DEMAND MANAGEMENT AT CONGESTED AIRPORTS: HOW FAR ARE WE FROM UTOPIA? by Loan Thanh Le A Dissertation Submitted to the Graduate Faculty of George Mason University in Partial Fulfillment of the the Requirements for the Degree of Doctor of Philosophy Systems Engineering and Operations Research Committee: George L. Donohue, Dissertation Director Chun-Hung Chen, Dissertation Co-Director Karla Hoffman, Committee Chair Jana Kosecka Daniel Menasc´ e, Associate Dean for Research and Graduate Studies Lloyd J. Griffiths, Dean, The Volgenau School of Information Technology and Engineering Date: Summer Semester 2006 George Mason University Fairfax, VA
Transcript
DEMAND MANAGEMENT AT CONGESTED AIRPORTS:HOW FAR ARE WE FROM UTOPIA?
by
Loan Thanh LeA Dissertation
Submitted to theGraduate Faculty
ofGeorge Mason University
in Partial Fulfillment of thethe Requirements for the Degree
ofDoctor of Philosophy
Systems Engineering and Operations Research
Committee:
George L. Donohue, Dissertation Director
Chun-Hung Chen, Dissertation Co-Director
Karla Hoffman, Committee Chair
Jana Kosecka
Daniel Menasce, Associate Dean forResearch and Graduate Studies
Lloyd J. Griffiths, Dean, TheVolgenau School of InformationTechnology and Engineering
Date: Summer Semester 2006George Mason UniversityFairfax, VA
DEMAND MANAGEMENT AT CONGESTED AIRPORTS: HOW FAR ARE WEFROM UTOPIA?
A dissertation submitted in partial fulfillment of the requirements for the degree ofDoctor of Philosophy at George Mason University
By
Loan Thanh LeBachelor of Science
University of Natural Sciences, Ho Chi Minh City, Vietnam, 1998Master of Science
University of Paris I-Pantheon-Sorbonne, Paris, France, 1999
Director: George L. Donohue, ProfessorCo-Director: Chun-Hung Chen, Associate Professor
Department of Systems Engineering and Operations Research
Early 2002, professor George L. Donohue gave me this invaluable opportunity of pur-suing a Ph.D. degree in Air Transportation, and I began my quest in the Departmentof Systems Engineering and Operations Research at George Mason University. With-out his trust in my capability, none of this would have happened. Over the years, Ihave learned so many things, accomplished a few things, and met people who havebeen genuine professors, colleagues and friends. I would like to thank all of them whomade this experience possible and so enjoyable.
I have had the privilege of working with Professor George Donohue, my researchadvisor, mentor, and role model, to whom I owe deep gratitude for many things.Dr. Donohue introduced me to the wonderful world of air transportation. His broadknowledge and outstanding vision in the aviation system guided me throughout thejourney. Dr. Donohue has high expectations of his students, and I thank him forchallenging me to carry through with the research. Beyond his academic virtues, Iam also grateful for many discussions with him that teach me the values of integrityand tolerance. I look forward to working with Dr. Donohue in the future.
In the same manner, Dr. Chun-Hung Chen, my research advisor, exerted a stronginfluence on me in daily research process. Not only did Dr. Chen convey to meinvaluable knowledge in discrete event simulation, he also made sure that my researchwas on the right track. Dr. Chen demonstrated how to be a good researcher and agood mentor by his academic rigorousness, diligence, and understanding towards hisstudents.
My sincere gratitude goes to Dr. Karla Hoffman, my committee chair, who taughtme invaluable knowledge in optimization theory, and difficult but fascinating prob-lems of the airline industry. Dr. Hoffman’s work ethics and professional qualitieshave always been a great source of inspiration for me, and will stay as such in myfuture endeavors. She also kindly helped revise this dissertation with great care andattention. I am deeply grateful for her time and efforts. Without her help, thisdissertation could not have been written as it is.
It is a pleasure for me to have Dr. Jana Kosecka in my committee. I would liketo express my thanks for her suggestions and warm encouragements throughout thecompletion of this dissertation. I am also very grateful to Dr. John Shortle, Dr. LanceSherry, Dr. Donald Gross, and Dr. Alexander Klein for their thoughtful commentsand advice about my research. Their insights were always very helpful. I also wouldlike to thank my colleagues at Center for Air Transportation System Research, ArashYousefi, Richard Xie, Danyi Wang, Bengi Menzhep, Babak Ghalebsaz, Ning Xu,and Jianfeng Wang, for enriching discussions regarding my research, and their warm
iv
friendship. Many thanks to Angel Manzo and Alerie Karen who were exceptionallyhelpful in taking care of all my paperwork throughput the program.
Last but not least, I deeply appreciate the distant support of my parents. Theirself-giving love and constant encouragement stand by me in my pursuit of the doctor-ate. I also would like to thank my relatives in Virginia for sharing with me so manyrelaxing and comforting moments. Finally, I thank Michael C. Ahlers for all of hiscomputer technical help, for the extra RAM he gave me to help boost my laptop’sspeed, and for always being there for me.
I can not express enough my thanks to all the people who have helped make thisexperience possible and memorable!
Modern CNS systems support air traffic flow management to better accommodate
demands on the day of operations. For long-term planning, viable procedures should
be devised to strategically bring demand in line with capacity. The recent US com-
mission on the future of the Aerospace Industry [6] recognizes that technology alone
will not solve the modernization and capacity limitation problem. Policies need to be
changed to cope with future operational and economic needs of the air transportation
system.
1.1.3 Demand management
Fan02 [7] defines demand management measures as any set of administrative or eco-
nomic measures - or combinations thereof - aimed at balancing demand in aircraft
operations against airport capacities. These measures intend to coordinate changes
of airline schedule. The International Air Transport Association (IATA) provides de-
mand management guidelines for 3 different categories of airports: Non-coordinated
airports, schedules facilitated airports, and coordinated airports. Slot allocation pro-
cedures rely on airlines’ voluntary cooperation through IATA coordination at bian-
nual conferences [8]. The reader is referred to “A Practical Perspective on Airport
Demand Management” [7] for a thorough survey on airport demand management
schemes around the world.
7
1.2 Congestion management by demand manage-
ment in the US
Today, at most U.S. airports, airlines have latitude to schedule flights with no limits
on access other than those imposed by ATM requirements or by resource constraints
such as availability of passenger terminal gates. Air traffic controllers follow a first-
come, first-served acceptance rule.
Congestion management by demand management measures was first implemented
in 1969 with the High Density Rule (HDR)3 instituted at the John F. Kennedy Inter-
national (JFK), LaGuardia (LGA), Newark International (EWR), Chicago O’Hare
International (ORD), and Ronald Reagan Washington National (DCA) airports4.
The HDR limits the number of Instrument Flight Rules (IFR) takeoffs/landings at
High Density Traffic Airports (HDTA) by hour or half hour during certain hours of
the day. The HDR classifies user groups as air carrier, commuter, and other operators.
Reservations, also called slots, for regularly scheduled IFR operations conducted by
air carrier and commuter operators are allocated in accordance with 14 CFR part 93,
subpart S, Allocation of Commuter and Air Carrier IFR Operations at HDTAs, which
consists of administrative approval by the Secretary of Transportation. A reservation
authorizes an operation only within the approved time period unless the flight en-
counters an air traffic control (ATC) traffic delay. Advisory Circular 93-1 provides
information for obtaining IFR and Visual Flight Rules (VFR) reservations for un-
scheduled operations at HDTAs. FAA stated that the rule would expire at the end of
1969 but then extended it to October 25, 1970. In 1973, it was extended indefinitely.
314 Code of Federal Regulations [CFR] part 93, subpart K, High Density Traffic Airports4HDR restriction was lifted at EWR in the early 1970s, and at ORD on July 2, 2002
8
In addition, the perimeter rule limits flights at DCA and LGA at maximum 1,250
miles and 1,500 miles for nonstop market distance, respectively5.
The deregulation in 1978 brought about the massive expansion of air travel and
also the competitive tension between airlines that had been historically present at the
HDTAs and new airlines that wanted to enter the markets. In 1985, “grand-father
rights” institutionalized the slot ownership for current holders of slots allocated to
domestic operations. These carriers may sell or lease their slots, and have to return a
slot back to a pool of unused slots for re-allocation if it is used by the current holder
for less than 80% of the time. This “use-it-or-lose-it” provision was initially designed
to prevent non-competitive holding of slots, promote efficiency in utilizing runway
capacity, and market entrance. However, there are two criticisms of this practice.
The first is that the airlines do not own these slots, and the airport operator should
be allowed to manage the allocation of these slots to assure safety, control congestion
and maximize passenger/freight throughput. The second is that airlines are accused
of being selective in choosing who is allowed to purchase slots from them, thereby
preventing competitors from gaining access to useful slots.
The Wendell H. Ford Aviation Investment and Reform Act for the 21st Century
(AIR-21), enacted in April 2000, initially intended to address the competition issue of
the grand-father rights at LGA, JFK and ORD. It exempted from the HDR limits cer-
tain flights by new entrant or limited incumbent air carriers using 70-seat or smaller
aircraft between a small hub or non-hub airport and these three airports. It also pro-
vided for ORD to eliminate slot controls in 2002, and for LGA and JFK to eliminate
5The controversial Wright and Shelby Amendments imposed perimeter rule and aircraft size at
Dallas Love Field airport in 1979 and 1997 respectively, although not for congestion reason
9
slot controls on January 1, 2007. Immediately, airlines filed exemption requests for
more than 600 daily flights at LaGuardia, which represented a daily increase of more
than 50 percent of operations. The additional 300 accepted flights then pushed Fall
2000 demand 20% above the airport’s capacity, as shown in Figure 1.1. This resulted
in record delays at LGA, with an average delay per aircraft of almost 90 minutes (see
Figure 1.2).
There were more than 9,000 delay flights at LaGuardia in September 2000, up
from 3,108 in September 1999, which constituted more than 25% of the delayed
flights in the entire country, up from 12% in the previous year. The percentage
of delayed flights at LaGuardia, 15.6%, was nearly twice that at the nearest airport,
Newark International, at 8%. Furthermore, as the problems caused by congestion and
delays worsened, a ripple effect was experienced at airports across the NAS. Airlines
routinely cancelled scheduled flights, especially in afternoon and evening hours, in an
effort to avoid greater delays on other flights that would depart for LGA late in the
day.
On September 19, 2000, in response to mounting delays, the Port Authority of
New York and New Jersey (PANYNJ) announced that it was imposing a moratorium
on additional flights at LGA. The FAA followed with its own plan to rescind the
AIR-21 LGA slot exemptions that had already been granted and redistribute those
exemptions by a lottery. FAA described this measure as temporary and said it would
terminate restrictions on September 15, 2001. The controversial slot lottery randomly
allocated 159 exemption slots to incumbent carriers serving small communities and
new entrant airlines. On June 7, 2001, FAA placed a Notice in the Federal Register
regarding demand management at LGA. The Notice solicited public comments on
10
Figure 1.1: Increasing traffic intensity at EWR, LGA, and JFK airports
Figure 1.2: Similar trends of average delay per aircraft at EWR, LGA, and JFK
airports
11
potential methods to allocate LGA airport capacity.
The events of September 11, 2001, followed by the economic slowdown in mid
2002, brought down demand and diverted attention from airport congestion to air-
port safety. The outcome of the lottery remains in effect today with minor changes
determined by an administrative process. Over the past few years, demands at the
three airports have increased back to pre-2001 levels, and at LGA it now surpasses the
airport’s capacity (see Figure 1.1, where facility-reported capacities are calculated by
averaging actual daily capacities throughout the observation period). The rebound
in operations has brought about resurgence in delays to pre-2001 levels, with EWR
having average delay per aircraft as high as one hour. Delay patterns of LGA, EWR,
and JFK are shown in Figure 1.2. They exhibit periodic behavior with mid-summer
and mid-winter having highest delays. The similarity in pattern of the three curves
reflects that the three airports, being close to each other, experience the same seasonal
traffic trend and weather effects.
The removal of HDR at ORD airport in July 2002 experienced the same over-
scheduling and severe congestion problems as at LGA airport in 2001. From April
2000 through November 2003, American and United Airlines, the two dominant carri-
ers that provide 85% of flights at ORD, increased their scheduled operations between
the hours of 12 p.m. and 7:59 p.m. by 10.5% and 41% respectively. However, seat
capacity by each carrier decreased more than 5.5 percent over the same period. By
November 2003, O’Hare was the most congested airport in the NAS with record num-
ber of delays: only 57% arrivals and 67% departures were on time, and delays averaged
about an hour per flight [3]. The government’s efforts in administrative congestion
regulation led to the two airlines’ two rounds of schedule cutbacks in March and June
12
2004, only to be met by other airlines’ addition of flights. Bilateral scheduling re-
duction meetings between DOT officials and individual airlines were then necessary.
