism and show that using this mechanism offers a substantial potential for
improved economic performance. Probably the most intriguing enhancement is allowing
“side payments” with any exchange as well as the buying and selling of slots. Ball,
Donohue and Hoffman (2005) provide a discussion of this and other aviation-related
market mechanisms.
4.5 Air Carrier Response Options
As the implementation of the CDM concept expands, it will become increasingly difficult
to designate certain controls as exclusive to the traffic managers or exclusive to the users
(airlines). In this section we describe the types of actions and types of problems that air
carriers can take in response to ATFM initiatives based on current practices. We start by
noting that the decision on whether or not a flight takes place on a given day rests with
the airlines, with the exception of extreme circumstances. Further, the airlines generally
control the route choice for a flight subject to constraints on access to portions of airspace
exercised by ATFM. The airlines can, of course, at their own discretion choose to delay
the departure of flights. On the other hand, ATFM exercises strong control over the
timing of operations. As described in the previous section, for GDPs in the U.S., ATFM
also exercises control over flight timing by allocating arrival time slots to airlines, which
in turn allocate the slots to individual flights.
For the case of GDPs, we can model an airline’s response problem as one of assigning
flights to the set of time slots that airline “owns”. A first-level approach to this problem
would select an assignment that minimizes the “cost” of the associated flight delays.
Such models should also consider the possibility and cost of canceling flights. Secondlevel models would also consider the downstream effects of the delayed flights. For
example, the immediate downstream effect involves the delays on flights and passengers
outbound from the GDP airport (Niznik, 2001). Broader airline network models would
consider the airport arrival slots as a resource to be allocated as part of a larger
optimization model.
The problem of choosing a route is traditionally addressed on a flight-by-flight basis.
There are a variety of safety regulations that constrain this problem. Typically, weather
conditions, including winds, turbulence, convective activity, etc., play a strong role in
solving this problem. Airspace congestion considerations, as well as ATFM control
actions are also playing an increasingly important role. There can be a high degree of
uncertainty in many of these factors leading to the need for stochastic, dynamic problem
solving approaches – see, for example, Nilim et al (2001). Furthermore, as CDM
concepts become pervasive, the air carriers may be allocated limited airspace resources
that in turn need to be allocated to individual flights. Under such a scenario, flight-byflight route planning may no longer be viable. Berge, Hopperstad and Heraldsdottir
(2003) describe a comprehensive optimization model that includes decision variables for
36
the three controls described earlier, i.e. flight cancellations, aircraft route choice and
ground delay. It assumes an environment in which airspace and airport resources have
been allocated to each airline. This model was developed for integration into a
comprehensive Boeing airspace simulation. It can, however, also be viewed as a
prototype for future operational airline decision models.
Sections 6 and 7 describe models for planning adjustments to airline operations based on
day-to-day changes in airspace conditions and airline resource status. Such models
typically are only invoked in the case of reasonably significant disturbances to “normal”
conditions and the underlying environment is called irregular operations. While these
models take into account some of the concepts described in this section, a full integration
of the emerging ATFM CDM philosophy with airline planning models represents a
research challenge.
5. Simulation Models
Simulation models are useful support tools in understanding and visualizing the impact of
certain types of disruptive events on airport, airspace and airline operations and on air
traffic flows, as well as in testing the effectiveness of potential responsive actions. This
section reviews briefly some of these tools.
For analyzing impacts at the local airport or airspace level or for testing the effectiveness
of tactical ATFM actions, simulation models need to be highly detailed. When it comes
to questions at a regional or strategic level, models of a more aggregate nature are often
more appropriate. Detailed (or “microscopic”) simulation models of airport and airspace
operations first became viable in the early 1980s and have been vested with increasingly
sophisticated features since then. The models that currently dominate this field
internationally are the Airport and Airspace Simulation Model (better known as
SIMMOD), the Total Airport and Airspace Modeler (TAAM), and the Reorganized ATC
Mathematical Simulator (RAMS). The first two are widely used in studies dealing with
the detailed planning and design of airports and/or of volumes of airspace. SIMMOD is
publicly available through the FAA, but more advanced proprietary versions can be
obtained through private vendors (see, e.g., ATAC, 2003). TAAM is a proprietary model
(Preston, 2002). Finally, RAMS (Eurocontrol, undated) is also a proprietary model
limited to detailed simulation of airspace operations and procedures and is used either as
a training tool for air traffic controllers or for studies of controller workload in airspace
sectors. To our knowledge, none of these, or any other, detailed simulation models is
currently utilized on a routine basis as a “real time” support tool for the types of dynamic
tactical or strategic ATFM actions described in Section 4. However, the models have
reached a state of development where such use is technically feasible. For example, in a
case where a runway at an airport is temporarily out of use (e.g., due to weather
conditions or to a disabled aircraft), one could simulate and compare the effectiveness of
alternative allocation schemes for the assignment of arrivals and departures to other
runways or of various runway-use sequences. Odoni et al (1997) provides detailed – and
somewhat dated, by now – descriptions of several microscopic simulation models,
including the three mentioned above.
37
Another class of models has been developed to support more aggregate analysis typically
involving a broader scope than the problems addressed by SIMMOD or TAAM. For
example, NASA has sponsored the development of FACET (Future ATM Concepts
Evaluation Tool – Bilmoria et al, 2000). Typical uses might involve analyzing the
impact over the entire national airspace of new traffic flow management initiatives, airground distributed control architectures and decision support tools for controllers.
FACET models system-wide en-route airspace operations over the contiguous United
States. It strikes a balance between flexibility and fidelity enabling the simultaneous
representation of over 5,000 active flights on a desktop computer.
The CDM activities have also required the extensive use of human-in-the-loop (HITL)
experiments in order to test new distributed decision-making ideas. These experiments
were initially supported by one-of-a-kind computer-communications architectures. More
recently the FAA has funded the development by Metron Aviation of the Jupiter
Simulation Environment (JSE). JSE can emulate the message stream generated by the
FAA’s Enhanced Traffic Management System (ETMS). ETMS provides real-time
information on the status of all flights operating within the U.S. Airline operational
control centers and FAA facilities can connect their traffic monitoring systems to the JSE
and participate in HITL experiments involving new decision support tools or operational
concepts. For example, the JSE allowed for the rapid testing and evaluation of the slot
credit substitution (SCS) concepts and tools prior to their release.
Simulation models are equally important on the airline operations side. To evaluate the
recovery procedures and plans for fleets and crews under operational conditions, it is
necessary to have them simulated by a model of airline operations. MEANS (Clarke et al
2004) and SIMAIR (Rosenberger et al 2002) are such simulations. The MIT Extensible
Air Network Simulation (MEANS) can be used to predict the effects of air traffic control,
traffic flow management, airline operations control and airline scheduling actions on air
transportation system performance, measured in terms of airport congestion and
throughput, and aircraft, crew, and passenger delay and disruption. MEANS has a
modular architecture and interface, with each module corresponding to a set of
operational decisions made by air transportation coordinators and controllers. For
example, flight cancellation and re-routing decisions are made in the Airline Module; the
amount of traffic allowed between airports is determined by the Traffic Flow
Management Module; and the sequencing and spacing of aircraft is performed by the
Tower/TRACON Module. This modular structure provides flexibility for implementing
additional and/or more complex modules without requiring changes to the core interfaces.
