Combining Robustness and Recovery for Airline Schedules

182 Pages·2009·1.34 MB·English

Combining Robustness and Recovery
for Airline Schedules
THÈSE NO 4556 (2009)
PRÉSENTÉE LE 11 DÉCEMBRE 2009
À LA FACULTE SCIENCES DE BASE
LABORATOIRE TRANSPORT ET MOBILITÉ
PROGRAMME DOCTORAL EN MATHÉMATIQUES
ÉCOLE POLYTECHNIQUE FÉDÉRALE DE LAUSANNE
POUR L'OBTENTION DU GRADE DE DOCTEUR ÈS SCIENCES
PAR
Niklaus EGGENBERG
acceptée sur proposition du jury:
Prof. F. Eisenbrand, président du jury
Prof. M. Bierlaire, Dr M. Salani, directeurs de thèse
Prof. C. Barnhart, rapporteur
Prof. T. Liebling, rapporteur
Prof. F. Margot, rapporteur
Suisse
2009

Fu¨r meine geliebte Familie
&
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A Fred
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Acknowledgments
It would be a more difficult task for me to thank all the people to whom I owe credit
for this thesis than it was to actually write it. I however want to express my deepest
gratitude to all people that, directly or indirectly, helped me to finalize this thesis.
My first thoughts and thanks go to Michel Bierlaire, my friendly thesis supervisor
who offered me the opportunity to work on this thesis. I especially want to thank him
for his friendship, his numerous pertinent and helpful thoughts and suggestions and,
last but not least, his undeniable talent for always being positive and stimulating!
I also thank Matteo Salani, my thesis co-director and colleague whom I worked
with during the last three years. The content of this thesis is in large majority the
result of our collaboration and I owe him a huge credit.
I especially thank the sponsors of the thesis project, namely the Swiss government
withinthefundfortechnologytransfer(CTI-Project8007.2ESPP-ES)andtheSwiss
National Science Foundation (SNSF - Project 200021-118547).
Next, I want to thank all the Transp-OR members for the great working atmo-
sphere in our lab. I especially thank Ilaria Vacca, with whom I was sharing the office,
Marianne Ruegg for her patience and infinitely appreciated help and Anne Curchod
for her talents to fix my IT problems. I also thank Emma Frejinger for helping me
plan my stay at MIT and for her technical contributions and Thomas Robin and
Javier Cruz for their friendship and useful comments.
Many thanks to Thomas Liebling and Dominique De Werra, whose lectures and
semester projects initiated my love for OR. I am specially grateful to the former
ROSO members with whom I experienced my first steps in OR, especially Gautier
Stauffer who directed my master thesis.
I also thank Cynthia Barnhart who welcomed me in her group at MIT for a couple
of months. I spend four extremely valuable and interesting months there, both from
the scientific and the personal point of view. I thank all the members of the ORC
and the School of Civil Engineering, especially Lavanya Marla, for many interesting,
challenging and helpful talks.
Cynthia Barnhart introduced me to one of her students, Virot Chiraphadhanakul.
The result of our collaboration is Chapter 5 and I am deeply grateful for Virot’s
patience, efficiency and his tremendous programming work. I also want to thank
Jeppessen1 for providing the data of the airline used in Chapter 5 and for their useful
1http://www.jeppesen.com
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comments on both the airline’s as well as the data structures.
The work in Chapter 3 results from a collaboration between EPFL and APM
Technologies, sponsored by the Swiss government within the fund for technology
transfer (CTI - Project 8007.2 ESPP-ES). I especially thank CTI for its funding and
APM Technologies, the industrial partner of this project, for its support and vital
information on the problem. I also thank Thomas Cook Airlines for providing their
data for our computational tests.
Words are missing to express my feelings for my family and friends, without whom
I would never have been able to complete this thesis. First of all, my parents who
always supported and loved me. Also a special thanks to my older sisters Anna and
Regula and my brother Urs, to whom I owe my curiosity for solving new problems. I
also think of Fred, whose tragic disappearance fills my heart with sadness and is an
every day evidence of how lucky I am. He helped me numerous times to move on in
difficult times.
I also thank St´ephanie with all my love for her infinite love, patience, support but
also for her language skills. And, last but not least, all people that helped me enjoy
the student’s life, mainly my flatmate Nicolas, my long-time friends Jonathann, Paul,
Sylvain and of course also all others that I did not cite here.
Abstract
In this thesis, we address different aspects of the airline scheduling problem. The
main difficulty in this field lies in the combinatorial complexity of the problems.
Furthermore, asairlineschedulesareoftenfacedwithperturbationscalleddisruptions
(bad weather conditions, technical failures, congestion, crew illness...), planning for
better performance under uncertainty is an additional dimension to the complexity of
the problem. Our main focus is to develop better schedules that are less sensitive to
perturbations and, when severe disruptions occur, are easier to recover. The former
property is known as robustness and the latter is called recoverability.
We start the thesis by addressing the problem of recovering a disrupted schedule.
We present a general model, the constraint-specific recovery network, that encodes all
feasible recovery schemes of any unit of the recovery problem. A unit is an aircraft,
a crew member or a passenger and its recovery scheme is a new route, pairing or
itinerary, respectively. We show how to model the Aircraft Recovery Problem (ARP)