In these meetings, the government mostly reinstated HDR for arrivals at ORD as a
temporary measure until April 2008.
1.3 Motivation
The over-scheduling that causes delay and congestion reflects increasing demand in
airline operations. However, this increasing demand is partly manifested by the inef-
ficiencies within the overall airline schedules.
At EWR airport, the increasing number of operations is contrasted by the decline
in passenger throughput. The blue time-series bars of the first chart in Figure 1.3 plot
the annual actual operations at EWR, and the red time-series bars show the annual
passengers. These time series do not have a common y-axis as the chart intends to
show the relative trend of individual time-series. One notices three trends: (i) the
number of operations has increased little over the period; (ii) the number of passengers
has decreased slightly and (iii) the size of aircraft used has decreased significantly.
Despite constantly high levels of operations, the average aircraft size is decreasing
from 133 seats in 2000 down to 105 seats in 2005.
One can see similar trends of aircraft size at LGA. The overall shift from large jets
to smaller aircraft increases the system workload while keeping passenger throughput
the same or decreasing. Systemwise, regional jets carry fewer passengers each flight
and represent 37 percent of the commercial traffic at the nation’s 35 busiest airports,
up from 30 percent in 2000 [1]. For the FAA, less weight-based landing fees due to
increasing proportion of small aircraft have resulted in less tax revenues flowing into
13
Figure 1.3: Increasing operations vs. decreasing enplanements at EWR, decreasing
aircraft size at EWR and LGA
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the Aviation Trust Fund, which pays for most of the FAA’s costs to run the system.
Due to the industry’s economics of scale and competition pressure, airlines have
incentive to schedule smaller aircraft at higher frequency, causing congestion to persist
even when the U.S. air traffic system builds more runways and/or improves computer
facilities. As a result, appropriate demand management measures have become more
critical to help regulate the demand, especially to prepare for the current planned
removal of HDR at LGA and JFK in January 2007. FAA’s 2001 “Notice of Alterna-
tive Policy Options for Managing Capacity at LaGuardia Airport” [9], DOT’s 2001
“Notice of Market-based Actions to Relieve Airport Congestion and Delay” [10], and
FAA’s 2005 “Notice of proposed rulemaking (NPRM), Congestion and Delay Re-
duction at Chicago O’Hare International Airport” were met with extensive response
from the industry [11] [12], the research community [7][13][14][15], and other inter-
ested parties [16][17][18][19] demonstrating the relevance of the issue. Subsequent
FAA-sponsored Congestion Game 1 conducted at George Mason University in Nov
2004 [20], and Congestion Game 2 conducted at University of Maryland in Febru-
ary 2005 [21] investigated the impacts of various administrative and market-based
options.
Similarly to those efforts, this dissertation aims to contribute to the understanding
of potential demand management solutions at congested airports such as EWR, LGA
and ORD. In particular, current slot restrictions at LGA and JFK are due to be
lifted on January 1, 2007. As of June 2005, no policy or plan is in place to manage
congestion after that time. If slot controls are extended in 2007, government goals of
increasing the fairness and efficiency of airport use will go unmet.
15
1.4 Statement of the problem
We demonstrate that the current congestion situation is caused in large part by the
existing rules. Specifically, we show that grand-father rights with 80%-use-it-or-lose-
it requirement, and slot exemptions lead to great inefficient use of airport capacity.
We point out that this inefficiency affects both airlines and airports. Faced with
projected traffic growth, the current rules at congested airports have to change.
We then examine the economics of providing air transport at congested airports
from both airline’s and airport’s perspective. We calculate average price elasticities
at various times of day based on sample ticket prices, actual sales and schedules.
We couple this with cost data for the airlines to determine the profit-maximizing
fleet size needed to accommodate demand. By examining such schedules, we can
determine goals that achieve better throughput without altering the natural behavior
of the flying public. By answering the above questions, we hope to better understand
incentives that would encourage a better reallocation of air traffic.
In order to better understand how to encourage efficient use of congested airports,
we state our research problem as follows:
Research Problem 1 Are current rules of slot allocation the main causes of the
congestion problem?
Research Problem 2 Focusing on LGA airport where the congestion problem has
been the most severe, and assuming that current slot allocation rules causing conges-
tion identified in research problem 1 are removed, can we identify flight schedules and
16
fleet mix that are profitable to airlines and that can accommodate the existing de-
mand yet reduce congestion, given current prices and price ellasticities? Specifically,
to accommodate profitably the current demand,
• What is the optimal fleet mix and frequency for each market?
• What would altering the schedule and fleet mix impact:
– Average delay per aircraft?
– Operation throughput?
– Enplanement opportunities?
– Fare?
– Number of markets?
Analyzing airline schedules requires the understanding of airline economics and
operations to avoid unduly affecting the business models of air carriers by forcing
impractical regulations. Therefore, modeling airline scheduling decisions is essential.
Initially, modeling individual airlines and their interaction in an N-side game setting
is theoretically desirable. However, this approach is impractical for many reasons:
• There is an infinite number of competition behaviors. Faced with incomplete
market information and competition pressures, an airline could react rationally
or irrationally, optimally or suboptimally depending on the market’s structure.
It is difficult, if not impossible, to model all possible behaviors or even be able
to identify such behaviors.
• Behavior of new entrants would require assumptions and data that are difficult
to validate.
17
• Publicly available data for individual airlines are limited, especially for small
carriers with little market presence. The data also contain inherent noise.
We therefore take a novel approach toward answering the above questions. We
model a single benevolent airline that seeks to optimize the profit of its operations at
LGA airport. While still modeled as profit-maximizing, this single airline is benevo-
lent in the sense that (i) the airline reacts to actual and realistic price elasticities of
demand that are estimated in a competitive market, and (ii) it is willing to cooperate
with the public goals. Its resulting optimal schedule can provide an analytical bench-
mark towards which a reallocation of air traffic load should be encouraged to move.
Clearly, the idea of a monopoly airline is neither practical nor desirable, but solv-
ing the scheduling from a single benevolent airline’s perspective might help airport
authorities understand how best to encourage efficient use of airport resources, may
indicate the relative cost of serving specific markets, and also better understand the
effects of altering traffic loads within given periods on delays and prices. On the other
hand, the real market data we use to estimate price elasticities incorporate actual de-
mand curves and prices of the current competitive market, not of a monopoly market.
Therefore, the concept of a single benevolent airline should not be too restrictive.
1.5 Contributions of this dissertation
The research presented in this dissertation seeks to validate the following hypothesis:
1.5.1 Primary hypothesis
Hypothesis 1 The current congestion situation is caused in large part by the exist-
ing rules of slot allocation. Specifically, grand-father rights with 80%-use-it-or-lose-it
18
requirement, and slot exemptions lead to great inefficient use of airport capacity.
Hypothesis 2 Without the restriction rules identified in hypothesis 1, there exist
profitable flight schedules that can accommodate the current passenger demand and
reduce flight delay.
1.5.2 Research scope
The case study of our research focuses on LGA airport. LGA is a typical non-hub
airport that serves mostly local traffic to and from domestic markets. The same
methodology can be used to examine other congested regions and expanded to con-
sider larger networks. Specifically, the research seeks the optimal domestic flight and
fleet schedules for nonstop markets at LGA from a single benevolent airline’s perspec-
tive. We only consider markets that have daily profitable schedules to LGA. When
the model does not accommodate all the demand of a certain market (because it is
unprofitable to do so regardless of airplane size), which leads to capacity reduction or
even removal, such results can highlight the cost of maintaining the current demand
levels.
Excess of operations, once identified, would be assumed to move to reliever airports
in the area such as Stuart, White Plains, Islip, or Teterboro. How this excess should
be reallocated is beyond the scope of this dissertation.
Additionally, runway capacity is used as a surrogate to airport capacity, with the
assumption that other facilities such as ATC, taxiway, ramps, gates, and terminals
have sufficient resources to support the operation of airport runways at their capacity
levels6. We evaluate the on-time performance of the resulting schedules, and other
6Klein et al. [22] investigated the constraints of these support facilities on the fleet mix at LGA
19
metrics of interest such as the operations throughput, enplanement opportunities,
changes in fare, changes in the number of markets, and aircraft size.
The research investigates different optimal reallocation benchmarks for scenarios
with different capacities and public goals, along with guidelines for potential transition
paths. However, detailed transition plans require in-depth investigation into different
allocation mechanisms (administrative or market-based) and therefore are beyond the
scope of this dissertation.
1.5.3 Contributions
Contributions of this dissertation are categorized into four main areas:
Development of an airline flight and fleet scheduling model that incor-
porates the interaction of demand and supply through price (Chapter 3)
Appropiate congestion measures require the understanding of airline economics and
operations to avoid unduly affecting the business models of air carriers by forcing
impractical regulations. Therefore, modeling airline scheduling decisions is a central
part of this research. Unlike existing flight scheduling models that use fare as a pa-
rameter, our flight and fleet scheduling model considers fare as a variable negatively
dependent on supply level. This design choice allows the analysis of effects of changes
in schedules on average fares.
Development of a computationally-efficient solution algorithm to find the
optimal set of schedules (Chapter 3) We devise at each of the airports a column
generation algorithm to determine the optimal collection of schedules for each of the
Origin-Destination pairs based on the capacity constraints of the airports in study.
20
The decomposition algorithm decomposes the problem into a master problem that
optimizes use of the airports while the subproblems find optimal O/D schedules based
on current prices and demand curves.
Development of a methodology for estimating demand curves by time of
the day from publicly available sources (Chapter 4) We perform data mining
of ASPM and BTS databases to break down the aggregate data by quarter of the
year to aggregate data by day and time of day.
Development of a delay stochastic simulation network model to evaluate
flight schedules (Chapter 5) We develop a simulation model that explicitly con-
siders wake vortex separation standards between categories of aircraft to simulate
runway capacity. Delays are estimated based on runway capacity. The simulation
model is simpler than the Total Airspace and Airport Modeler (TAAM), and yet
capable of evaluating the implications of fleet mix on runway operations throughput.
Demonstration of the existence of profitable airline schedules that reduce
congestion and accommodate current passenger throughput level (Chapter
6) We find the optimal demand allocation benchmarks for scenarios that assume
different capacity levels and public goals. The public goals investigated in this disser-
tation are (i) maximizing profit, (ii) maximizing seat throughput, and (iii) maximizing
the number of markets and seat throughput. The resulting schedules are then eval-
uated against the metrics of interest: Operations throughput, average flight delay,
seat throughput, average aircraft size, number of regular markets, and average fare.
The results show that at Instrument Meteorological Condition (IMC) rate of runway
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capacity, airlines’ profit-maximizing responses can be expected to find scheduling so-
lutions that offer 70% decrease in flight delays, 20% reduced in number of flights with
almost no loss of markets and no loss of passenger throughput.
1.6 The potential readers
This research should be of interest to both the public policy makers and airport
authorities. With modifications to include specific business constraints, airlines could
also extend this model to analyze and restructure the flight networks.
1.7 Dissertation outline
The next chapter answers the first hypothesis by conducting data analysis. We use
flight load factors and aircraft sizes as two main metrics to point out the inefficiency
in current slot usage. Current policy that affects these two metrics is then identified.
Chapter 3 provides a review of current research on demand management. We
present different proposals, studies and experiments, and summarize their premises,
analysis techniques, findings, pros and cons. In addition, we also investigate the
literature of works related to our research approach. These include integrated models
of flight scheduling and fleet assignment, and models of flight delay simulation.
In Chapter 4, we develop the mathematical formulation for our airline scheduling
model and government’s allocation model. While the airline scheduling model only
seeks to maximize profit, we formulate three different objective functions for the
government’s model. The interaction between demand and supply through prices is
explicitly incorporated in the airline model by the use of revenue functions and their
22
piecewise linear approximations. The concept of nesting revenue functions to model
demand spill and recapture is introduced next. Column generation is then used to
link these problems to find the final solution.
Chapter 5 explains how we estimate parameters for the scheduling models using
publicly available databases. To build the arcs of the flight network for each market,
we calculate flight lengths for different fleets. Cost is then added to the arcs using
estimated direct operating cost and fuel consumption. To estimate revenues, we
contract the daily demand curves for time windows of two time granularities.
Our stochastic delay simulation network model presented in Chapter 6 serves to
evaluate the output schedules. The model simulates the aircraft dynamics through
queuing systems of the enroute airspace and various airport facilities. We assume that
runway capacity is the main chokepoint. Wake vortex separation between pairs of air-
craft determines runway throughput. We present delay and cancellation propagation
to simulate network effects.