Another stochastic model of airline operations, SIMAIR, uses an Event Generator
module to generate events such as arrivals, departures and repaired planes. The generator
samples random ground time delays, block time delays and unscheduled maintenance.
SIMAIR contains two modules for decision-making. The Controller module maintains
the state of the system. It emulates an Airline Operational Control Center in the sense
that it recognizes disruptions and implements recovery policies. If a disruption prevents a
38
leg from being flown as planned, the Controller requests a proposed reaction from the
Recovery Module, which it can accept or request another, time permitting.
SIMAIR has been used to evaluate the recovery procedures and robust plans presented in
several of the papers discussed in Sections 6 and 7. A SIMAIR Users Group is in place,
consisting of several research groups and airlines that have used or contributed to the
development of SIMAIR.
6. Airline Schedule Recovery
When disruptions occur, airlines adjust their flight operations by delaying flight
departures, canceling flight legs, rerouting aircraft, reassigning crews or calling in new
crews, and re-accommodating passengers. The goal is to find feasible, cost-minimizing
plans that allow the airline to recover from the disruptions and their associated delays.
To address this challenge, airlines have established Airline Operational Control Centers
(AOCC) to control safety of operations, exchange information with regulatory agencies,
and manage aircraft, crew and passenger operations. The AOCC is comprised of (Bratu
2003, Clarke, Lettovsky and Smith 2000, and Filar, Manyem and White 2000):
•
Airline operations controllers who, at the helm of the AOCC, are
responsible for aircraft re-routing, and flight cancellation and delay decisions
for various types of aircraft.
•
Crew planners who find efficient recovery solutions for crews and coordinate
with airline operations controllers to ensure that considered operations
decisions are feasible with respect to crews.
•
Customer service coordinators who find efficient recovery solutions for
passengers and coordinate with airline operations controllers to provide an
assessment of the impact on passengers of possible operations decisions.
•
Dispatchers who provide flight plans and relevant information to pilots.
•
An air traffic control group that collects and provides information, such as
the likelihood of future ground delay programs, to airline operations
controllers.
The AOCC is complemented by Station Operations Control Units, located at airport
stations, responsible for local decisions, such as the assignment of flights to gates, ground
workforce to aircraft and personnel for passenger service.
Airline operations recovery is replete with challenges, including:
1. The recovery solution must take into account the recent flying history of the
aircraft, crews and passengers to ensure that crew work rules are satisfied,
39
aircraft maintenance and safety regulations are met, passengers are transported
to their desired destinations, and aircraft are positioned appropriately at the
end of the recovery period.
2. The recovery solution can utilize additional resources, namely reserve crews
and spare aircraft (Sohoni et al 2002 and Sohoni, Johnson and Bailey 2003).
3. There are multiple recovery objectives, namely: minimizing the cost of
reserve crews and spare aircraft used; minimizing passenger recovery costs;
minimizing the amount of time to resume the original plan; and minimizing
loss of passenger goodwill.
4. The recovery problem often must be solved quickly, often within minutes.
To meet these challenges, most airline recovery processes are sequential (Rosenberger,
Johnson and Nemhauser 2003). The first step in the process is to recover aircraft, with
decisions involving flight leg cancellation or delay, and/or aircraft re-routing. The
second step is to determine crew recovery plans, assigning crews to uncovered flight legs
by reassigning them or utilizing reserve crews. Finally, the third step is for customer
service coordinators to develop passenger re-accommodation plans for disrupted
passengers. A disrupted passenger is one whose planned itinerary is broken and
impossible to execute during operations because: 1) at least one of the flight legs in the
itinerary is canceled; or 2) the connection time between consecutive flight legs in the
itinerary is too short due to flight delays. While the AOCC decision process is
hierarchical in nature, airline operations controllers, crew planners and passenger service
coordinators consult with one another during the process to assess the feasibility and
impact of possible decisions.
This sequential decision process, first aircraft, then crew and finally passenger recovery,
is reflected in the research on airline recovery performed to date. In the following
subsections, we present selected airline recovery research.
6.1 Aircraft Recovery
When schedule disruptions occur, the aircraft recovery problem is to determine flight
departure times and cancellations, and revised routings for affected aircraft. Re-routing
options include ferrying (repositioning an aircraft without passengers to another location,
where it can be utilized); diverting (flying to an alternate airport); over-flying (flying to
another scheduled destination); and swapping (flight legs are re-assigned among different
aircraft). These modifications must satisfy maintenance requirements, station departure
curfew restrictions and aircraft balance requirements, especially at the start and end of the
recovery period. At the end of the period, aircraft types should be positioned to resume
operations as planned.
The aircraft balance requirements add complexity to cancellation decisions. Normally, to
ensure that aircraft are positioned where needed to fly downstream flight legs,
40
cancellations involve cycles of 2 or more flight legs. To cancel only a single flight leg l
and still be able to execute the remaining schedule, it is necessary to deploy a spare
aircraft of the type assigned to the destination of leg l. Because spare aircraft are
typically in very limited supply, canceling only a single flight leg is not usually an option.
Beyond the inherent complexities of re-routing aircraft, scheduling delayed flight
departures and making cancellation decisions, an effective aircraft recovery solution
approach accounts for the downstream costs and impacts on crew and passengers. The
extent to which these complexities are captured in models varies, with increasing
sophistication achieved over time.
Arguello, Bard and Yu (1997) present an integrated aircraft delays and cancellations
model and generate sequentially, for each fleet type, a set of aircraft routes that minimize
delays, cancellations and re-routing costs. Their model ensures aircraft balance by
matching aircraft assignments with the actual aircraft locations at the beginning of the
recovery period and with the planned aircraft locations at the end of the period (that is,
the end of the day).
The model includes two types of binary decision variables; namely, maintenance-feasible
aircraft routes and schedules, and flight cancellation decisions. An aircraft route is a
sequence of flight legs spanning the recovery period, with the origin of a flight leg the
same as the destination of its predecessor in the sequence, and the elapsed time between
two successive legs at least as great as the minimum aircraft turn time. Routes for
aircraft with planned maintenance within the recovery period are not altered to ensure
that the modified routes satisfy maintenance requirements.
Let P be the set of aircraft routes, Q be the set of aircraft, and F be the set of flight legs.
Aircraft route variable x kj equals 1 if aircraft k is assigned to route j and 0 otherwise. Its
cost, denoted d kj , equals the sum of the delay costs associated with flight delays implied
by assigning aircraft k to route j. Note that d kj is infinite for each aircraft route j
commencing at an airport location other than that of aircraft k at the start of the recovery
period. A flight cancellation variable, denoted y i , is set to 1 if flight leg i is cancelled
and 0 otherwise. The approximate cost associated with the cancellation of each flight leg
i is ci ; ht equals the number of aircraft needed at airport location t at the end of the
recovery period to ensure that the next-day plan can be executed; δ ij is equal to 1 if flight
leg i is covered by route j; and btj is equal to 1 if route j ends at the airport t.
The aircraft recovery model is:
MIN
∑ ∑d
k∈Q
j∈P
k
j
x kj + ∑ ci y i
i∈F
subject to
41
∑ ∑δ
k∈Q
ij
x kj + y i = 1
tj
x kj = ht for all airports t at the end of the recovery period
for all flight legs i,
(1)
j∈P
∑ ∑b
k∈Q
j∈P
∑x
k
j
=1
for all aircraft k
(2)
(3)
j∈P
x kj ∈ {0,1}
for all routes j and aircraft k
(4)
y i ∈ {0,1}
for all flights i in F.
