fleet type assignment and robust airline scheduling with chance constraints under environmental ...

115 Pages·2013·1.24 MB·English

FLEET TYPE ASSIGNMENT AND ROBUST
AIRLINE SCHEDULING WITH CHANCE
CONSTRAINTS UNDER ENVIRONMENTAL
EMISSION CONSIDERATIONS
a thesis
submitted to the department of industrial engineering
and the graduate school of engineering and science
of bilkent university
in partial fulfillment of the requirements
for the degree of
master of science
By
¨
Ozge S¸AFAK
August, 2013
I certify that I have read this thesis and that in my opinion it is fully adequate,
in scope and in quality, as a thesis for the degree of Master of Science.
Prof. Dr. M. Selim Aktu¨rk (Advisor)
I certify that I have read this thesis and that in my opinion it is fully adequate,
in scope and in quality, as a thesis for the degree of Master of Science.
Assoc. Prof. Dr. Sinan Gu¨rel (Co-Advisor)
I certify that I have read this thesis and that in my opinion it is fully adequate,
in scope and in quality, as a thesis for the degree of Master of Science.
Assoc. Prof. Dr. Oya E. Kara¸san
I certify that I have read this thesis and that in my opinion it is fully adequate,
in scope and in quality, as a thesis for the degree of Master of Science.
Assist. Prof. Dr. Sakine Batun
Approved for the Graduate School of Engineering and Science:
Prof. Dr. Levent Onural
Director of the Graduate School
ii
ABSTRACT
FLEET TYPE ASSIGNMENT AND ROBUST AIRLINE
SCHEDULING WITH CHANCE CONSTRAINTS
UNDER ENVIRONMENTAL EMISSION
CONSIDERATIONS
¨
Ozge S¸AFAK
M.S. in Industrial Engineering
Supervisor: Prof. Dr. M. Selim Aktu¨rk
Co-Supervisor: Assoc. Prof. Dr. Sinan Gu¨rel
August, 2013
Fleet Type Assignment and Robust Airline Scheduling is to assign optimally
aircraft to paths and develop a flight schedule resilient to disruptions. In this
study, a Mixed Integer Nonlinear Programming formulation was developed using
controllable cruise time and idle time insertion to ensure passengers’ connection
service level with the objective of minimizing the costs of fuel consumption, CO
2
emissions, idle time and spilled passengers. The crucial contribution of the model
is to take fuel efficiency of aircraft into considerations to compensate for the idle
time insertion as well as the cost of spilled passengers due to the insufficient
seat capacity. The nonlinearity in the fuel consumption function associated with
controllable cruise time was handled by second order conic reformulations. In
addition, the uncertainty coming from a random variable of non-cruise time arises
in chance constraints to guarantee passengers’ connection service level, which
was also tackled by transforming them into conic inequalities. We compared the
performance of the schedule generated by the proposed model to the published
schedule for a major U.S. airline. On the average, there exists a 20% total cost
saving compared to the published schedule. To solve the large scale problems in a
reasonable time, we also developed a two-stage algorithm, which decomposes the
problem into planning stages such as fleet type assignment and robust schedule
generation, and then solves them sequentially.
Keywords: fleet type assignment, airline scheduling, cruise time controllability,
second order conic programming, chance constraints.