In Chapter 7, the solution procedures are applied to LGA airport. We investigate
scenarios corresponding to different objective functions andn airport operational rates.
Metrics of interest are evaluated, compared, and interpreted.
Finally, chapter 8 summarizes the major contributions and findings of this disser-
tation. We also outline future improvements, and potential directions for research in
demand management.
Chapter 2: Literature Review of Prior Research
This chapter presents a survey of the latest proposals for congestion management,
followed by current developments of existing analytical tools that are needed in our
approach. We start with demand management measures and discuss the general ad-
vantages and limitations of each option. As airline scheduling reactions are important
in the assessment of new demand management procedures, we next describe models
that could be potentially used to simulate airline responses. The resulting schedules
then need to be evaluated in terms of delay performance. Therefore, we conclude the
chapter by looking at some major delay and cancellation estimation models.
2.1 Congestion Management by Demand Manage-
ment Measures
When capacity expansion is either not possible or will not occur prior to serious de-
lays without some congestion management tool, one needs procedures for limiting
the demand into a congested airport. Government agencies (e.g. the Department of
Transportation, the FAA, the House of Representatives), industry spokesmen, and the
research community have identified and studied potential methods to allocate runway
capacity at airports with high demand. Such options include administrative proce-
dures, market-based options and some hybrid approaches. Administrative options
consider removing certain users, restricting entry of unscheduled flights, and alter-
ing the mix of users through lottery or legislature. Market-based proposals advocate
23
24
congestion pricing and slot auctions. We present many of these ideas next.
2.1.1 Administrative options
The Subcommittee on Aviation’s Hearing on The Slot Lottery at LaGuardia Airport
[23], FAA’s 2001 Notice of Alternative Policy Options for Managing Capacity at
LaGuardia Airport and Proposed Extension of the Lottery Allocation [9], and FAA’s
2005 Notice of proposed rulemaking (NPRM), Congestion and Delay Reduction at
Chicago O’Hare International Airport [24] suggest the following:
Reallocate general aviation (GA) aircraft slots. Six slots per hour at La-
Guardia are allocated for general aviation flights by corporate jets. These unsched-
uled private flights could move to Teterboro airport in New Jersey, which is only
12 miles to midtown Manhattan and functions as a general aviation reliever airport.
However, Teterboro airport is currently highly congested as well.
Eliminate extra sections. An extra section is an additional flight that is added
dynamically by airlines to accommodate the overflow passengers. Extra sections are
popular on the Washington to New York and Boston to New York hourly shuttles
when the first flight (or section) fills up. Airlines do not need a slot or slot exemption
to operate an extra section.
Eliminate the use-or-lose-it requirement. The requirement that airlines use
their slots at least 80% of the time was imposed to ensure these limited assets would
actually be used and not hoarded. This has, in the past, forced carriers to operate
unwanted flights just to maintain their slots for “better times”, resulting in inefficient
25
use of runway capacity. If airlines did not have to be concerned about the loss of a
slot, they might be more willing to reduce their schedule.
Increase the use-or-lose-it requirement to 90% of the time for a two-month
period The option expects to create a faster turn-around of unused slots so that
scarce public resource can be exploited to the greatest possible extent. However, a
higher threshold of utilization rate is likely to increase the inefficiency created by the
80% limit.
Suspend leases under the buy-sell rule. The buy-sell rule allows the slot holder
to lease unused slots to other air carriers. Under this rule, a carrier could use a slot for
weekday flights and then lease the same slot to another carrier for weekend operations.
The Notice suggests that suspending leases under the buy-sell rule would reduce slot
usage rates by only allowing one carrier to use a slot during any given week.
Extend the lottery from slot exemptions mandated by AIR-21 to all slots
and slot exemptions. Slot lottery was initially considered as a temporary measure
as randomly allocating scarce resources obviously can not be optimal. Slot lottery
remains in effect until today because better solutions identified so far are not ready
to be implemented. The lottery of slot exemptions involves only a small number of
exemption flights by new entrants and small, non-incumbent carriers, to small and
non-hub airports. We argue that extending the lottery to all slots would unduly
disrupt the existing market structure with long established schedules of incumbent
airlines, and demand. Consequently, this option would only exacerbate the allocation
inefficiency and provoke strong opposition from incumbent airlines.
26
Allow antitrust immunity. Before the Airline Deregulation Act in 1978, the Civil
Aeronautics Board (CAB), FAA’s predecessor agency, had antitrust immunity au-
thority that allowed airlines to meet and coordinate their schedule within capacity
constraints at an airport. However, such capacity reduction agreements were consid-
ered anti-competitive and were prohibited by the Deregulation Act. CAB retained
the authority to grant anti-trust immunity and that authority transferred to DOT
when the CAB was abolished at the end of 1984. DOT granted anti-trust immunity
to the airlines in 1987 so that they could meet and agree to adjustments in their
schedules in order to reduce the delays that were occurring at that time. In 1989,
DOT’s antitrust immunity authority expired. If this provision of antitrust immunity
was in effect, several small communities that gained service from more than one air-
line under the AIR-21 slot exemptions could coordinate to reduce their frequencies
and consolidate their capacities [23].
Various government agencies, the industry and research community provide qual-
itative assessment of these administrative options. “Reallocate GA aircraft slots”
would remove these small aircraft to make more slots available to larger airliners.
However, the healthy GA community at LGA would want to maintain their easy ac-
cess to downtown Manhattan [17][18]. On the other hand, we think that “Eliminate
the use-or-lose-it requirement” is not practical. Faced with competition pressures
of the economics of scale, airlines would still schedule flights to compete for market
presence. Otherwise, this would allow slot hoarding, airlines will hold on to their
slots without using them, and therefore this option would hinder market access by
other carriers. As such, neither efficiency nor competition gain can be achieved. “In-
crease the use-or-lose-it requirement” might also cause airlines to lose their slots due
27
to unforeseen scheduling conflicts that they could have used productively at a lower
threshold, or force the airlines to fly even more unwanted flights [11][18]. “Suspend
leases under the buy-sell rule” could force airlines reveal their true slot demands but
could also aggravate the inefficiency of the use-or-lose-it requirement as airlines try to
hold on to their slots [23][12]. Similarly, random allocation of scarce runway capaci-
ties to airlines without consideration of economic implications on the markets served
in “Extend the lottery” option is highly inefficient and disruptive to long-standing
tive effects on competition and price, which are the main reasons for AIR-21 slot
exemptions. [18] pointed out that “competition-related problems are inherent in any
administrative allocation of slots. These problems will not be fixed by incremental
changes but only by a more comprehensive market-based approach”.
2.1.2 Market-based options
Let the market decide, laissez-faire. An FAA-mandated 1995 study of the slot
rules concluded that lifting the HDR and allowing laissez-faire would double average
all-weather delays at HDTAs, leading to increased delays at other airports because
of the ripple effects on the Nation Aviation System (NAS) [25]. The delays that
occurred following the passage of AIR-21, and the removal of HDR at ORD airport
[26] demonstrated the impracticality of this option.
Congestion or peak-hour pricing. The current scheme of weight-based landing
fees incentivizes airlines to schedule higher frequencies of smaller aircraft. A small
aircraft occupies the same slot as a large one. Thus passenger throughput declines as
28
smaller aircraft is employed. In contrast, congestion pricing consists of charging a flat
landing fee based upon demand at a particular time of day. Therefore, fees for peak
periods will be higher than for off-peak periods, preventing low-value flights from
being scheduled in peak periods. Increasing per flight cost is expected to encourage
airlines to upguage, and therefore increase the passenger throughput.
While being relatively under-explored in aviation, congestion pricing of transport
networks has been common in road traffic. Examples include traditional methods
using toll booths such as turnpikes and toll roads, as well as more modern schemes
employing electronic toll collection such as the London congestion charge [27], and the
Trondheim toll scheme in Norway [28][29] which both use flat rate. Singapore’s Elec-
tronic Road Pricing [30] imposes time and location-varying rates for access into the
central business district with no toll during off-peak hours. The Highway 407 bypass
of Toronto, Ontario not only allows transponder-equipped cars but also uses digital
video technology to read license plates of cars without transponder, matches them
against the Motor Vehicle Registry’s database, and sends out a monthly bill. High-
way 407 uses variable pricing: higher fees during the morning and evening commuting
times cause discretionary trips to shift to other times of the day, easing congestion for
those paying the higher rates. High-occupancy toll lanes (such as SR-91 in Orange
County, California and Interstate 15 in San Diego, California) charge single-occupant
vehicles who wish to use lanes or entire roads that are designated for the use of high-
occupancy vehicles (HOVs, also known as carpools). There is a pre-determined toll
schedule for every hour of the day. Overall, these implementations, although faced
with initial objection and skepticism, have helped to tweak road usage patterns, de-
crease demand and average trip time in the tolled areas, eventually gaining public
29
acceptance.
Congestion pricing of airport runway access can be considered as a reactive mea-
sure in the sense that prices are adjusted in response to recorded delay levels. Price
regulator would set time-based prices for slots and airlines would set their demands
accordingly. As a result, airline long-term planning is subject to cost uncertainty.
Comments of The US Department of Justice on congestion pricing [18] pointed out
that “a drawback to congestion pricing is the regulator’s lack of knowledge about
what price to set. A regulator may not have good enough information to allow it
to set the right price without frequent experimentation”. Therefore, convergence of
the pricing process is uncertain. In addition, congestion pricing does not consider
the fact that airlines also need gates and ticket counters to operate. The flexibility
in scheduling might not be fully realized if dynamic allocation of support facilities is
not guaranteed.
The U.S. Department of Justice (DOJ) strongly advocates moving to a market-
based slot allocation system [17],[18]. [18] mentioned a congestion pricing application
to highway traffic in Southern California. Corbett (2002) [19] however raised the
concern that flights by small aircraft or to small communities are most likely to suffer
under a congestion pricing approach.
In addition to qualitative references above, recent research contributes more an-
alytical analysis of congestion pricing. Daniel [14] models and estimates equilibrium
congestion prices at a hub airport. Daniel utilizes stochastic queuing theory to com-
pute delays which then translate to congestion costs and prices. The stochastic queu-
ing model is similar to that of Koopman [31] where arrival demands are modeled
30
as nonstationary Poisson distributions. However, it allows multiple servers in treat-
ing departure queues and arrival queues independently, and it assumes deterministic
service time. At the beginning of each 10-min period t, the probability distribution
of the number of aircraft in the system is estimated by solving a set of Chapman-
Kolmogorov equations. These equations are valid for all non negative values of the
utilization rate ρ in contrast to the steady state results which apply only to situations
where 0 ≤ ρ < 1. Specifically, Chapman-Kolmogorov equations solve for the prob-
ability pi(t), i=0,1,2...,m, of having i customers in the system at time t. Expected
queue length at t is then derived and expected waiting time at t can be calculated.
A bottle neck model of airline response adjusts traffic patterns to react to queuing
delays and congestion fees. Operations at hub airports form closely scheduled arrival
and departure banks to increase load factor and decrease connection time. The bottle
neck model assumes costs for each unit of deviation time when an aircraft (i) arrives
before the scheduled arrival time, (ii) arrives after the scheduled arrival time, (iii)
departs before the scheduled departure time, and (iv) departs after the scheduled
departure time. Individual airlines maximize their cost; the social-cost minimizing
planner minimizes the total cost to find congestion prices for actual flight times. Con-
gestion prices are calculated mathematically by evaluating first-order derivatives of
cost formulas. Airlines use congestion prices to update flight costs and solve for the
optimal schedule. The process iterates until equilibriums are found. The approach
was illustrated with an empirical application of the model to Minneapolis-St. Paul
airport (MSP). The research demonstrated a mechanism to compute congestion prices
and attain equilibriums. The results in [14] showed that congestion pricing causes a
reallocation of small aircraft to off-peak periods or to other airports.
31
Pels [32] argued that “several characteristics of aviation markets may make naive
congestion prices equal to the value of marginal delays a non-optimal response”. Pels
pointed out the differences between congestion pricing for road traffic and for aviation:
road traffic considers link-based tolls and road users typically do not have market
power, air transportation is rather node-constrained and airlines often compete under
oligopolistic conditions. Pels’ airport pricing model reflects that (i) “airlines typically
have market power and are engaged in oligopolistic competition at different sub-
markets”, and that (ii) “part of external delays that aircraft impose are internal to
an operator and hence should not be accounted for in congestion tolls”. Pels analyzed
market power distortions in congestion pricing with a two-airport two-airline example
using test data.