(5)
Constraints (1), together with constraints (4) and (5), require each flight to be included in
an assigned route or to be cancelled. Constraints (2) ensure that at the end of the day
(that is, at the end of the recovery period), aircraft are repositioned so that the plan can be
resumed at the start of the next day. Finally, constraints (3) enforce the requirement that
each aircraft be assigned to exactly one route, commencing at its location at the start of
the recovery period. The objective is to minimize flight cancellation and delay costs.
A challenge in formulating this model is to estimate the objective function costs.
Because passengers and crews often travel on more than one aircraft route, the costs of
delays and cancellations cannot be expressed exactly as a function of a single flight-leg,
or as a function of a single aircraft routing. Instead, these costs depend on the pairs or
subsets of flight legs comprising the passenger and crew connections. Hence,
approximate delay and cancellation costs are used in the model.
The Arguello, Bard and Yu model and heuristic solution approach is applied to a
relatively small data set representing the Continental Airlines flight schedule for Boeing
757 aircraft, with 42 flights, 16 aircraft, and 13 airport locations. They report that for
over 90% of the instances tested, their approach produces a solution within 10% of the
lower bound within 10 CPU seconds.
Rosenberger, Johnson and Nemhauser (2003) extend the Arguello, Bard and Yu model to
include supplementary slot constraints. Let A equal the set of allocated arrival slots,
Rk(a) equal the set of routes for aircraft k that include legs landing in arrival slot a, and let
H ( j , a ) represent the number of flight legs in route j using slot a. Then, the slot
constraints are of the form:
∑ ∑
H ( j , a ) x kj ≤ α a
for all a in A.
(6)
k
j∈R ( a ) k∈Q
These constraints ensure that the number of aircraft arriving in each allocated time slot in
the recovery period does not exceed the airport’s restricted capacity, as mandated by
ground delay programs, described in Section 4. Additional work on recovering airline
operations under conditions of insufficient airport capacity are reported in VasquezMarquez (1991), Richetta and Odoni (1993), Hoffman (1997), Luo and Yu (1997),
42
Andreatta, Brunetta and Guastalla (2000), Carlson (2000), Chang et al (2001), and
Metron Inc. (2001).
The body of literature on aircraft recovery is growing as information technology
capabilities expand. Selected additional references include Teodorovic and Guberinic
(1984), Teodorovic and Stojkovic (1990), Jarrah et al (1993), Teodorovic and Stojkovic
(1995), Yu (1995), Mathaisel (1996), Rakshit, Krishnamurthy and Yu (1996), Talluri
(1996), Yan and Yang (1996), Yan and Young (1996), Cao and Kanafani (1997), Clarke
(1997), Lettovsky (1997), Yan and Lin (1997), Yan and Tu (1997), and Thengvall, Yu
and Bard (2000).
6.2 Expanded Aircraft Recovery
Bratu and Barnhart (2005a) analyze the operations of a major U.S. airline for the months
of July and August 2000, and report that:
(a) Flight delays are not indicative of the magnitude of delay experienced by disrupted
passengers. On the same day that disrupted passengers experienced average delays of
419 minutes, the average delay of non-disrupted passengers was only 14 minutes, nearly
matching the average flight delay that day; and
(b) Disrupted passenger delays and associated costs are significant. Bratu and Barnhart
estimate for the airline they study that disrupted passengers represent just about 4% of
passengers but account for more than 50% of the total passenger delay. Associated with
these disrupted passengers are direct and indirect costs, which can include lodging,
meals, re-booking (possibly on other airlines), and loss of passenger goodwill.
Bratu and Barnhart conclude that delay cost estimates that do not take into consideration
the costs of disruption cannot be accurate. Recognizing this, Rosenberger, Johnson and
Nemhauser (2003) expand their aircraft recovery model to identify disrupted crews and
passengers, and their associated costs, by adding constraints and variables to: (i) compute
the delay of each flight leg that is not cancelled; (ii) determine if a connection is
disrupted; and (iii) identify disrupted crews and passengers. They then estimate delay
costs, separately, for disrupted passengers and crews, and for non-disrupted passengers
and crews. These, in turn, are included in the objective function of their extended model
to achieve a more accurate estimate of delay costs.
To solve their model, Rosenberger, Johnson and Nemhauser limit the number of aircraft
routes considered using an aircraft selection heuristic in which routes are generated only
for a selected subset of aircraft. They evaluate their approach using a stochastic model
(Rosenberger et al, 2002) to simulate 500 days of airline operations. Simulated
disruptions include two-day unscheduled maintenance delays and severe weather
disruptions at hub airports. They compare the results of their extended model that
accounts for crew and passenger disruptions with those of the simplified model. They
report that, compared to the simplified model’s solutions, those generated with the
extended model exhibit significant reductions in passenger inconvenience and
43
disruptions, at the expense of on-time schedule performance degradation, increased
overall delay, and increased incidence of flight cancellation.
Bratu and Barnhart (2005b) report similar findings. They also consider disrupted
passengers and crews, and develop an aircraft recovery model to determine flight
departure times and cancellations that minimize recovery costs, including the costs of reaccommodating disrupted passengers and crews, re-routing aircraft, and canceling flight
legs. Unlike many of the more recent models, their aircraft routing decision variables are
flight-leg based, rather than route-based. This reduces the number of decision variables
significantly, allowing them to generate recovery solutions for aircraft, crew and
passengers simultaneously. To ensure the satisfaction of maintenance requirements, they
do not allow modification of routes for maintenance-critical aircraft, that is, aircraft for
which maintenance is scheduled that day. They apply their approach to problem
instances containing 303 aircraft, 74 airport locations (3 of which are hubs), 1088 flight
legs per day on average, and 307,675 passenger itineraries. They achieve solutions
within 30 CPU seconds on a PC and report expected reductions of more than 40% in the
number of disrupted passengers, more than 45% in the number of passengers required to
overnight at a destination other than that planned, and more than 33% in the total delay
minutes of disrupted passengers. To achieve this, total delay minutes of non-disrupted
passengers increased by 3.7% and the airline’s on-time performance, as measured by the
US DOT 15-minute on-time performance metric, worsened. This is an expected result
when one considers that intentionally delaying aircraft that otherwise would be onschedule can reduce passenger misconnections and hence, reduce overall passenger
delays.
6.3 Crew Recovery
Although aircraft recovery decisions repair broken aircraft schedules, they often result in
the disruption of crew schedules. Flight cancellations, delays, diversion and swap
decisions, together with crew illness, all result in the unavailability of crews at the
locations needed.
Crew recovery options include deadheading of crews (i.e. repositioning crews by flying
them as passengers) from their point of disruption to the location of a later flight leg to
which they are assigned. Once repositioned, the crews can then resume their original
work schedule. Another option is to assign a reserve crew to cover the flight legs left
unassigned by the crew disruption. Reserve crews are back-up crews, not originally
assigned to the flight schedules, but pre-positioned at certain locations and available to
report to duty, if needed. They are guaranteed a minimum monthly salary, whether or not
they are called into work, and they are limited to a maximum number of flying hours per
month. In addition to possibly incurring additional reserve crew costs when using reserve
crews, airlines usually must also pay the replaced crew the entire amount originally
planned, even if the work was not performed. A third recovery option is to reassign a
crew from its original schedule to an alternative schedule. In this case, the new
assignment must satisfy all collective bargaining agreements and work rule regulations,
including maximum crew work time, minimum rest time, maximum flying time,
44
maximum time-away-from-home, etc. When reassigned, crews are typically paid the
maximum of the pay associated with the original schedule or with the new schedule to
which they are assigned.