and the Passenger Recovery Problem (PRP), and provide computational results for
both of them.
Next, we present a general framework to solve problems subject to uncertainty:
the Uncertainty Feature Optimization (UFO) framework, which implicitly embeds
the uncertainty the problem is prone to. We show that UFO is a generalization
of existing methods relying on explicit uncertainty models. Furthermore, we show
that by implicitly considering uncertainty, we not only save the effort of modeling an
explicit uncertainty set: we also protect against possible errors in its modeling. We
thenshowthatcombiningexistingmethodsusingexplicituncertaintycharacterization
with UFO leads to more stable solutions with respect to changes in the noise’s nature.
We illustrate these concepts with extensive simulations on the Multi-Dimensional
Knapsack Problem (MDKP).
We then apply the UFO to airline scheduling. First, we study how robustness
is defined in airline scheduling and then compare robustness of UFO models against
existing models in the literature. We observe that the performance of the solutions
closely depend on the way the performance is evaluated. UFO solutions seem to
perform well globally, but models using explicit uncertainty have a better potential
when focusing on a specific metric.
Finally, we study the recoverability of UFO solutions with respect to the recovery
algorithm we develop. Computational results on a European airline show that UFO
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solutions are able to significantly reduce recovery costs.
Keywords: airline scheduling, recovery, constraint-specific recovery network, opti-
mization under uncertainty, robustness, recoverability, column generation.
R´esum´e
Dans cette th`ese, nous consid´erons diff´erents aspects du probl`eme d’organisation
op´erationnelle d’horaires a´eriens. La difficult´e majeure de cette discipline r´eside
dans la complexit´e combinatoire des probl`emes `a r´esoudre. De plus, les compag-
nies a´eriennes sont souvent confront´ees `a des perturbations (mauvaises conditions
m´et´eorologiques, d´efaillances techniques, congestion, employ´es malades...). Planifier
pour atteindre une meilleure performance dans cet environnement incertain ajoute
une dimension suppl´ementaire `a la complexit´e du probl`eme. Notre objectif premier
est de d´evelopper des horaires moins sensibles `a ce type de perturbations et qui, si
ces perturbations sont suffisamment graves, peuvent ˆetre r´epar´es `a moindre couˆt. La
premi`erepropri´et´eestconnuesouslenomderobustesse etlasecondeestlar´eparabilit´e
de l’horaire.
Pour commencer, dans cette th`ese, nous consid´erons le probl`eme de r´eparation
d’un horaire perturb´e. Nous pr´esentons un mod`ele g´en´eral, appel´e constraint-specific
recovery network, contenant toutes les routes de r´eparation admissibles pour chaque
unit´e du probl`eme. Une unit´e peut ˆetre un avion, un membre du personnel ou un
passager et sa route de r´eparation correspond respectivement `a un nouveau trac´e,
une nouvelle rotation ou un nouvel itin´eraire. Nous d´emontrons comment le mod`ele
s’applique au probl`eme de r´eparation des routes d’avions (ARP) et au probl`eme de
r´eparation des itin´eraires des passagers (PRP) et pr´esentons des r´esultats num´eriques
pour les deux probl`emes.
Nous pr´esentons ensuite une m´ethodologie g´en´erale, appel´ee Uncertainty Feature
Optimization (UFO), pour r´esoudre des probl`emes dont les donn´ees sont incertaines.
La m´ethodologie consid`ere l’incertitude d’un probl`eme de mani`ere implicite. Nous
prouvons qu’UFO est une g´en´eralisation d’autres m´ethodes s’appuyant sur un mod`ele
explicite de l’incertitude. De plus, nous montrons que, grˆace `a la consid´eration im-
plicite de l’incertitude, nous n’´epargnons non seulement l’effort de mod´elisation, mais
nous nous prot´egeons ainsi, par la mˆeme occasion, contre d’´eventuelles erreurs dans le
mod`ele. Nous montrons ´egalement que la combinaison de m´ethodes existantes bas´ees
sur un mod`ele explicite avec UFO am´eliore la stabilit´e des solutions par rapport `a
d’´eventuels changements de la nature de l’incertitude des donn´ees. Nous illustrons ces
concepts avec des simulations extensives sur le probl`eme du sac-`a-dos `a dimensions
multiples (MDKP).
Nous appliquons ensuite la m´ethodologie UFO au probl`eme d’organisation
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op´erationnelle d’horaires a´eriens. Nous commen¸cons par analyser la mani`ere dont
la robustesse est d´efinie dans le domaine a´erien et comparons la robustesse des solu-
tions obtenues avec UFO avec des solutions de m´ethodes trouv´ees dans la litt´erature.
Nous observons que la performance d’une solution d´epend fortement de la mani`ere
dont celle-ci est ´evalu´ee. Les solutions obtenues avec UFO semblent globalement ef-
ficaces pour les diff´erents crit`eres de performance utilis´es. En revanche, les mod`eles
b´en´eficiant d’un mod`ele explicite de l’incertitude ont un meilleur potentiel si
l’´evaluation de la performance se limite `a un crit`ere unique.
Finalement, nous ´etudions la r´eparabilit´e des solutions obtenues avec UFO par
rapport `a l’algorithme de r´eparation d´evelopp´e grˆace au mod`ele constraint-specific re-
covery network. Nous pr´esentons des r´esultats num´eriques sur des donn´ees provenant
d’une compagnie europ´eenne. Les r´esultats montrent que les solutions UFO r´eduisent
consid´erablement les couˆts de r´eparation.
Mots cl´es : planification d’horaires a´eriens, r´eparation d’horaires perturb´es, r´eseau
de r´eparation sp´ecifique `a une unit´e, optimisation sous incertitude, robustesse,
r´eparabilit´e, g´en´eration de colonne.