Fan [33] demonstrated the effects of demand management when reducing the to-
tal number of flights or spreading out the demand profile. Fan estimated delay in
hour and in aircraft-hour of different schedules: (i) 1,348/day that causes 1 hour
and 20 minutes of delay/flight from 8pm-10pm, (ii) 1,205/day (-10%) that causes
20min/flight (-80%) for the same period, runway capacity set at 75ops/hour, and (iii)
a hypothetical schedule of 1,205/day with demand evenly distributed throughput the
day. The delay estimates suggested that a reduction in total demand is necessary for
airports with constantly high demand profile (LGA), and a shift in demand profile for
airports that have peaks and off-peaks. Fan then investigated the economic benefits
resulting from adopting fine versus coarse congestion tolls for markets with both sym-
metric and asymmetric carriers [13]. Time-based congestion prices were calculated as
the marginal delay cost (=marginal delay * average unit operating cost) caused by
adding a flight at different times of day. The results show that the current landing
32
fees are a lot less than the estimated marginal costs, which can be over $7000 for half
of the day when demand is 1,348/day. Fan concluded that given reasonably elastic
responses in terms of frequency adjustments, the benefits to carriers of instituting
congestion pricing generally exceed the amount of tolls collected.
Schank [34] looked at Boston, LaGuardia and Heathrow airports where conges-
tion pricing had been implemented. He identified institutional barriers that prevent
effective implementation of this option. The identified institutional barriers include
the problem of displaced passengers when low-value flights are displaced, the political
and social equity issues. Social equity is defined as fair treatment vis--vis all groups
of aircraft size. As a result, the research does not recommend the use of congestion
pricing without adequate alternatives for displaced passengers.
Strategic slot auction in primary market Optimal allocation would require
that those flights that are most able to switch to off-peak slots do so, leaving peak
capacity to those that are willing to pay more for the service. Conventional eco-
nomic wisdom suggests that auctions are an efficient allocation mechanism for scarce
resources. Auctions have been successfully used for radio spectrum allocation with
large numbers of interrelated regional licenses [35]. Although modifications would be
required for slot allocation, the use of auctions by the Federal Government to allocate
scarce resources demonstrates the feasibility of using auctions even for complex allo-
cation problems. Airport slots could be packaged with gates and ticket counters. A
strategic auction would establish the rights for airlines to schedule service in specific
time slots. However, since the network is highly stochastic, flights might not be able
to depart/arrive during the designated slots. Therefore, on the day of operations,
33
slots could also be exchanged tactically. Altogether, auctioning slots at the strategic
level could synchronize traffic demand with limited system capacity, and provide a
legal basis for tactical slot exchange to encourage extensive usage of scarce resources.
Proposals to allocate airport time slots using market-driven mechanisms such as
auctions date back to 1979 with the work of Grether, Issac, and Plot [36]. Their proce-
dure was based upon the competitive (uniform-price) sealed-bid auctions for primary
market, complemented by the oral double auction for the secondary market. Rassenti
and Smith [37] explored the use of combinatorial sealed-bid package auctions as the
primary market for allocating airport runway slots. This auction procedure permits
airlines to submit various contingency bids for flight-compatible combinations of in-
dividual airport landing or take-off slots. These studies carried out lab experiments
with cash-motivated subjects and hypothetical slot values. The focus was mainly
on the efficiency and robustness of the auction design in terms of demand revelation,
provided that bidders know the values of the slots and would perform truthful bidding
as their best strategy in a sealed bid auction. However, the assumption that airlines
know the values of slots to submit in a sealed bid auction may be impractical. More-
over, airline network constraints and the large number of slot combinations imply
that an iterative bidding process is indispensable to allow for bidders’ adjustments
without the need for enumerating an exponential number of alternative bids.
The 2001 study by DotEcon Ltd [38] investigated the use of slot auctions at
Heathrow and Gatwick airports in London. In addition to a thorough summary of
the current slot allocation schema in E.U., governed by E.U. Regulation 95/93, and
their implications, [38] proposed simultaneous multiple round auctions of “lot” com-
plemented by a last sealed-bid round. A lot includes the right to use both the runway
34
and terminal facilities. To ensure incentive compatibility, the study proposed pricing
based on opportunity costs rather than the amount winners bid, i.e. winners pay the
highest value alternative use of the capacity. This pricing scheme can be thought
of as second-price payment for single item auctions or Vickrey-Clarke-Groves (VCG)
mechanism for multi-unit multi-item auctions [39][35][40]. The study concluded that
in general, slot auction in primary trading and bilateral buy-sell negotiations in sec-
ondary trading would benefit consumers by increased volume of flights and decreased
fares. However, this conclusion is drawn from qualitative analyses and highly aggre-
gate calculations. There is no modeling of airline scheduling decisions.
A follow-up study by National Economic Research Associates (NERA) [41] ex-
tended DotEcon’s study [38] to provide a more systematic assessment of different
slot allocation schemes at 32 E.U. Category 1 airports. [41] suggested that market
mechanisms in both primary and secondary trading have the potential to address
many of the inefficiencies of current schema. Specifically, a simultaneous ascending
auction, where all lots are sold (either individually or in combination) is most suitable
for the allocation of airport slots. The study concluded that proper implementation
of market mechanisms will result in higher passenger volumes, higher load factors,
reallocation of flights to off-peak times or to uncongested airports, and lower fares
on average. Similarly to [38], the conclusion is highly qualitative with illustrative
calculations of aggregate statistics.
Fan [13] recommended simultaneously ascending auctions for airports with sym-
metric carriers. Interestingly enough, Fan suggested that a market-based demand
management policy can comprise both congestion pricing and slot lease auctions.
Ball (2005) et al. [42] reviewed slot allocation in the U.S and presented a framework
35
for airport slot auction design. The authors put forward the need for three types
of market mechanisms: an auction of long-term leases of arrival and/or departure
slots, a secondary market that supports inter-airline exchange of long-term leases and
a near-real-time market that allows for the exchange of slots on a particular day of
operation. [42] showed that not only would auctions assure that demand is in line
with capacity, but also that the proceeds from auctions would provide the investment
in aircraft avionics to increase capacity in the future by allowing a safe reduction
in aircraft separation. By including many public policy constraints in the design,
an auction encouraging new entries (by providing bidding credits), and discouraging
or disallowing monopolistic control over markets by not allowing a single career to
be awarded more than a given percentage of the available slots. Similarly to [38],
the auction design was a simultaneous multiple round ascending bid auction which
lumps landing/takeoff rights with gates, ticketing and baggage handing facilities. [42]
however did not provide any experimental results.
As an effort to identify potential demand management measures, the FAA and
the Department of Transportation (DOT) requested the member universities of The
National Center of Excellence for Aviation Operations Research (NEXTOR) to design
and conduct a series of government-industry strategic simulations or games to help the
government evaluate three candidate policy options [20]. George Mason University
(GMU) and the University of Maryland (UMD) conducted the fist game in November
4-5, 2004 to explore the HDR and congestion pricing options for LGA airport. Within
the context of the first game, a “Potential Notification of Proposed Rule Making for
an FAA Slot Auction” solicited comments about an ascending clock auction design
with intra-round and package bidding. The proposal suggested the auctioning of 20%
36
of the slots per 15-minute period at LGA every year, with a slot referring to both a
take-off and a landing. The auction determines winning bids for arrivals, and requires
that the associated departures be scheduled within 1.5 hours after the scheduled
landing time of the arrival. Vouchers are introduced as a way to offset the loss of
incumbents’ grandfather rights. A second game took place in February 24-25, 2005
where the industry played a mock auction of LGA landing slots. Both games involved
interested persons from the airline industry, academia, the FAA, airport operator
and federal government communities. Participants played decision-making roles in
simulated real-world scenarios. Due to time limitations, the few simulation rounds run
for each option are not enough to draw significant conclusions about airline scheduling
responses or to find equilibriums. However, the games achieved their design goal:
allowing interested parties to experience first-hand the process of congestion pricing,
and also introducing the industry to how an auction might be run for their application.
The researchers obtained much feedback from the participants. Of particular note
were (i) carriers’ requirement that slots to be combined with other facilities such as
gates, baggage handling facilities, ticket counters, and overnight parking spaces; (ii)
and the need of a transparent disposition of proceedings. Additionally, off-record
discussions proposed auctioning slots at two different levels of priority: high-priority
and low-priority slots. High-priority slots would be guaranteed access during IMC
when airport capacity is reduced, whereas low-priority slots would not. Although
this idea appeared interesting from the research point of view, it was considered too
complicated for implementation.
37
2.1.3 Hybrid options
Maintain HDR and Blind Buy/Sell in secondary market Although HDR
does not create property rights of runway slots, airlines are allowed to sell or lease
unused slots in the secondary market. The purchase, sale or lease of slots in the
secondary market can promote efficient use of slots. These transactions usually in-
volve bilateral negotiation between airlines, on-going government intervention in the
secondary market slot transactions is minimal. However, airlines can discriminate
buyers/tenants to their benefits by giving slots to non-competing carriers and pre-
venting access to competing ones. A blind auction of slots available in the secondary
market that is overseen by the FAA could prevent airlines from engaging in collusion
or purposely not selling/leasing to a particular competitor.
[18] pointed out that “competition-related problems are inherent in any adminis-
trative allocation of slots. These problems will not be fixed by incremental changes
such as adding a blind buy/sell rule as suggested in the Notice [9], but only by a more
comprehensive market-based approach”.
2.1.4 Summary
Table 2.1 summaries administrative and market-based options for demand manage-
ment.
38
Measure Pros Cons
Am
inis
trat
ive
Reallocate GA slots Remove small aircraft, increase slots Objection by GA communityavailable to larger planes
Eliminate extra sections Maintain demand predictability Remove the expansion flexibility of shuttle serviceEliminate the use-or-lose-it Incentivize airlines not to Airlines hold on to their slots w/o using them orrequirement use unprofitable slots continue scheduling to maintain market presenceIncrease the use-or-lose-it Faster turn-around Airlines might fly even more unwanted flightsrate to 90% for 2 months of unused slots or lose slots due to unforeseen disruptive eventsSuspend leases under Reveal airlines’ true slot demand Force airlines to maintain inefficientthe buy-sell rule Faster turn-around of unused slots flights to keep the slotsExtend the lottery Simple Inherent inefficiency of random
allocation of valuable slotsHighly disruptive to long-standing services
Antitrust immunity Facilitate the consolidation Hinder competition, requireof service among airlines on-going government intervention
Mar
ket-
bas
ed
Laissez-faire Simple, airlines would eventually Unconstrained demand creates severe congestionfigure out the market equilibrium Convergence uncertain
Congestion PricingAllocate peak times to Overscheduling, hence congestion, might remainmore valuable services Cost uncertainty for airlinesFlat rate to incentivize aircraft upgauge Convergence uncertainSchedule flexibility for airlines Unfavorable to small markets
Slot auction
Allocate peak times to Require complex packaging with other facilitiesmore valuable services Subject to unpredictable bidding behaviorsFixed cost incentivizes aircraft upgauge Require airline commitment, no warrantyDemand, hence delays, is controlled of slot availability on the day of operations
Hybri
d HDR and blind auction Prevent slot hoarding among airline Does not address grand-father rightsin secondary market coalition in sell/lease of slots in the primary market
Promote secondary market access
Table 2.1: Review of demand management measures
39
Despite very little practical experience of the application of market mechanisms
in airport slot allocation, researchers have made significant progress in trying to
understand the feasibility and implications of these options based on auction and
game theory as well as the use of market-based mechanisms in other domains. Market-
based mechanisms for airport slots raise many issues, including the implementation,
the effect on airfares, consideration of applicable legal requirements, the treatment
of international services, the use of any new revenues, as well as the impact on new
entrants, small airlines, competition, and service to small communities.
Overall, analytical analyses of congestion pricing focus on the convergence of the
pricing algorithm, whereas proposals for slot auction focus on the robustness and
demand revelation requirements of the auction design. However, they all require the
simulation of potential airline responses. Different approaches use different sets of as-
sumptions about the airlines’ slot valuation models and the market’s structure. There
assumptions are not exhaustive nor are they easily validated. In addition, modeling
individual airlines leads to the difficult issue of simulating competition behaviors.
There can be an infinite number of competition behaviors. Faced with incomplete
market information and competition pressures, an airline could react rationally or
irrationally, optimally or suboptimally depending on the market’s structure. In auc-
tions, bidders may attempt to game the auction rules by parking (bidding on low-value
items), signaling (indirectly showing interest on certain items to other bidders with-
out actually bidding for them to keep the standing prices down) and bid shading
(placing a bid that is below what the bidder believes a good is worth). Although re-
cent auction designs have become more robust, new behaviors are expected to emerge
constantly. Therefore, it is difficult, if not impossible, to model and validate all these
40
behavioral potentials. On the other hand, public policy decisions will be made only
with the best information available at the time.