The crew recovery problem then is to construct new schedules for disrupted and reserve
crews to achieve coverage of all flights at minimum cost. Because crew costs constitute a
significant portion of airline operating costs, second only to fuel costs, crew planning has
garnered significant attention. Crew recovery, however, has received much less
attention. One reason is that the crew recovery problem is significantly more difficult.
First, because of the time horizon associated with recovery operations, recovery solutions
must be generated quickly, in minutes instead of the hours or weeks allowed for planning
problems. Moreover, information pertaining to the location and recent flying history of
each crew member must be known at all times in order to generate recovery plans for the
crew that satisfy the myriad of crew rules and collective bargaining agreements. Finally,
the objective function of the crew recovery problem is multi-dimensional. Researchers
often cast the crew recovery objective as a blend of minimizing the incremental crew
costs to operate the modified schedule, while returning to the plan as quickly as possible
and minimizing the number of crew schedule changes made to do so. By limiting the
number of crews affected, the quality of the original crew plans will be preserved to the
greatest extent possible. Moreover, returning to plan as quickly as possible helps to avoid
further downstream disruptions to aircraft, crew and passengers.
Due to these challenges, the crew recovery literature is relatively limited. Although both
cabin and cockpit crews are disrupted and must be recovered, most recovery research
focuses on cockpit crews, who are both more costly and more constrained than cabin
crews. Pilots have fewer recovery options because they are qualified to fly only aircraft
types with the same crew qualifications.
Yu et al (2003) focus on cockpit crews and present a crew recovery model and solution
approach. They consider a set of aircraft types with the same crew qualifications and a
set of crews who (i) are qualified to fly these aircraft; and (ii) are disrupted or are
candidates who are likely to improve the crew recovery solution through swaps. For
each of these crews, they construct a set of feasible pairings, each beginning at the crew’s
current location and commencing at or later than the time at which the crew is available.
Moreover, the generated pairings satisfy all work rules and regulations, considering the
amount of work completed by the crew up to the point of disruption. Pairings selected in
the recovery solution satisfy cover constraints ensuring that each flight leg is either
cancelled or assigned to one or more crews. When more than one crew is assigned, the
additional crews are deadheaded and repositioned to their home location or to another
location where they can resume work. The objective is to minimize the sum of: (1)
deadheading costs; (2) modified crew schedule costs; and (3) cancellation costs due to
leaving flight legs uncovered.
Yu et al define the following sets and parameters:
e
equipment type (consisting of one or more crew compatible aircraft types)
45
I
K
Jk
set of active flights to be covered by crews of equipment type e
set of active and reserve crews available for equipment type e
set of potential feasible pairings for crew k
c kj
cost of assigning crew k to pairing j
ui
cost of not covering flight leg i
qk
cost of not assigning a pairing to crew k
di
cost of each crew deadheading on flight i
a ij
equal to 1 if flight leg i is included in pairing j; and 0 otherwise.
The variables are:
x kj
equal to 1 if crew k is assigned to pairing j ; and 0 otherwise
zk
equal to 1 if crew k has no pairing assigned; and 0 otherwise
yi
equal to 1 if flight leg i is not covered (is cancelled); and 0 otherwise
si
equal to the number of crews deadheading on flight leg i.
They then formulate the crew recovery problem as:
MIN
∑ ∑c
k∈K
k
j
x kj + ∑ u i y i + ∑ q k z k + ∑ d i si
j∈J k
i∈I
k∈K
i∈I
subject to
∑ ∑a
k∈Q
ij
x kj + y i − si = 1
for all i∈I
(7)
j∈J k
∑x
k
j
for all k∈K
(8)
x kj ∈ {0,1}
for all k∈K, all j∈Jk
(9)
y f ∈ {0,1}
for all f∈I
(10)
z k ∈ {0,1}
for all k∈K
(11)
s f ∈ {0,1,2,…}
for all f∈I.
(12)
+ zk = 1
j∈J k
Constraints (7) ensure that all flight legs are cancelled or covered at least once, with si
representing the number of crews deadheading on flight leg i. Constraints (8) determine
whether crew k is assigned to a pairing or must be deadheaded to its crew base, that is, its
domicile. Integrality of the solution is guaranteed by constraints (9)-(12).
Yu et al state that, for typical instances, there are millions of potential crew pairings and
hence, the size of the crew recovery model renders exact solution approaches impractical.
46
Using a procedure of Wei, Yu and Song (1997), they search heuristically for solutions.
They modify or generate a few pairings at a time and test the quality of the solution, and
then repeat the process if necessary. Using data provided by Continental Airlines, they
evaluate their heuristic approach on instances corresponding to disruptions affecting 1-40
flight legs of the airline’s Boeing 737 fleet. Within 8 minutes at most, they generate
near-optimal solutions, achieving at most an average 5% optimality gap.
Lettovsky (1997) and Lettovsky, Johnson and Nemhauser (2000) present a similar model,
but they include additional constraints restricting the number of crews deadheading on
each flight leg to the maximum available capacity. Moreover, their flight cancellation
costs include costs of re-assigning passengers to other flights, associated hotel and meal
costs, and estimates of the loss of passenger goodwill. They design a heuristic solution
approach for their model that keeps intact as many as possible of the crew schedules,
altering only those of disrupted crews and of a few additional crews who greatly facilitate
the recovery of crew operations. In restricting the set of crews for which new schedules
are generated, optimality of the original crew schedules is preserved for crews not
affected by modifications to the plan, and the size of the problem is contained, improving
tractability and allowing quicker solution times. Lettovsky and Lettovsky, Johnson and
Nemhauser describe heuristics to select the crews whose schedules might be altered.
Stojkovic, Soumis and Desrosiers (1998) also address the operational crew scheduling
problem, and present a set partitioning model and a branch-and-price algorithm to
determine modified monthly schedules for selected crew members. The objective is to
cover all tasks at minimum cost while minimizing the number of changes to the planned
crew schedules. They generate test problems from pairings of a U.S. airline and report
that quality solutions are obtained in reasonable run times.
6.4 Passenger Recovery
Just as aircraft recovery decisions result in crew disruptions, aircraft and crew recovery
decisions lead to passenger disruptions. The next step of the recovery process then is to
reassign disrupted passengers to alternative itineraries, commencing at the disrupted
passenger locations after their available times, and terminating at their destination, or a
location nearby. Disrupted passengers can be assigned to itineraries beginning at least
some minimum connection time after the time of their disruption. Only disrupted
passengers can be reassigned, and non-disrupted passengers cannot be displaced by
reassigned passengers. Clarke (2005) presents modeling strategies for re-accommodating
passengers who are disrupted by operations, or by schedule changes resulting from
considerations such as revenue management. Barnhart, Kniker and Lohatepanont (2002)
cast this problem as a multi-commodity network flow problem. They let xpr represent the
number of disrupted passengers originally scheduled on itinerary p who are reaccommodated on itinerary r. In addition to other itineraries offered by the airline,
passengers can be accommodated on itineraries offered by other airlines, or itineraries on
different modes of transportation. In fact, an alternate itinerary might be the null itinerary
representing canceled trips, a valid choice for passengers who are disrupted before
departing their origin. The planned arrival time at the destination of itinerary p is l(p),
47
and a(r) represents the actual arrival time at the destination of itinerary r. The set of
flight legs is F; df is the number of seats available for disrupted passengers, that is, the
total number of seats less the number of seats occupied by non-disrupted passengers, on
flight f; δfr equals 1 if flight f is contained in itinerary r, and equals 0 otherwise; and np is
the total number of disrupted passengers of type p. The passenger re-assignment model is
then formulated as:
MIN
∑ ∑ (a(r ) − l ( p))x
r
p
(13)
p∈P r∈R ( p ) k
subject to
∑ ∑δ
r
f
x rp ≤ d f
for all f∈F
(14)
for all p∈P
(15)
for all p∈P, all r∈R(p).