2.2 Route development, flight scheduling and fleet
assignment models
The policy objective of congestion management is to optimize the utilization of airport
capacity by maximizing passenger throughputs within safe capacity and acceptable
delay levels. However, one can not overlook the objectives of air carriers, as com-
mercial entities, to optimize profit or market share. Appropriate congestion measures
therefore require the understanding of airline economics and operations to create the
right incentives. In scheduled passenger air transportation, airline profitability is crit-
ically influenced by the airline’s ability to construct flight schedules containing flights
at desirable times in profitable markets (defined by origin-destination pairs). This
chapter describes the economic model of airline schedule planning, the policy model
of airport authorities, and the process that seeks the optimal compromise between
their conflicting objective functions.
Airline schedule planning includes route development, and schedule development.
Schedule development further entails frequency planning, timetable development and
fleet assignment. The output of these tasks is the ”external” schedule offered to
the flying public. Internally, aircraft routing, crew scheduling, and airport resource
planning allocate airline resources to accommodate the schedule, making sure the
offered schedule is operational. Figure 2.1 depicts the major tasks of airline scheduling
process. For more details of the process, see [43][44]
Route development is typically undertaken together through detailed analysis
41
Figure 2.1: Overview of airline scheduling tasks (Barnhart)
of market entrance possibility and profitability. Frequency (or service level) and
timetable are determined to maximize market coverage from a marketing standpoint
based on various considerations of market conditions, namely competition, passengers’
preference for travel times, and operational constraints such as allowed operating time
windows, rights of park aircraft overnight at certain airports, direct itineraries with
one stop, mandatory or optional flight legs. Most airlines make significant changes to
their schedules at least twice a year to accommodate marketing objectives and to ad-
just for seasonal changes in traffic patterns. Minor and incremental changes are made
to the schedule on a monthly basis to reflect holiday travel patterns or competitors’
scheduling changes.
While the timetable design problem involves selecting an optimal set of flight legs
to be included in the schedule, the fleet assignment problem assumes a flight schedule
with specified departure and arrival times and seeks to optimally assign aircraft types
42
to flight legs to maximize profit. Analysis of aircraft economics combined with seg-
ment demand is essential to determine the right fleet for the right market distances
in order to achieve cost efficiency, subject to the airline’s fleet availability constraint.
Airlines with heterogeneous fleets flying large networks with different haul ranges
have therefore harder fleet assignment problems to solve.
In this dissertation, as the goal is to model airline scheduling practice from the
perspective of airport authorities, we focus on the route, flight and fleet schedule
development. There has been little research on formal models for finding optimal
routes, frequencies and schedule times. Often, decisions involving these tasks are
made through ad-hoc analysis, and they are highly subjective. In contrast, the fleet
assignment problem has been studied extensively in the literature, traditionally as
a separate problem [45][46][47] and later in conjunction with the aircraft routing,
maintenance and crew scheduling problems [48][49].
Lohatepanont [44] integrates timetable planning and fleeting problems. In addi-
tion to the set of mandatory flights, flights are selected among a given set of optional
flights to find the optimal schedule. Linearly spilled and recaptured demand due to
the choice of fleets and optional flights require estimates for pairs of flight legs and
pairs of itineraries, which are difficult to estimate even with airline propietary data.
Within the “Congestion Management at US Airports” project by NEXTOR uni-
versities [20], Barnhart and Harsha [50] developed an airline slot valuation model
that simulates airline response to a slot auction. The proposed model is a mix integer
problem designed for individual airlines, and required demand and cost proprietary
data as inputs. The assumptions include (i) a multiple round package auction (ii)
43
airlines can bid for bundles of slots to build their daily schedules, (iii) incumbent air-
lines are given vouchers for their currently held slots and unused vouchers can be sold
after the auction, (iv) average fare is constant. The demand curves are functions of
frequency, and are given by piecewise input parameter values. The model maximizes
the total profit.
All these models use ticket prices as a parameter that does not correlate with
changes in supply: ticket prices stay constant regardless of the total number of seats
in the resulted schedule. This simplistic assumption helps keep the fleet assignment
model tractable and may be a reasonable assumption from a single airline’s perspec-
tive given the highly competitive nature of the market. However, when looking across
the industry, excess of aggregate capacity leads to decreasing average fares, even when
such fares are unprofitable.
2.3 Delay and cancellation estimation models
Delay and cancellation have been extensively estimated by a large number of models as
principal metrics to evaluate schedule performance. Two main approaches categorize
these models into analytical methods or simulation tools which have focus on the
processing speed or the level of details respectively.
2.3.1 Analytical models
Principal fast-time analytical models reviewed in [51] such as MIT’s DELAYS and
AND, and more newly developed models such as the delay and cancellation component
in FAA Strategy Simulator [52] are macroscopic models where aggregate values of
input parameters, namely traffic demand and airport capacity, are given or generated
44
to obtain approximate closed-formed estimates of delay. DELAYS is a dynamic and
stochastic queuing model that estimates queuing delay for access to an airport’s
runway system, excluding en route or terminal area airspace congestion, or bottlenecks
on the taxiways or aprons. AND connects individual airports by a simulation module,
which propagates delay among airports and updates their demand profiles. DELAY
and AND assume no cancellation.
We present these models in more details next.
DELAYS and AND The analytical queuing model DELAYS was developed and
extended by Koopman [31], Kivestu [53], Malone [54]. DELAYS models an individual
airport in isolation as a single server queue. It estimates the probability distribution
of aircraft number in the queue at a local airport, and from which derive local queuing
delays. Malone [55] connected airports in the network through a schedule of flights
with the simulation model AND, Approximate Network Delay. Figure 2.2 outlines
the interaction between DELAYS and AND.
DELAYS approximates the M(t)/Ek(t)/1/m queuing systems with nonstationary,
i.e. time dependent, Poission arrival processes and kth-order Erlang service times,
m is the finite capacity of the system. Erlang is chosen to approximate a wide
variety of service-time distributions having characteristics similar to the kth-order
Erlang. The approximation approach uses far less memory and CPU time for large
Erlang orders. When k=1, the system reduces to M(t)/M(t)/1, and as k → ∞, it
approaches asymptotically the M(t)/D(t)/1. The model performs calculations for
each time period, ex. by hour. The hourly arrival rates (or service rates) combine
the hourly demands (or runway rates) for landings and takeoffs. Beginning with
45
Figure 2.2: Overview of DELAYS and AND models
initial setting at time t=0 and iteratively for t=1h, 2h, 3h, ..., the model solves a
set of Chapman-Kolmogorov equations to compute the probability distribution of
the number of aircraft in the system. These equations are valid for all non negative
values of the utilization rate ρ in contrast to the steady state results which apply only
to situations where 0 ≤ ρ < 1. Specifically, Chapman-Kolmogorov equations solve
for the probability pi(t), i=0,1,2...,m, of having i customers in the system at time t.
Expected queue length at t is then derived and expected waiting time at t can be
calculated.
AND uses DELAYS iteratively to estimate flight delays for each time window.
For departure flights, delays calculated by DELAYS can be absorbed in-flight up to a
percentage cutoff (10%) of the total deterministic en-route time, the remaining delay
is propagated downstream to the arrival phase. At the arrival airport, the flight is
46
added to the queue of the corresponding time window, updating the arrival airport’s
demand profile. Arrival delays can also be absorbed on the ground up to a percentage
cutoff (10%) of the deterministic turn-around time. The remaining delay is added
to the next departure, and the demand profile is updated. AND was tested with a
prototype 3-airport network with an additional sink-source airport.
NAS Strategy Simulator The UMD-built NAS performance component in the
FAA Strategy Simulator is a high level analytical model that estimates monthly de-
lays and cancellations in the NAS. The model studies the distribution of the hourly
utilization rate (ρ=scheduled demand/capacity) at an airport for each month. The
monthly 50th and 95th percentiles of ρ at all airports are weighted averaged based
on the fraction of NAS operations at each airport to obtain the monthly 50th and
95th percentiles of ρ for the whole NAS. The model then builds over a 6-year period
statistical models of monthly probabilities of cancellation vs. monthly NAS 50th per-
centiles of ρ, and of monthly average flight delays vs. monthly NAS 95th percentiles
of ρ. Figure 2.3 outlines the main steps of the approach.
To estimate flight cancellation probability of future scenarios, load factor is used
as follows:
Cancellation probability = e−3.75 ∗ (load factor ∗ (1− ρ50))−3.34
and average flight delay is determined as:
Average delay = 38.62 ∗ (ρ95(1− Cancellation probability))− 23.84
47
Figure 2.3: Overview of NAS Strategy Simulator’s delay and cancellation component
2.3.2 Simulation models
Large-scale microscopic simulation models such as Total Airspace and Airport Mod-
eler (TAAM) [56], Reorganized ATC Mathematical Simulator (RAMS) [57], and the
more recent NASA Airspace Concepts Evaluation System (ACES) [58][59] developed
by the VAMS project. Designed to be comprehensive, these models offer detailed
gate-to-gate simulation, including airport ground movement, terminal area depar-
ture/arrival sequencing, and en-route cruising phase. They can be used to as plan-
ning tools or to conduct analysis and feasibility studies of new ATM concepts. In
addition to numerical outputs, they also provide real time graphical visualization.
The Detailed Policy Assessment Tool (DPAT) developed by MITRE [60] is also a fast
time simulation without graphical support. These complex models typically require
48
long learning curves and extensive data input efforts. They often have little support
for stochastic events that often perturbate the system, nor do they allow a flexible
way of canceling flights and propagating delays.
Total Airspace and Airport Modeler (TAAM) simulates the physical aircraft
movement in all phases of flight from gate to gate, airport operations, and ATC’s
decision-making process. Developed in and continuously improved since 1987, TAAM
has become a state-of-the-art fast time simulation model that offers specialized fea-
tures such as Conflict Detection/Resolution (CDR), user-defined rules, and unlimited
zooming capability to display the smallest details in 2D or 3D. TAAM has been used
extensively in the literature to model ATC workload [61], redesign airspace sectoriza-
tion [62], evaluate the impacts of Reduced Vertical Separation Minimum (RVSM) [63],
study changes in runway usage and implications on airline schedules [64], and other
applications.
Reorganized ATC Mathematical Simulator (RAMS) is a fast-time, discrete-
event computer simulation model developed and supported by the Model Develop-
ment Group (MDV) at Eurocontrol, France. RAMS offers 4-dimensional flight profile
Airline scheduling submodels take as input estimates of demand, price elasticities of
demand by time of day, and costs of operating different fleets, to build the timetable
of flights such that profits are maximized. The timetable includes origin airport,
destination airport, departure time and arrival time of each flight and the fleet type
assigned to that flight. In network optimization theory, a fleet assigned to a flight is a
commodity flow and fleet mix scheduling is a multi-commodity flow problem defined
57
on a time-line network. As timetables for individual nonstop domestic markets at
LGA can be built separately (although not independently as they are all subject to
capacity constraints at LGA), we develop a time-line network for each market with all
potential flows and solve the optimization to find the schedule of profit-maximizing
flows.
4.2.1 The timeline network
A timeline network is built for each pair of airports (o, o′). At each airport, time of day
is partitioned into time windows represented by nodes: nodes in T are time windows
of airport o, and nodes in T ′ are time windows of airport o′, all nodes ordered in Zulu
time. The set of directed ground arcs (i, j) ∈ AG with i, j ∈ T (i, j ∈ T ′) represent
ground flows where aircraft stay at airport o (o′) from time window i to time window
j. For each valid fleet k ∈ K at o and o′, a set of directed flight arcs (i, j) ∈ AF
with i ∈ T and j ∈ T ′ or vice versa constructs potential flights for that fleet in the
timetable. Similar to Lohatepanont [44], any outgoing arc at any node is considered
to happen after any incoming arc at that node, and an additional directed ground
arc from the last time window to the first time window is added at each airport to
represent aircraft parking overnight.
Specifically, let:
fk,o,o′ block time by fleet k from airport o to airport o
′, in time windows
gk minimum turnaround time of fleet type k, in time windowst(i) order of time window i in Zulu time
then the directed arcs emanating from nodes in T are created as follows:
58
u uu uu uu uu uu uu uu uu uu u
- - - - - - - - -
- - - - - - - - -
PPPPPPPPPq
PPPPPPPPPq
PPPPPPPPPq
PPPPPPPPPq
PPPPPPPPPq
PPPPPPPPPq
PPPPPPPPPq1
1
1
1
1
1
1airport 1
airport 2
(b) subnetwork for fleet 2that requires 3 time windows for a flight arc
u uu uu uu uu uu uu uu uu uu u
- - - - - - - - -
- - - - - - - - -
HHHHHHj
HHHHHHj
HHHHHHj
HHHHHHj
HHHHHHj
HHHHHHj
HHHH
HHj
HHHH
HHj
airport 1
airport 2 *
*
*
*
*
*
*
*
flight arcs
ground arcs
?