(16)
p∈P r∈R ( p ) k
∑x
r
p
= np
r∈R ( p )
x rp ∈ {0,1}
The objective (13) is to find the disrupted passenger reassignments that minimize the
total delay experienced by disrupted passengers. Flight capacity constraints (14) ensure
that only seats not occupied by non-disrupted passengers are assigned to disrupted
passengers. Constraints (15) and (16) ensure that each disrupted passenger is reassigned,
albeit perhaps to the null itinerary.
The passenger re-assignment model can be solved exactly, but its solution time can
become prohibitive for real-time operations as the number of disrupted passengers grows,
thus causing the need for column generation solution approaches to be employed. Bratu
and Barnhart (2005a), however, solve this problem using a flexible heuristic, termed the
Passenger Delay Calculator, that allows passenger recovery policies (such as frequent
flyers first, or first-disrupted-first-recovered) to be enforced. Using their Passenger
Delay Calculator, Bratu and Barnhart analyze two months of airline operations and
recovery data for a major airline, as well as numerous simulated scenarios. They
conclude that:
1. Connecting passengers are almost three times more likely to be disrupted than
passengers without connections. However, connecting passengers who miss their
connections are often re-accommodated on their best alternative itineraries, that
is, on itineraries that arrive at their destinations at the earliest possible time, given
the timing of the disruptions. In comparison, only about one-half of the
passengers disrupted by flight leg cancellations are re-accommodated on their
best itineraries. This occurs because the number of misconnecting passengers per
flight leg is small relative to the number of passengers disrupted by a flight leg
cancellation.
48
2. The inability to re-accommodate disrupted passengers on their best itineraries is
exacerbated by high load factors, with average delay for disrupted passengers
increasing exponentially with load factor.
3. Alternative metrics measuring schedule performance, namely flight cancellation
rates and the percentage of flights delayed by more than 45 minutes, are better
indicators of passenger disruptions than the US DOT 15-minute on-time
performance metric.
7. Robust Airline Scheduling
Robust planning attempts to deal with data uncertainty in a planning model. In airline
schedule and resource allocation planning, there are two primary sources of uncertainty:
passenger demand and schedule execution. Here we only deal with uncertainties in the
execution of the planned schedule.
In the traditional stochastic programming approach to robust planning, it is necessary to
estimate the probability of each possible outcome. One then minimizes the expected cost
of the planning decisions plus the cost of the recovery that takes place as a result of the
decision and outcome. Unfortunately, this approach is completely intractable in the case
of airline planning at present because one has to deal with literally millions of very low
probability events. Moreover, there is no obvious way to aggregate meaningfully these
events in a way that would simplify the analysis. One could consider planning for only
the worst possible outcome, but this would be far too conservative and costly.
Nevertheless, the basic idea of including the anticipated costs of recovery into the
planning model can be very useful. A planner needs to think of an optimal plan as being
one for which the combined planned and recovery costs, that is, the realized costs, are
minimized. This definition of optimality is at odds with the one typically employed by
airline optimizers, who have historically excluded recovery costs and optimized only
planned costs. In doing so, resource utilization is maximized, with non-productive time
on the ground, i.e., slack time, minimized. Lack of slack, however, makes it difficult for
disruption to be absorbed in the schedule and limits the number of options for recovery.
One should not think of this omission as an oversight on the part of the airlines. Rather,
it is based on recognition of the inherent difficulty of including recovery costs in a
planning model.
Enhancing schedule planning models to account for recovery costs presents both
modeling and computational challenges. A number of researchers have begun to
consider this challenge, recognizing that robust planning is a problem rich in opportunity
and potential impact. To facilitate the generation of robust plans, they have developed
various proxies of robustness, mainly focused on finding flexible plans that provide a rich
set of recovery options for passengers, crews and aircraft; or plans that isolate the effects
of disruptions, requiring only localized plan adjustments.
49
In the following subsections, we highlight selected work on robust airline planning, while
outlining briefly the various modeling and algorithmic approaches employed.
7.1. Robust Schedule Design
In this section, we describe some recent work that represents a step towards achieving
flight schedule designs that are resilient when it comes to passenger disruption. It
extends the cost minimization approaches described in Simpson (1966), Chan (1972),
Soumis, Ferland and Rousseau (1980) Etschmaier and Mathaisel (1985), Berge (1994),
Marsten, Subramanian and Gibbons (1996), Erdmann et al (1999), Armacost, Barnhart
and Ware (2002) and Lohatepanont and Barnhart (2004).
Lan, Clarke and Barnhart (2005) develop a new approach to minimize the number of
passenger misconnections by re-timing flight departures, while keeping all fleeting and
routing decisions fixed. Moving flight leg departure times provides an opportunity to reallocate slack time to reduce passenger disruptions and maintain aircraft productivity.
Levin (1971) proposed the idea of adding time windows to fleet routing and scheduling
models. Related research can be found in Desaulniers et al (1997 ), Klabjan et al (2002),
Rexing et al (2000) and Stojkovic et al (2002).
To illustrate the idea, consider the example in Figures 7.1a, 7.1b and 7.1c. In the planned
first-in-first-out aircraft routing, flight leg f1 is followed by leg f2 in one aircraft’s
rotation, and leg f3 is followed by leg f4 in another aircraft’s rotation. Assume that f1 is
typically delayed, as indicated in Figure 7.1a. Because insufficient turn time results from
the delay, some of the delay to f1 will propagate downstream to f2, as shown in Figure
7.1b. Then, assuming that f3 is typically on-schedule, expected delays are reduced by
changing the planned aircraft rotations to f1 followed by f4, and f3 followed by f2, as
shown in Figure 7.1c.
Lan, Clarke and Barnhart apply their re-timing model to the flight schedule of a major
U.S. airline and compare passenger delays and disruptions in the original schedules with
those expected from the solutions to their re-timing model. They find that a 30-minute
time window, allowing each flight leg to depart at most 15 minutes earlier or later than in
the original schedule, can result in an expected reduction in passenger delay of 20% and a
reduction in the number of passenger misconnections of about 40%; a twenty-minute
time window can reduce passenger delays by about 16% and reduce the number of
passenger misconnections by over 30%; and, finally, a ten-minute time window can
reduce passenger delays by roughly 10% and passenger misconnections by 20%.
50
Figure 7.1a: First-In-First-Out Routings and Delayed Flight Leg f1
Figure 7.1b: Delay Propagation due to Delay of Flight Leg f1
Figure 7.1c: Revised Routings Minimizing Delay Propagation
7.2 Robust Fleet Assignment
Rosenberger, Johnson and Nemhauser (2004) present a robust fleet assignment approach,
building on the work reported in Barnhart et al (1998a). They identify hub interconnectivity as an important indicator of schedule robustness. Because schedules are
51
sensitive to disruptions at hubs, a more robust schedule is one in which hubs are isolated
to the greatest extent possible. They quantify the degree to which a hub is isolated using
a hub connectivity metric; the smaller the value of hub connectivity, the more isolated the
hub.
Rosenberger, Johnson and Nemhauser characterize a robust fleet assignment as one with
limited total hub connectivity and many short cycles (cycles with a small number of
flight legs). Short cycles allow an airline to limit the number of flights cancelled when a
cancellation is necessary, thereby lessening the impact of disruptions and facilitating
recovery. They let J denote the set of fleets and S be the set of strings, or sequences of
flight legs beginning at a hub, ending at a hub, and flown by the same aircraft. The hub
connectivity metric hjs for string s∈S and aircraft of type j∈J equals the number of legs in
s if s begins and ends at different hubs, and equals 0 otherwise. The maximum value of
hub connectivity is specified by a threshold value ς. For each fleet type j∈J and string
s∈S, cjs is the cost of flying s with aircraft of type j and decision variable xjs equals 1 if j is
assigned to s, and 0 otherwise. The set of feasible fleet assignment solutions is χ. Their
model to determine robust fleet assignments with hub isolation and short cycles is then:
MIN ∑
s∈ S
∑c
js
x js
j∈J
subject to
∑∑
h js x js ≤ ς
s∈S j∈J
x∈χ .
The objective is to find the minimum cost fleet assignment with total value of hub
connectivity not greater than ς. They propose a related model in which the objective is to
maximize hub isolation and limit total fleeting costs to some pre-specified threshold.
Using SIMAIR, they compare the solutions to their robust fleet assignment models with
those obtained solving a traditional FAM model. They report that with small increases in
planned costs it is possible to reduce cancellations significantly and also improve on-time
performance.
Smith (2004) focuses on the revenue aspects of robustness in fleet assignment. He adds
purity to fleet assignment solutions, which means that he limits the number of fleet types
at spokes to at most one or two. This, of course, increases planned cost, but purity adds
robustness in operations by enhancing the possibility of crew swaps. It also decreases
maintenance cost because the need for spare parts is reduced. Interestingly, adding the
upper bound constraints on fleet types at spokes makes the FAM model much harder to
solve. Smith introduces a station decomposition approach to solve this more difficult
FAM model.
52
7.3 Robust Aircraft Routing
Maintenance routing, as surveyed in Klabjan (2003), provides an attractive opportunity
for adding robustness because modifying routes has a minimal impact on planned cost.
Therefore it is not necessary to make an explicit tradeoff between planned cost and
robustness.
7.3.1 Degradable Airline Scheduling
Kang and Clarke (2002) attempt to achieve robustness by isolating the effects of
disruptions. They partition the legs of the flight schedule into independent sub-networks,
which are determined through alternative models and approaches, each applicable at a
particular step of schedule planning, such as schedule design, fleet assignment, or aircraft
maintenance routing. The model solutions are constrained to ensure that aircraft (and
ultimately, crew) are assigned only to flight legs within a single sub-network, prohibiting
them to operate between sub-networks. (Passengers, on the other hand, can travel within
multiple sub-networks.) The sub-networks are prioritized based on the total revenue of
the flights legs they contain, with the maximum-revenue sub-network having the highest
priority. When disruptions occur, the top priority sub-networks are recovered first,
shielding the associated crew, aircraft and passengers to the greatest extent possible from
the resulting delays. This has the effect of relegating disruptions to the low priority subnetworks, and minimizing the revenue associated with delayed and disrupted passengers.
An advantage of the approach of Kang and Clarke is that it can simplify recovery.
Because delays and propagation effects are contained within a single subnetwork, the
recovery process needs only to take corrective action on the flights in the affected
subnetwork, and not on the entire airline network.
7.3.2 Robust Aircraft Routing: Allocating Slack to Minimize Delays
Lan, Clarke and Barnhart (2005) propose aircraft routing models and algorithms aimed at
minimizing delay propagation and passenger delay and disruption. They partition flight
leg delays into two categories, namely: propagated delay, that is, delay occurring when
the aircraft to be used for a flight leg is delayed on its preceding flight leg; and nonpropagated, or independent, delay. Propagated delay is a function of an aircraft’s routing,
while non-propagated delay is not. The premise underlying their approach is that
propagated delay can be reduced through intelligent aircraft routing, that is, by allocating
slack optimally to absorb delay propagation. By reducing propagated delay, they expect
to achieve a corresponding reduction in passenger delays.
Using historical delay data, they first estimate the expected independent delay for each
flight leg, and then, using these estimates, compute the expected propagated delay for
each possible aircraft routing by sequentially computing the earliest departure time for
each subsequent flight leg in the routing, given the expected independent delay for that
flight leg plus the resulting propagated delay accumulated to that point. Next, for each
fleet type, they solve a daily model (that is, one that assumes the flight schedule repeats
53
daily) to select aircraft routes that satisfy maintenance requirements while minimizing
propagated delay. In their model, they let S be the set of feasible strings, where a string
is a sequence of connected flight legs (that is, the departure station for flight leg f is the
same as the arrival station of f’s predecessor and the departure time of flight leg f is not
earlier than the arrival time plus minimum turn time of flight leg f’s predecessor)
beginning and ending at a maintenance station and with elapsed time not greater than the
maximum time between maintenance checks. The set of daily flight legs is F, F+ is the
set of flight legs originating at a maintenance station, and F- is the set of flight legs
terminating at a maintenance station. The set of ground arcs (including the overnight or
wrap-around arcs to ensure that the flight schedule can repeat daily) is denoted by G.
The set of strings ending with flight leg i is Si-, and the set of strings beginning with flight
leg i is Si+. They include one binary decision variable xs for each feasible string s, and
ground variables y to count the number of aircraft on the ground at maintenance stations.
The delay propagated from flight leg i to flight leg j if flight leg i and flight leg j are in
string s is pdijs. If flight leg i is in string s, ais equals 1, otherwise it equals 0. Ground
variable yi,d- equals the number of aircraft on the ground before flight leg i departs, and
ground variable yi,d+ equals the number of aircraft on the ground after flight leg i departs.
Similarly, ground variable yi,a- equals the number of aircraft on the ground before flight
leg i arrives, and ground variable yi,a+ equals the number of aircraft on the ground after
flight leg i arrives. The count time is a point in time when aircraft are counted. The
number of times string s crosses the count time is rs ; pg is the number of times ground arc
g crosses the count time; and N is the number of planes available.
The model to determine robust aircraft routes is:
MIN E (∑
∑ pd
s∈S
s
ij
x s ) = E (∑ x s
( i , j )∈s k
s∈S
∑ pd
s
ij
) = MIN (∑ x s E (
( i , j )∈sk
s∈S
∑ pd
s
ij
))
(17)
( i , j )∈sk
subject to
∑a
for all i∈F
(18)
x s − y i−,d + yi+,d = 0
for all i∈F+
(19)
x s − y i−,a + y i+, a = 0
for all i∈F-
(20)
is
xs = 1
s∈S
∑
s∈ Si +
∑
s∈ Si
−
∑r x
s
s
+
s∈ S
∑p
g
yg ≤ 0
(21)
g∈ G
yg ≥ 0
for all g∈G-
(22)
x s ∈ {0,1}
for all s∈S-.