(a) subnetwork for fleet 1that requires 2 time windows for a flight arc
Figure 4.2: Timeline network example for a city pair having the same time zone.
i ∈ T , j ∈ T ′, (i, j) ∈ AF if t(i) + fk,o,o′ + gk = t(j)i, j ∈ T , (i, j) ∈ AG if t(i) + 1 = t(j)i, j ∈ T , (j, i) ∈ AG if t(i) ≤ t(k) ≤ t(j) ∀k ∈ T
Similarly, the directed arcs emanating from nodes in T ′ are created as follows:
i ∈ T ′, j ∈ T , (i, j) ∈ AF if t(i) + fk,o,o′ + gk = t(j)i, j ∈ T ′, (i, j) ∈ AG if t(i) + 1 = t(j)i, j ∈ T ′, (j, i) ∈ AG if t(i) ≤ t(k) ≤ t(j) ∀k ∈ T ′
Figure 4.2 is an example of the timeline network for a city pair that has the
same time zone. Figure 4.2a constructs the flight arcs for fleet 1 that requires 1.5
time windows for flight time in both directions, and 0.5 time window for minimum
turnaround time. Figure 4.2b builds the flight arcs for fleet 2 that needs 1.5 and
2.5 time windows for flight time in different directions, and 0.5 time window for
minimum turnaround time. The subnetworks for all valid fleets put together create
the multi-commodity flow timeline network for that city pair.
59
4.2.2 Interaction of demand and supply through price
In microeconomics, it is well known that demand and supply interact through price
following the generic relationship depicted in Figure 4.3. The law of demand states
that given other things remaining the same, the higher the price of a good, the smaller
is the quantity demanded. This clearly reflects the observations that overcapacity
in certain competitive markets have driven airlines to reduce ticket prices even to
unsustainable levels.
Figure 4.3: Nonlinear relationship of demand vs. price and the effect on renenues
Changes in frequencies and aircraft size, i.e. supply of seats, would lead to changes
in prices. This interaction affects demand and therefore the airlines’ bottom line.
From an airport’s point of view, price is also important in the overall evaluation of
the quality of air transportation service. Therefore, we explicitly model price as a
variable by using directly the revenue functions and their linear approximations.
The demand curve D for air service of any time window t exhibits a convex
nonlinear form as in Figure 4.3a. Demand is diluted to substitute services (namely
flights to the neighboring airports in the cluster or other means of transportation such
60
as car, train) as price increases. Demand curves of peak periods shift rightward and
those of off-peak periods shift leftward. Corresponding to a convex demand curve is
a concave revenue curve (see Figure 4.3b) where the maximum y-value is the optimal
revenue for that time window. Similarly, revenue curves of peak periods lie on top of
those of off-peak periods.
A certain fleet mix configuration corresponds to a supply curve where the move-
ment along the supply curve translates to changes of frequency. Larger aircraft ratios
in the fleet mix shift the supply curve rightward. Price as a regulator establishes
market equilibriums at the intersection points of demand and supply curves. S1, S2,
and S3 in Figure 4.3a intersect the demand curve D at quantities equal to 500, 1000,
and 1300 respectively where the resulting revenues of S1 and S3 are sub-optimal
compared to the revenue of S2.
4.2.3 Piecewise approximation of non-linear revenue func-
tions
An arbitrary continuous function of one variable y = f(x) can be approximated by
a function of the form y = f(x1, ..., xq) =∑q
i=1 fi(xi) where fi(xi) is piecewise linear
for each i. Given the segment endpoints (ai, f(ai)) for i=1,...,q, any a1 ≤ x ≤ aq can
be written as
x =
q∑i=1
aiλi,
r∑i=1
λi = 1, λ ∈ Rq+.
The λi are not unique, but if ai ≤ x ≤ ai+1 and λ is chosen so that x = λiai +
λi+1ai+1 and λi + λi+1 = 1, then we obtain f(x) = λif(ai) + λi+1f(ai+1). In other
61
Figure 4.4: Approximating a nonlinear function by a piecewise linear function
words,
f(x) =
q∑i=1
f(ai)λi,r∑
i=1
λi = 1, λ ∈ Rq+
where at most two of the λi’s are positive and if λj and λk are positive, then
k = j +1 or j−1. This condition, identified as a Special Ordered Set (SOS) contraint
of type 2, can be modeled using binary variables yi for i = 1, ..., q − 1 (where yi = 1
if ai ≤ x ≤ ai+1 and yi = 0 otherwise) and the constraints
λ1 ≤ y1
λi ≤ yi−1 + yi for i = 2, ..., q − 1
λq ≤ yq−1 (4.1)
q−1∑i=1
yi = 1
y ∈ Bq−1.
62
For convex (concave) functions in a minimization (maximization) problem, SOS2
constraints in 4.1 can be removed, as the optimization process always chooses 2 ad-
jacent endpoints. However, generic piecewise linear functions or convex (concave)
functions in a maximization (minimization) problem require 4.1 to ensure the non-
negative values of 2 adjacent λi’s. On the other hand, when only a finite set of values
of x’s are valid, segment endpoints can assume those values and the SOS2 constraint
set can be replaced by the SOS1 constraint:
q∑i=1
λi = 1 λi ∈ Bq.
4.2.4 Nesting revenue functions
Different time windows are not independent as spilled demand of this time window can
be recaptured by other time windows. Spill and recapture occur because passengers
can choose alternative time windows when their desired times are capacitated, too
expensive or not provided in the schedule. Therefore, the supply levels of alternative
(closely adjacent) time windows determine these spill and recapture effects. As the
schedule is not known in advance, we first estimate revenues independently for each
time window, then use nesting revenue functions to include the interdependency
between time windows.
Revenue functions can be estimated for different granularities: by 15min, 30min,
1hour, or by peak and off-peak time windows at each airport (see Chapter 4 for
estimation method). Figure 4.5 estimates revenue functions of ORD→LGA market
for all 15-min time windows in the first half of the day and the aggregate revenue
63
function for the whole period. Note that some time windows have the same estimates
of revenue functions and therefore are superimposed on top of each other. The sum
of demands and revenues of all 15-min time windows are therefore expected to be
constrained by the aggregate, or nesting, revenue function of the compounding period.
Figure 4.5: Nesting revenue functions
If λiq are the piecewise variables for the revenue function of time window i with
q ∈ Q(i) being the segment indexes,
∑q∈Q(i)
λiq = 1, λiq ∈ R+
xi =∑
q∈Q(i)
aiqλiq
fi(xi) =∑
q∈Q(i)
fi(aiq)λiq
and a nesting revenue function of a period p that contains i, i.e. i ∈ E(p), having
64
piecewise variables βpr, r ∈ Q(p),
∑r∈Q(p)
βpr = 1, βpr ∈ R+
xp =∑
r∈Q(p)
aprλpr
fp(xp) =∑
r∈Q(p)
fp(apr)βpr
then the nesting constraints is:
∑i∈E(p)
xi = xp
∑i∈E(p)
fi(xi) ≤ fp(xp)
4.2.5 Assumptions
• The constraint on fleet availability is removed, i.e. we assume the airlines will
procure whatever aircraft is optimal to fly,
• Aircraft sizes are grouped into increments of a fixed number of seats,
• Arrival time rather than departure time drives demand,
• Demands are estimated for non-stop domestic flights to/from the airports in
study. Scheduling decisions are therefore limited to the nonstop markets,
• If arrival time windows at different airports are substitutable, they have the
65
same chronological values,
• There is only one level of nesting for the revenue functions. The finer granularity
time windows are compounded into only one coarser granularity time window.
The sets of substitutable time windows at one airport are mutually disjoint and
complete.
4.2.6 Formulation
Assuming concave revenue functions, we define:
Sets:
T time windowsAG ground arcsAF flight arcsK fleet types operable at the 2 airports of the marketQ(i) linear segment indexes for the revenue function of i ∈ T
Parameters:
Sk seating capacity of fleet type k ∈ KCk
ij direct operating cost for one flight of fleet type k ∈ K for (i, j) ∈ AF
Aiq linear segment quantities for the revenue function of i ∈ T , q ∈ Q(i)Riq linear segment revenues for the revenue function of i ∈ T , q ∈ Q(i)l average load factor
Variables:
xkij number of flights of fleet type k ∈ K for (i, j) ∈ AF ∪ AG
λiq linear segment variables for the revenue function of i ∈ T , q ∈ Q(i)
Subproblem formulation:
max z =∑i∈T
∑q∈Q(i)
Riqλiq −∑
(j,i)∈AF
∑k∈K
Ckjix
kji (4.2)
66
subject to:
∑(j,i)∈A
xkj,i −
∑(i,j)∈A
xkij = 0 ∀ i ∈ T , k ∈ K (4.3)
l∑k∈K
∑(j,i)∈AF
Skxkji −
∑q∈Q(i)
Aiqλiq = 0 ∀ i ∈ T (4.4)
∑i∈E(p)
∑q∈Q(i)
Aiqλiq −∑
r∈Q(p)
Aprβpr = 0 ∀ p ∈ P (4.5)
∑i∈E(p)
∑q∈Q(i)
Riqλiq −∑
r∈Q(p)
Rprβpr ≤ 0 ∀ p ∈ P (4.6)
∑q∈Q(i)
λiq = 1 ∀ i ∈ T (4.7)
∑r∈Q(p)
βpr = 1 ∀ p ∈ P (4.8)
x ∈ Z|AF |x|K|+ , λi ∈ R
|Q(i)|+ , βp ∈ R
|Q(p)|+
For any time window i,∑
(j,i)∈AF
∑k∈K Ck
jixkji in the objective function (4.2) is the
total operating cost of arrivals at i. The resulting total capacity∑
k∈K∑
(j,i)∈AF Skxkji
multiplied by the average factor estimates the number of revenue passengers arriving
at i. This value is then decomposed in (4.4) into a convex combination of segment
endpoints (Aiq, Riq) with q ∈ Q(i) using non-negative real variables λiq. Therefore,∑q∈Q(i) Riqλiq is the piecewise linear approximation of the revenue function of time
window i. Subtracting the sum of all the cost terms over all flights from the sum of
all the revenue terms over all time windows yields the total profit that (4.2) seeks to
67
maximize. (4.3) enforces flow balance constraint that at each node i in the timeline
network, for each fleet, the number of incoming aircraft is equal to the number of
outcoming aircraft.
As explained earlier,∑
q∈Q(i) Aiqλiq is the estimate of realized arrival demand at
time window i. i can have other substitutable time windows that are all included
in a coarser compounding time window p, i.e. i ∈ E(p). Similarly, (4.5) decomposes
the aggregate arrival demand of p into a convex combination of segment endpoints
(Apr, Rpr) with r ∈ Q(p) using non-negative real variables βpr. (4.6) states that
the sum of revenues of substitutable time windows in p,∑
i∈E(p)
∑q∈Q(i) Riqλiq, is
constrained by the revenue of the compounding time window p,∑
r∈Q(p) Rprβpr. (4.7)
and (4.2.6) are the sets of convex constraints for λiq and βpr.
The solution of a subproblem creates two schedule vectors: the arrival vector
aj where aj =∑
k∈K∑
(i,j)∈AF xkij, and the departure vector dj where dj =∑
k∈K∑
(j,i)∈AF xkji, j ∈ T are time windows at the capacitated airport study in
the master problem.
4.3 Airport’s allocation problem
The master problem at a capacitated airport collects the schedules of individual
markets and solves a set packing problem with side constraints to maximize public
goals.
Let:
Sets:
68
S schedule vector indexesT time window indexesM market indexesS(m) column indexes of market m’s schedule vectors, m ∈M
Parameters:
a|T |x|S| matrix of arrivals by time window: aij is the number of arrival flights at
time window i in schedule jd|T |x|S| matrix of departures by time window: dij is the number of departure flights
at time window i in schedule jZj coefficient of the schedule vector j ∈ S, determined by the public goal to
optimizeCi arrival/departure rates of time window i ∈ TGi ground capacities in time window i ∈ T
Variables:
yj binary variable equal to 1 if schedule vector yj is in the optimal solution
Formulation of the master problem:
max∑j∈S
Zjyj (4.9)
subject to:
69
∑j∈S
aijyj ≤ Ci ∀i ∈ T (4.10)
∑j∈S
dijyj ≤ Ci ∀i ∈ T (4.11)
∑j∈S(m)
yj ≤ 1 ∀m ∈M (4.12)
y ∈ B|S|
The sets of constraints (4.10) and (4.11) reflect airport operational rate con-
straints. As each market can have many alternative schedules from which at most
one schedule can be in the solution, each market has a SOS1 side constraint in (4.12).