(23)
54
The objective (17) is to select strings that minimize the expected total propagated delay.
Constraints (18) ensure that each flight leg is contained in exactly one string, while
constraints (19) and (20) guarantee that the number of aircraft arriving at a location equal
the number departing. Constraint (21) ensures that the total number of aircraft in the
solution does not exceed the number available. Constraints (22) and (23) guarantee a nonnegative number of aircraft on the ground at all times, and ensure that the number of
aircraft assigned to a string is either 0 or 1, respectively. Because each ground variable
can be expressed as a sum of binary string variables, the integrality constraints on the
ground variables can be relaxed (Hane et al 1995).
Their solution approach applies the branch-and-price algorithm (Barnhart et al, 1998),
with column generation to enumerate a relevant subset of string variables. They apply
their approach to four different networks, each corresponding to a different fleet type
operated by a major US network carrier. They compare their robust routing solution with
the routing solution generated by the airline and estimate that their solution can yield
average reductions of 11% in the number of disrupted passengers, and 44% in total
expected propagated delay minutes. They further report that their solution corresponds to
an expected improvement of 1.6% in the airline’s Department of Transportation (DOT)
on-time arrival rate. This is significant because a 1.6% improvement would allow the
airline to improve its position in the DOT’s airline on-time rankings, which are publicly
available and are often cited as an important indicator of airline performance.
7.3.3. Robust Routing through Swap Opportunities
Ageeva and Clarke (2004) use the constraints of the string-based routing model of Lan,
Clarke and Barnhart (2005) but change the objective function to optimize a different
robustness criterion. They attempt to build flexible aircraft routings with maximal
potential for modification during recovery by adding a reward for each opportunity to
swap aircraft. Their objective is to maximize the number of swap opportunities in the
routing solution. Aircraft swapping is possible when the routings of two aircraft intersect
at least twice. To understand how swaps can mitigate the impact of a delayed or
unavailable aircraft, consider an example in which aircraft a1 is scheduled to depart
station s at time t1 but is delayed until time t2. Further, assume that aircraft a2 is
scheduled to depart s at time t3 (with t3>t2>t1) but is available for departure at t1.
Without swapping, the flight legs assigned to aircraft a1 experience delays as great as t2
– t1, while the flight legs assigned to aircraft a2 are not delayed. With swapping,
however, none of the flights legs originally assigned to a1 or a2 is delayed.
Ageeva and Clarke measure the robustness of their solutions using an opportunity index,
defined as the ratio of the number of actual to potential intersecting partial rotations.
They report that using their approach, optimal costs are maintained and robustness of the
aircraft routing solution, as measured by the opportunity index, are improved up to 35%
compared to solutions generated by a basic routing model devoid of robustness
considerations.
55
7.4 Robust Crew Scheduling
The crew pairing problem, with a focus on minimizing planned crew-related cost, has
been studied by many researchers. Survey papers on the subject include Yu (1997),
Desaulniers et al (1998), Clarke and Smith (2000) and Barnhart et al (2003a). The focus
of the more recent body of research on robust crew scheduling has instead been on
minimizing realized cost. The underlying motivation stems from the observation that the
realized cost associated with a crew pairing solution often differs significantly in practice
from the planned cost. Large additional crew costs are incurred, for example, when
reserve crews are called in to complete work assigned to disrupted crewmembers no
longer able to perform their originally assigned work. The causes might include
crewmembers in the wrong location due to one or more flight leg cancellations, or
crewmembers reaching the limit on the maximum allowable duty time before completing
their work due to flight delays. The resulting cost increases can be of the order of many
millions of dollars for a large airline. To address this issue, researchers, such as Ehrgott
and Ryan (2002), Schaefer et al (2005), Yen and Birge (2000), and Chebalov and Klabjan
(2002) have developed approaches to minimize the sum of planned and unplanned crew
cost.
7.4.1 Robust Crew Pairing: The Role of Crew Connections between Different
Aircraft
Ehrgott and Ryan (2002) propose an approach to balance costs and robustness in
generating crew pairing solutions. For each pairing, they compute its value of nonrobustness by approximating downstream effects of delays within the pairing. In their
approximation, the value of non-robustness is zero if crews do not change planes, but
equals the potential disruptive effects of delays if the plan requires crews to connect
between different aircraft. The objective is to minimize the value of non-robustness,
while maintaining the cost of the corresponding crew pairing solution to less than that of
the minimum-cost crew pairing solution plus some pre-specified positive value.
Ehrgott and Ryan report that small increases in cost allow considerable robustness gains.
In one instance, by increasing costs by less than 1%, they were able to reduce their metric
of “non-robustness” by more than 2 orders of magnitude. Their more robust solutions are
characterized by longer ground times between successive flights on different aircraft
within a pairing; fewer aircraft changes within pairings; slightly longer duty times; and a
slight increase in the number of pairings in the solution.
7.4.2 Minimizing Expected Crew Costs
Yen and Birge (2000) and Schaefer et al (2005) develop approaches that include both
planned and unplanned costs in the objective function of the crew model. Yen and Birge
develop a stochastic crew scheduling model and corresponding solution approach, while
Schaefer et al solve a deterministic crew pairing problem with an objective to minimize
56
expected crew pairing costs. In Schaefer et al, expected costs are approximated for each
pairing under the assumptions that there are no interactions between the pairings and
recovery is achieved simply by delaying the next flight in the pairing until the crew is
available (pushback). Pushback recovery helps to justify the no interactions
assumption, but much more sophisticated recovery procedures are used in practice at
hubs. Even with these simplifying assumptions, it is still not possible to calculate the
realized cost of pairings analytically. Thus the cost of each pairing considered in the
optimization is determined by Monte Carlo simulation.
Schaefer et al denote J as the set of feasible pairings, F the set of flight legs, c~j the
expected cost of pairing j, and let a ij equal 1 if flight leg i is covered by pairing j. The
decision variable x j , for all all j∈P , equals 1 is pairing j is included in the solution, and
equals 0 otherwise.
The robust crew model of Schaefer et al is:
MIN
∑ c~
j
(24)
xj
j∈J
subject to
∑a
ij
xj =1
for all i∈F-
(25)
for all j∈P-.
(26)
j∈J
x j ∈ {0,1}
The objective (24) is to minimize the expected crew costs associated with the pairings in
the solution. The set of selected pairings must contain each flight leg exactly once (25).
Crew schedules obtained with these expected pairing costs are compared with those
obtained by using the standard deterministic costs and also a set of penalty costs whereby
attributes of pairings that might lead to poor operational performance are penalized. The
attributes considered are sit times between flights when a crew changes planes, flying and
elapsed times of duties, and rest time between duties. The operational performance of
crew schedules are evaluated using SIMAIR, with only mild disruptions considered, that
is, individual delays rather than major disruptions such as those which reduce airport
capacity. The standard cost measure of FTC, which is total cost in minutes of pay minus
minutes of flying time divided by flying time, is used to compare schedules. For the
fleets considered from a major airline, the planned FTCs were typically in the 2 - 4 %
range and increased only slightly when either the expected costs or penalty costs were
used. The operational FTCs ranged from 4% to 9% and were lowest for the expected
cost method and very close to a lower bound. However, in an absolute sense the
expected cost solutions performed only marginally better than the deterministic solutions
57
perhaps because of the assumption of mild disruptions only. Note that more severe
disruptions would have invalidated the pushback assumption.