The objective function maximizes public goals such as:
• Profit where Zj is the profit of schedule j, given by the value:
∑i∈T
∑q∈Q(i)
Riqλiq −∑
(j,i)∈AF
∑k∈K
Ckjix
kji
from the subproblem that produces schedule j.
• Seat throughput where Zj is the total seat of schedule j, given by the value:
∑k∈K
∑(j,i)∈A
Skxkji
from the subproblem that produces schedule j.
70
4.4 Solution method
Figure 4.6 depicts our method to find the optimal collection of schedules. Initially,
the mixed integer subproblems, i.e. the determination of schedules for each O/D
pair, provide optimal arrival demand and departure demand columns to the mas-
ter problem. The master problem solves its linear relaxation, called the LP master
problem, to compute dual price for each constraint. The dual price of a constraint
reflects the contraint’s value, or its contribution to the objective function. There are
three sets of dual prices corresponding to the three sets of constraints in a master
problem: αi for (4.10), πi for (4.11), and µj for (4.12). For a maximization problem,
a new column with coefficient zj can be added to the master problem if its contribu-
tion to the objective function, zj, is larger than the value of resources it would use,∑i∈T (αiaij + πidij) + µj, or when zj −
∑i∈T (αiaij + πidij)− µj > 0. In other words,
a new column can be added if it prices out favorable with respect to the objective
function. This process is called “column generation”, often used to solve large scale
combinatorial optimization problems.
Therefore, we update the formulation of the subproblems to include this condition
as an additional side constraint, with the initial dual prices set to zero:
z −∑i∈T C
αi
∑k∈K,(j,i)∈AF
xkj,i −
∑i∈T C
πi
∑k∈K,(i,j)∈AF
xkij − µ ≥ 1 (4.13)
where the expressions for z are different for different objective functions of the
master problem, as explained in airline scheduling subproblems.
When the objective function of the master problem is not profit maximization,
71
Figure 4.6: Branch-and-price solution method
72
it is inconsistent with the profit-maximizing objective functions of the subproblems.
Therefore, when the column generation process finds new feasible schedules, they
can be suboptimal. We can parametrically set a lower bound on these suboptimal
schedules: a suboptimal schedule is valid if it is within some percentage of the optimal
solution’s value.
The initial solutions, or columns, of the subproblems initialize the root node of
the LP branch tree of the master problem. At the root node and subsequent nodes,
a two-phase solution process takes place: the node is first solved to calculate dual
prices which will serve as input to MIP subproblems to generate new columns (if any)
to be added to the current node, then the node is solved again and branches if there
are integer variables with fractional values. In contrast to regular branch-and-bound
algorithms where a node with an LP solution less than the incumbent integer value
can be pruned (in a maximization problem), branch-and-price requires storing all the
unprocessed nodes for later column generation processing, as new columns added to
a node can increase its objective function value. In our branch-and-price algorithm, a
node is pruned if it is either infeasible or it has an integer solution after the two-phase
solution process. To optain optimality, the process should continue until all the nodes
are processed.
4.5 Implementation details
As the current version of CPLEX Concert Technology does not allow for dynamic
addition of new columns into a problem at each node of the branch tree, we implement
our own branch-and-price tree and use CPLEX to solve the LP problems at each node.
Specifically,
73
• At each node, we branch on the most fractional variable that has largest coef-
ficient in the objective function,
• We store all unprocessed nodes in a ordered list and use best-bound strategy to
select the next candidate node,
• We add columns to the master problem and at each node, we store the list of
variables that (i) come from the parent node, (ii) are generated at the node,
(iii) are fixed to 0 and (iv) are fixed to 1 from the root node down the tree to
the current node. When we move from one node to another, we reset all the
bounds of the stored variables, and fix to 0 all other variables.
Interested readers are encouraged to see Appendix C for the code listing of our
branch-and-price implementation.
Chapter 5: Parameter estimation for scheduling
models
Modeling airline scheduling decisions usually require proprietary cost and revenues
data along with constraints of airline business models. Each airline’s data can be
largely different from others’. To mitigate this effect, we use aggregate data across
airlines available in public databases. Aggregate data is also more effective in reducing
the inherent noise in any data set, especially for airlines with little public data.
Parameter estimation for scheduling models consists of building the timeline networks
and calculating revenue functions.
5.1 Timeline networks
A timeline network is built for each city pair. The monthly T-100 Segment table,
compiled by the Bureau of Transportation Statistics (BTS [68]), reports domestic
and international operational data by U.S. and foreign air carriers. Only data of
domestic carriers are considered as we look at domestic schedules. For each segment,
it contains, among other data items, carriers, aircraft types, distance, total number
of performed departures and seats, total ramp to ramp times, and total air times.
Aircraft types are provided as identification codes. We calculate the size of each
aircraft type by performed departuresperformed seats
. Aircraft sizes are then grouped into increments of
25 seats (or any fixed number of seats) called fleet. The fleets identified as such for a
74
75
segment determines the number of commodities in the multi-commodity flow network
for that segment.
For this study, we use the data of Q2, 2005 and categorize fleets available at LGA’s
domestic nonstop markets into the following ranges of seats:
5.1.1 Arcs and arc lengths
Flight arcs depart and arrive within 5:15 and 24:00 local times at any airport. To
estimate arc lengths, or leg lengths, we use Aviation System Performance Met-
rics (ASPM) database [69] that provides on-time performance of individual flights.
Recorded scheduled block times are typically padded with some time buffer built into
the schedule so that reasonable delays can be absorbed. Actual block times can be
higher than scheduled block times due to unexpected excessive congestion, or smaller
due to unexpected low congestion. If we can reasonably assume that airlines adjust
their delay buffers over time to cope with congestion, then the minimum of scheduled
block times and actual block times is more likely to reflect the average block times.
However, the minimum of the two block times can still contain airborne or ground
delays. In reduced demand scenarios, airlines would incur less delay on the day of
operations, and so they would eventually reduce both scheduled and actual block
times. As airborne phase is less subject to delay than ground operations, we could
further adjust estimates of block times to:
actual air time + 2 * min(scheduled block time, actual block time)
3
Averaging estimates of block times adjusted as above for all aircraft types in a
fleet provides the arc length for that fleet. In addition, an arc arriving at a node
76
Fleet Aircraft Average Size Fleet Aircraft Average Size
Table 7.13: Daily average statistics of fall-out markets at 8 ops/runway/15min, com-
promise scenarios, Source: ASPM Q2, 2005. (*revenue per passenger mile)
Frequency and delay distribution by time of day Figure 7.11 and Figure 7.14
plot the number of flights (arrivals and departures) by their scheduled 15-min time
windows, our estimates of flight delay are shown in Figure 7.12 and Figure 7.15. Note
that the output schedule includes only nonstop domestic flights that are profitable
147
on a daily basis. These flights come from 64 airports. Other demands not accounted
for are other flights, which include international flights, non-daily and non-scheduled
flights that can come from 275 airports having nonstop service to LGA. We stack
the other flights on top of the output schedule to approximate the total final demand
of this scenario. Time series of average total of actual demand is also plotted for
comparison purpose.
We notice that the 90% scenario with tighter lower bound on schedule profit
leads to reduction of schedule in the off-peak time windows of afternoon, while the
frequency profile approximates relatively well the morning and late evening traffic.
This results in less delays for arrivals and departures in early evening of the 90%
scenario, averaged at 8min, compared to 10-12min for the 80% scenario.
Chapter 8: Conclusion and Future Work
Air traffic growth is putting substantial pressure on airport infrastructure. Within
the next 10 years, forecasts by [3] predicted that there will be as many as 1.1 billion
air travelers per year in the U.S.. MITRE’s analysis of airport and metropolitan
area future demand and operational capacity [4] revealed that 15 airports, some not
currently in the OEP, will need additional capacity by 2013, and eight more will face
capacity limitations by 2020.
The currently planned improvements in aircraft, airport, and airspace systems
and operational procedures may not be sufficient to safely, securely, and efficiently
meet the U.S. transportation needs of the next 10 years. This concern is reflected
by various congestion management efforts, initiated by the FAA and by regional
airport management entities. Congestion management includes the construction of
new runways and/or airports, improvement of technology, and demand management
measures that control use in order to manage delays and congestion.
At congested airports where there are limited possibilities for expansion, appropri-
ate demand management measures prove to be critical in coping with the projected
traffic growth. High Density Rule (HDR) currently imposed at LGA and JFK airports
aims to maintain demand at available capacity levels. However, the initial restrictions
of this rule along with many temporary fixes over time have resulted in recurring in-
efficiencies: small markets with small aircraft competing access with larger markets,
airlines flying large number of flights at low load factor just to maintain their slots
148
149
due to the “use-it-or-lose-it” rule.
With HDR scheduled to end in Jan 2007, appropriate demand management mea-
sures are critically needed to avoid overscheduling and severe congestion at this proba-
bly most important business airport in the Nation. Many potential proposals discuss
the use of congestion pricing and auctions of airport slots. However, appropriate
demand management measures require the understanding of airline operations and
market economics to design the right incentives, as well as beforehand study of im-
plications on enplanement opportunities, average fare, markets served, aircraft size,
and flight delay.
Our methodology addresses this requirement. We take a novel approach in as-
suming a profit-seeking, single benevolent airline, and develop an airline economic
model to simulate scheduling decisions. This airline is defined as benevolent in the
sense that the airline reacts to price elasticities of demand in a competitive market.
These price elasticities of demand and cost data are estimated using publicly avail-
able databases. On the government side, airline schedules are selected to maximize
enplanement opportunities such that these schedules fit into the capacity constraints
at LGA airport. To reconcile the two conflicting objective functions, we find the
optimal solutions for each side, and identify compromise solutions. The compromise
scenarios maximize the number of seats while ensuring that airlines operate within
90% or 80% of profit optimality.
Our results show that in the compromise scenarios at 8 operations/runway/15min,
the total output seats are higher (increased by 1.1% and 3.4% for seat maximizing
within 90% or 80% of profit optimality respectively) than that of the baseline while
average flight delay is reduced significantly (dropped 72% and 66% respectively).
150
The number of flights is decreased by 21% and 19%; aircraft size is increased by
27% and 28%. As result of small increase in supply level, average fare is decreased
slightly by 4% and 6%. There is no penalty in the number of markets at 8 opera-
tions/runway/15min compared to 10 operations/runway/15min, which is the current
Visual Meteorological Condition (VMC) rate for good weather condition. Therefore,
having aggregate airline schedules at 8 operations/runway/15min will reduce signif-
icantly congestion problem at LGA, increase the predictability of air transportation
and improve the quality of service expected by the flying public.
8.1 Contributions
We summarize our contributions into four main areas:
Development of an airline flight and fleet scheduling model that incor-
porates the interaction of demand and supply through price (Chapter 3)
Appropriate congestion measures require the understanding of airline economics and
operations to avoid unduly affecting the business models of air carriers by forcing
impractical regulations. Therefore, modeling airline scheduling decisions is a central
part of this research. Unlike existing flight scheduling models that use fare as a pa-
rameter, our flight and fleet scheduling model considers fare as a variable negatively
dependent on supply level. This design choice allows the analysis of effects of changes
in schedules on average fares.
Development of a computationally-efficient solution algorithm to find the
optimal set of schedules (Chapter 3) We devise at each of the airports a column
151
generation algorithm to determine the optimal collection of schedules for each of the
Origin-Destination pairs based on the capacity constraints of the airports in study.
The decomposition algorithm decomposes the problem into a master problem that
optimizes use of the airports while the subproblems find optimal O/D schedules based
on current prices and demand curves.
Development of a methodology for estimating demand curves by time of
the day from publicly available sources (Chapter 4) We perform data mining
of ASPM and BTS databases to break down the aggregate data by quarter of the
year to aggregate data by day and time of day.
Development of a delay stochastic simulation network model to evaluate
flight schedules (Chapter 5) We develop a simulation model that explicitly con-
siders wake vortex separation standards between categories of aircraft to simulate
runway capacity. Delays are estimated based on runway capacity. The model is
capable of evaluating the implications of fleet mix on runway operations throughput.