7.4.3 Move-Up Crews
In an approach analogous to the idea in Ageeva and Clarke (2004) of providing flexibility
through aircraft swapping, Chebalov and Klabjan (2002) develop the concept of
enhancing recovery flexibility through move-up crews. A move-up crew for flight i is a
crew, not actually assigned to i, but capable of being assigned to i, if necessary. For
feasibility of this potential assignment, the move-up crew must have the same crew base,
or domicile, as the crew currently assigned to i, must be ready to operate i before the
departure time of i, and must end the pairing on the same day as the pairing currently
covering i. Chebalov and Klabjan consider move-up crews only for flights i that depart
hub locations and do not begin a pairing. The objective is to maximize the number of
move-up crews so that recovery is more likely to be effected by swapping the assigned
pairings of the delayed crew and an available, alternative crew.
Let J represent the set of feasible pairings; F be the set of flight legs; a ij equal 1 if flight
leg i is covered by pairing j; HL designate the set of hub locations; CB be the set of crew
base locations; D be the set of the possible number of days remaining in a pairing; J cb,d
represent the set of pairings starting at the crew base cb with d days remaining after flight
leg i to the end of the pairing; J i be the set of pairings whose first leg is i; J i ,cb,d be the
set of pairings that yields a move-up crew for flight i covered by a crew originating at cb
with d days remaining from flight leg i to the end of the pairing; r be the robustness factor
denoting the maximum allowable percentage increase in the cost of the solution to allow
increased robustness; and M be an arbitrary number (usually 2 or 3). Chebalov and
Klabjan solve the standard crew pairing problem minimizing operating costs with
constraints (25) and (26) to obtain the minimum planned crew pairing costs, copt . They
then include in their model four sets of decision variables. If pairing j is included in the
solution, x j , for all all j∈P, is equal to 1, otherwise it equals 0. If flight leg i is covered
by a pairing starting at the crew base cb with d days remaining after flight leg i to the end
of the pairing, y icb,d is equal to 1, otherwise it equals 0. If flight leg i is covered by a
pairing whose first leg is i, wi is equal to 1, otherwise it equals 0. The number of moveup crews for flight leg i , if i is a leg originating at a hub h∈HL, is denoted by z icb,d .
The Chebalov and Klabjan model is:
MAX
∑ ∑ ∑
i∈F
z icb,d
(27)
cb∈CB d ∈D
subject to
58
∑a
ij
x j = y icb,d
for all i∈F originating at any hub
(28)
for all i∈F originating at any spoke
(29)
j∈J cb , d
∑a
ij
xj =1
j
= wi
j∈J
∑x
for all i∈F originating at any crew base
j∈J i
(30)
∑ ∑y
wi +
cb
i ,d
=1
for all i∈F originating at any crew base
cb∈CB d ∈D
(31)
∑ ∑y
cb
i ,d
=1
for all i∈F originating at a hub but not a crew base
cb∈CB d ∈D
(32)
∑x
j
≥ z icb,d
for all i∈F originating at any hub
(33)
for all i∈F originating at any hub
(34)
j∈J i , cb , d
z icb,d ≤ My icb, d
∑c
j
x j ≤ (1 + r )copt
(35)
j
x j ∈ {0,1}
for all j∈J
(36)
wi ∈ {0,1}
for all i∈F
(37)
y icb,d ∈ {0,1}
for all i∈F, d∈D, cb∈CB
(38)
z icb,d ∈ {0,1,…, M}
for all i∈F, d∈D, cb∈CB.
(39)
Constraints (29) and (36) ensure that each flight leg i is covered by exactly one pairing.
With constraints (37)-(39), constraints (30) identify flight legs that are the first leg in a
pairing and constraints (28), (31) and (32) identify flight legs that are candidates for
move-up crews. The number of move-up crews for flight leg i is bounded by 0
(constraints 33) if i originates at a spoke location or is the first leg in a pairing, and
otherwise it is bounded by the minimum of M (usually 2 or 3), and the number of eligible
move-up crews for i (constraints 34). Constraint (35) ensures that the pairing solution has
cost no greater than an allowable tolerance above the minimum cost pairing. The
objective (27) is to maximize the total number of move-up crews for all flight legs.
59
Chebalov and Klabjan present a Lagrangian decomposition method to solve their model.
They perform computational experiments and report, that for certain instances, there are
crew solutions characterized by only slightly higher planned costs and by a 5- to 10-fold
increase in the number of move-up crews, compared to the optimal solutions to the more
conventional, cost-minimizing crew pairing problem.
8. Conclusions
Flight and crew schedules and passenger itineraries have become increasingly “fragile”
as a result of the growing complexity of the air transportation system and the tight
coupling of its various elements. The resulting direct and indirect economic costs are
very large, certainly amounting to several billion dollars annually. The airline industry
has a vital stake in research aimed at mitigating the effects of severe weather and other
disruptive events and at expediting recovery from “irregular” operations.
As this chapter has indicated, a very significant body of recent and ongoing work has led
to major progress toward these objectives. Two breakthrough developments have been
the primary drivers behind this progress. First, Collaborative decision making has made
it possible to apply the principles of information sharing and distributed decision making
to ATFM, by expanding the databases available to airline and FAA (and, soon, European)
traffic flow managers, creating common situational awareness and introducing shared
real-time tools and procedures. And second, there is growing recognition in the airline
industry of the fact that planning for schedule robustness and reliability may be just as
important as planning for minimizing costs in the complex, highly stochastic and
dynamic environment of air transportation. Specific achievements that have been
described herein include: improved understanding and better modeling of the physics of
airport and airspace capacity and delays (Section 2); realization of the need for marketbased mechanisms to supplement widely-used administrative methods for allocating
scarce airport capacity among prospective airport users (Section 3); development of
models and optimization tools to support GDP decision-making under a wide range of
conditions, including the presence of uncertainty regarding forecast capacity and demand
(Section 4); development and implementation of airline-based models for efficient
“recovery” of aircraft, crews and passengers following schedule disruptions (Section 6);
and the nascent appearance of increasingly viable models for introducing robustness in
airline route design and in the scheduling of aircraft, crews and passengers (Section 7).
At the same time, it is fair to describe all this work as still being in its early stages in
many respects – an assessment that applies equally well to the domains of both the
airlines and the providers of air traffic management services. For example, in the case of
the latter, approaches for dealing with uncertainty – an altogether critical issue in the
ATM and ATFM context – are still quite far removed from being applied in practice.
Integrated consideration and optimization of both arrival and departure schedules at GDP
airports could also offer significant improvements over the existing approaches that focus
solely on arrivals. Research on collaborative routing is still in its infancy. On the side of
the airlines, decision support software for recovery is perhaps at the stage where planning
60
software was 15 years ago. While research is active and hardware and data support have
improved substantially, optimization-based decision support tools for rapid recovery are
still at an early stage of implementation at the major airlines. Finally, and most
important, a full integration of the emerging ATFM CDM philosophy and associated
models with airline recovery planning models and robust scheduling models has not even
begun. This represents a difficult, but crucial future research challenge.
9. Acknowledgements
The work of the first and fourth authors was supported in part by NEXTOR, the National
Center for Excellence in Aviation Operations Research, under Federal Aviation
Administration cooperative agreement number 01CUMD1. The work of the second and
fourth authors was supported in part by the Alfred P. Sloan Foundation as part of the MIT
Global Airline Industry Program.
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