Demonstration of the existence of profitable airline schedules that reduce
congestion and accommodate current passenger throughput level (Chapter
6) We find the optimal demand allocation benchmarks for scenarios that assume
different capacity levels and public goals. The public goals investigated in this disser-
tation are (i) maximizing profit, (ii) maximizing seat throughput, and (iii) maximizing
the number of markets and seat throughput. The resulting schedules are then eval-
uated against the metrics of interest: Operations throughput, average flight delay,
seat throughput, average aircraft size, number of regular markets, and average fare.
152
The results show that at Instrument Meteorological Condition (IMC) rate of runway
capacity, airlines’ profit-maximizing responses can be expected to find scheduling so-
lutions that offer 70% decrease in flight delays, 20% reduced in number of flights with
almost no loss of markets and no loss of passenger throughput.
8.2 Recommendations for future work
We identify the following potential ground for future work:
Adding layover costs When airlines choose service frequency and larger aircraft
size, they might increase the turnaround time between flights. Moreover, passenger
schedule delays increase. Schedule delay refers to the time between the most preferred
time of travel time of a passenger and the closest available flight.
Finer grouping of substitutable time windows into airport-specific peak
and off-peak periods For simplicity purpose, our study of LGA uses generic
grouping of substitutable time windows that assumes at any market, all time windows
in the morning (afternoon, or evening) are substitutable. While this is a simplistic
assumption to allow analytical convenience, it neglects the difference in travel time
preferences among markets. Plus, some time windows in the morning might be valued
more by the passengers than others. Therefore, we recommend more detailed group-
ing of substitutable time windows to reflect better peak and off-peak times at each
airport. We also suggest including the daily level of nesting revenue functions. With
only one level of nesting, there is the possibility that all time windows of a certain
group are not in the output schedule, resulting in a supply decrease while ticket prices
153
are still determined independently by the remaining groups.
Extend the sampling periods to include the whole calendar year We esti-
mates model parameters using data of Q2, 2005. Future studies can use data of the
full year. Separate analyses with data of each quarter could also be done to maintain
the seasonal patterns, and propose some average solution.
Extend the methodology to airports that have good mixture of local and
through traffic Our methodology is appropriate for airports with mostly local traf-
fic like LGA. EWR or JFK airports, however, have a significant connect, or through
traffic. The demands of individual markets are no longer independent: reduction or
increase of capacity on one market segment affects others. In addition to modeling
difficulty, the lack of Origin-Destination demand data also presents a challenge for
this research direction.
154
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155
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Appendix A: Airport Codes, Locations and Names
162
ACK Nantucket, MA: Nantucket MemorialALB Albany, NY: Albany CountyATL Atlanta, GA: Hartsfield-JacksonBGR Bangor, ME: Bangor InternationalBHM Birmingham, AL: Birmingham MunicipalBNA Nashville, TN: Nashville MetropolitanBOS Boston, MA: Logan InternationalBTV Burlington, VT: Burlington InternationalBUF Buffalo/Niagara Falls, NY: Greater Buffalo InternationalBWI Baltimore, MD: Baltimore/Washington InternationalCAE Columbia, SC: Columbia MetropolitanCAK Akron/Canton Regional, OH: RegionalCHO Charlottesville, VA: Charlottesville AlbemarleCHS Charleston, SC: Charleston InternationalCLE Cleveland, OH: Hopkins InternationalCLT Charlotte, NC: Douglas MunicipalCMH Columbus, OH: Columbus InternationalCVG Covington, KY: Cincinnati/ Northern Kentucky InternationalDAY Dayton, OH: James M Cox/Dayton InternationalDCA Washington, DC: Washington NationalDEN Denver, CO: Denver InternationalDFW Dallas/Ft.Worth, TX: Dallas/Ft Worth InternationalDTW Detroit, MI: Detroit Metro Wayne CountyFLL Fort Lauderdale, FL: Fort Lauderdale InternationalGSO Greensboro/High Point, NC: Greensboro High Point WinstGSP Greenville/Spartanburg, SC: Greenville/Spartanburg AirportHOU Houston, TX: William P HobbyHYA Hyannis, MA: Barnstable MunicipalIAD Washington, DC: Dulles InternationalIAH Houston, TX: Houston IntercontinentalILM Wilmington, NC: New Hanover CountyIND Indianapolis, IN: Indianapolis InternationalITH Ithaca/Cortland, NY: Tompkins CountyJAX Jacksonville, FL: Jacksonville InternationalLEB Lebanon-Hanover, NH: Lebanon MunicipalLEX Lexington/Frankfort, KY: Blue Grass
163
MCI Kansas City, MO: Kansas City InternationalMCO Orlando, FL: Orlando InternationalMDW Chicago, IL: Chicago MidwayMEM Memphis, TN: Memphis InternationalMHT Manchester/Concord, NH: Grenier Field /Manchester MunicipalMIA Miami, FL: Miami InternationalMKE Milwaukee, WI: General Mitchell FieldMSP Minneapolis/St. Paul Int, MN: Minneapolis-St PaulMSY New Orleans, LA: Louis Armstrong InternationalMVY Martha’s Vineyrd, MA: Marthas VineyardMYR Myrtle Beach, SC: Myrtle Beach International AirportORD Chicago, IL: O HareORF Norfolk/Va.Bch/Ptsmth/Chpk, VA: Norfolk VaROA Roanoke, VA: Roanoke MunicipalROC Rochester, NY: Rochester Monroe CountyPBI West Palm Beach/Palm Beach, FL: Palm Beach InternationalPHF Newport News/Williamsburg, VA: Patrick Henry InternationalPHL Philadelphia, PA: Philadelphia InternationalPIT Pittsburgh, PA: Pittsburgh InternationalPVD Providence, RI: Theodore Francis GreenPWM Portland, ME: Portland International JetportRDU Raleigh/Durham, NC: Raleigh DurhamRIC Richmond, VA: Richard Elelyn Byrd InternationalROC Rochester, NY: Rochester Monroe CountySAV Savannah, GA: Savannah InternationalSDF Standiford Field, KY: Standiford Field AirportSTL St. Louis, MO: Lambert/St Louis InternationalSYR Syracuse, NY: Syracuse Hancock InternationalTPA Tampa, FL: Tampa InternationalTYS Knoxville, TN: Mcghee TysonXNA Fayetteville, AR: Northwest Arkansas Regional
164
Appendix B: Problem formulations for ORD-LGA
market in MPL
Used for profit-maximizing goal of the master problem
k := DATABASE("mpl_aircraft_data","aircraft" WHERE market="ORD" and cluster_airport="LGA");
flight_arc[k,i,j] := DATABASE("mpl_flight_arc",k="aircraft",i="i",j="j" WHERE market="ORD" and cluster_airport="LGA");
iq := DATABASE("mpl_pw_revenue","i" WHERE market="ORD" and cluster_airport="LGA");
q := DATABASE("mpl_pw_revenue","segment" WHERE market="ORD" and cluster_airport="LGA");
165
piecewise_revenue[iq,q] := DATABASE("mpl_pw_revenue",iq="i",q="segment" WHERE market="ORD" and cluster_airport="LGA");
p := DATABASE("mpl_pw_periodic_revenue","p" WHERE market="ORD" and cluster_airport="LGA");
r := DATABASE("mpl_pw_periodic_revenue","segment" WHERE market="ORD" and cluster_airport="LGA");
periodic_pw_revenue[p,r]:=DATABASE("mpl_pw_periodic_revenue",p="p",r="segment" WHERE market="ORD" and cluster_airport="LGA");
period_epoch[p,p_i] := DATABASE("mpl_pw_revenue",p_i="i",p="p" WHERE market="ORD" and cluster_airport="LGA");
DATA
N = count(node);
T = N / 2;
S[k]:=DATABASE("mpl_aircraft_data","seats",k="aircraft" WHERE Market="ORD");
C[k,i,j]:=DATABASE("mpl_flight_arc","cost",k="aircraft",i="i",j="j" WHERE market="ORD" and cluster_airport="LGA");
A[iq,q]:=DATABASE("mpl_pw_revenue","demand",iq="i",q="segment" WHERE market="ORD" and cluster_airport="LGA");
R[iq,q]:=DATABASE("mpl_pw_revenue","revenue",iq="i",q="segment" WHERE market="ORD" and cluster_airport="LGA");
pA[p,r]:=DATABASE("mpl_pw_periodic_revenue","demand",p="p",r="segment" WHERE market="ORD" and cluster_airport="LGA");
pR[p,r]:=DATABASE("mpl_pw_periodic_revenue","revenue",p="p",r="segment" WHERE market="ORD" and cluster_airport="LGA");
SS[k]:= S[k]*0.8;
INTEGER VARIABLES
x[k,i,j in flight_arc];
VARIABLES
y[k,i,j] WHERE (i<T AND j=i+1) OR (i>T AND j=i+1) OR (i=T AND j=1) OR (i=N AND j=T+1);
pl[p,r in periodic_pw_revenue];
l[iq,q in piecewise_revenue];
166
MACRO
REVENUE = sum(iq,q in piecewise_revenue: R[iq,q]*l[iq,q]);
COST = sum(k,i,j in flight_arc: C*x);
FREQUENCY = sum(k,i,j in flight_arc: x);
THROUGHPUT = sum(k,i,j in flight_arc: S*x);
MODEL
MAX REVENUE - COST;
SUBJECT TO
! new column generation
cg: REVENUE - COST >= 0;
! flow balance contraints
flow[k,i,temp=i] when (i<=T-1 and i>=2) or (i>=T+2 and i<=N-1): sum(j in flight_arc:x[k,i,j]) + sum(j: y[k,i,j=i+1]) - sum(i,j in flight_arc:x[k,i,j=temp]) - sum(j:y[k,i-1,j=i])= 0;
flow[k,i,temp=i] when i=T+1 or i=1: sum(j in flight_arc:x[k,i,j]) + sum(j:y[k,i,j=i+1]) - sum(i,j in flight_arc:x[k,i,j=temp]) - sum(j:y[k,i+T-1,j=i])= 0;
flow[k,i,temp=i] when i=N or i=T: sum(j in flight_arc:x[k,i,j]) + sum(j:y[k,i,j=i-T+1]) - sum(i,j in flight_arc:x[k,i,j=temp]) - sum(j:y[k,i-1,j=i])= 0;
! piecewise balance contraints
pw[iq] when (iq+3<=T) or ((iq>T) and (iq+3<=N)): sum(k,i,j in flight_arc: round(SS[k])*x[k,i,j=iq+3]) - sum(q: A[iq,q]*l[iq,q]) = 0;
pw[iq] when ((iq+3>T) and (iq<=T)) or (iq+3>N): sum(q: A[iq,q]*l[iq,q]) = 0;
s[iq]: sum(q: l[iq,q]) = 1;
167
ppw[p]: sum(p_i in period_epoch, iq,q in piecewise_revenue: A[iq=p_i,q]*l[iq=p_i,q]) - sum(r: pA[p,r]*pl[p,r]) = 0;
ps[p]: sum(r: pl[p,r]) = 1;
nested_pw[p]: sum(p_i in period_epoch, iq,q in piecewise_revenue: R[iq=p_i,q]*l[iq=p_i,q]) - sum(r: pR[p,r]*pl[p,r]) <= 0;
BOUNDS
x <= 5;
END
Used for seat-maximizing goal of the master problem
Appendix D: Price elasticities estimates for several
key markets
Figure D.1: Log-fit of major markets (O’Hare, Boston, National, and Fort Laud-
erdale) untruncates demand in lower price ranges
219
Figure D.2: Mid-sized markets (Atlanta, Tampa, Palm Beach, and Philadelphia) use
empirical extrapolated curves to avoid overestimation by the log-fit right tail
220
Figure D.3: Smaller markets (Charlottesville, Fayetteville, Lebanon and Nantucket)
use linear fit
221
Curriculum Vitae
Loan Le obtained in 1998 her B.S. in Information Technology at University of NaturalSciences in Ho Chi Minh City, Viet Nam. She then received a scholarship to finisha Diplome d’Etude Approfondie (DEA), a research-oriented Master’s degree, in thefield of Database Engineering, jointly offered by University of Paris I - Pantheon -Sorbonne and University of Paris XI. After graduation in 1999, she worked at Centrede Recherche en Informatique at University of Paris I from Sep 1999 to May 2001.She joined France Telecom - Research and Development in summer 2001 to work as asystem architect intern. In spring 2002, she began her Ph.D. program at Systems En-gineering and Operations Research Department at George Mason University. Duringher doctoral studies, she was a research assistant in the Center for Air TransportationSystems Research (CATSR). Her research interests include optimization problems inthe airline industry. Loan Le will start working for American Airlines, Operations Re-search and Decision Support Department upon the completion of her Ph.D. program.She can be reached by email at [email protected].