iii
¨
OZET
˙ ¨ ¨ ¨
C¸EVRESEL EMISYONU GOZ ONUNDE
˙
BULUNDURARAK S¸ANS KISITLARI ILE DAYANAKLI
˙ ˙ ˙ ˙
HAVAYOLU C¸IZELGELEME VE FILO TIPI ATAMA
˙
MODELI
¨
Ozge S¸AFAK
Endu¨stri Mu¨hendislig˘i, Yu¨ksek Lisans
Tez Yo¨neticisi: Prof. Dr. M. Selim Aktu¨rk
E¸s-Tez Yo¨neticisi: Do¸c. Dr. Sinan Gu¨rel
Ag˘ustos, 2013
Filo tipi atama ve gu¨rbu¨z havayolu ¸cizelgelemesi, u¸cakların rotalara optimal bir
¸sekilde atanması ve aksamalara kar¸sı dayanaklı bir u¸cu¸s ¸cizelgesi geli¸stirilmesi
anlamına gelir. Bu c¸alı¸smada; yakıt tu¨ketimi, CO emisyonu, atıl zaman ve
2
ta¸san yolcu maliyetlerini en aza indirmeyi hedefleyen ve yolcuların bag˘lantı
hizmet seviyelerini sag˘lamak amacıyla, kontrol edilebilen seyir zamanı ve atıl
zaman kullanılarak, Karma Tamsayılı Do˘grusal Olmayan Programlama formu-
lasyonu geli¸stirilmi¸stir. Modelin kritik katkısı, yetersiz oturma kapasitesin-
den kaynaklı ta¸san yolcu maliyetiyle birlikte atıl zaman yerle¸stirmeyi telafi et-
mek amacıyla uc¸a˘gın yakıt verimlig˘ini hesaba katmasıdır. Kontrol edilebilir
seyir su¨releleriyle ili¸skili yakıt tu¨ketim fonksiyonundaki dog˘rusalsızlık, ikinci
derece konik reformu¨lasyonlarla i¸slenmi¸stir. Buna ek olarak, seyir dı¸sı su¨rede
bulunan bir raslantısal deg˘i¸skeninden kaynaklanan belirsizlik, yolcu ba˘glanma
hizmet seviyesini garanti etmek u¨zere ¸sans kısıtlarnda ortaya ¸cıkmaktadır ve
¨
bu da, konik e¸sitsizliklere do¨nu¨¸stu¨ru¨lerek ele alınmı¸stır. Onerilen model
tarafından olu¸sturulan planlamanın performansını ABD’li bu¨yu¨k bir havayolu
¸sirketi tarafından yayımlanan planla kar¸sıla¸stırdık. Yayımlanan plana kıyasla
toplamda ortalama 20%’lik bir maliyet tasarrufu sag˘landı. Bu¨yu¨k o¨l¸cekli prob-
lemleri makul bir zamanda ¸co¨zmek ic¸in de, problemi, filo tipi ataması ve gu¨rbu¨z
¸cizelgeleme gibi planlama a¸samalarına ayıran ve sonra sırasıyla ¸co¨zen iki a¸samalı
bir algoritma geli¸stirdik.
Anahtar s¨ozcu¨kler: filo tipi atama, u¸cu¸s c¸izelgeleme, kontrol edilebilir seyir za-
manları, konik e¸sitsizlikler, ¸sans kısıtları.
iv
Acknowledgement
I thank my advisor Professor M. Selim Aktu¨rk for his invaluable support during
my M.S. study. He has always been an understanding advisor. I have learned
many valueable lessons from him. I also thank my co-advisor Associate Professor
Sinan Gu¨rel for his time, help and patient. His advice contributed greatly to this
work. It was and will be a pleasure to work with them.
I also would like to acknowledge the financial support of The Scientific and
Technological Research Council of Turkey (TUBITAK) for the Graduate Study
Scholarship Program they awarded.
I would like to thank my officemates. It has always been fun in the same
office with them. Special thanks go to Damla Kurugo¨l and her family for offering
me a room in their house whenever I got bored and for her invaluable friendship.
We shared the same anxiety and excitement with Bilgesu C¸etinkaya, Dilek Keyf,
Ay¸segu¨l Onat, Gu¨lce C¸uhacı, Kumru Ada, Malek Ebadi and Ramez Kian as
graduate students. I will also remember my homemate Nil Karaco˘glu with her
great friendship that made any boring times enjoyable at home.
My sincere gratitude goes to my aunt and her husband who enriched my time
in Ankara. My aunt has always been an understanding family member. Her
advice contributed in large measures to success in my life.
Lastly, I owe everything that I have achieved to my parents. Their support,
love and encouragements through my life are most precious to me. I love them
all.
v
Contents
1 Introduction 1
1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 Overview. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2 Literature Review 6
2.1 Airline Scheduling Process . . . . . . . . . . . . . . . . . . . . . . 6
2.1.1 Robust Airline Scheduling . . . . . . . . . . . . . . . . . . 7
2.2 Fleet Type Assignment . . . . . . . . . . . . . . . . . . . . . . . . 9
2.3 Cruise Time versus Fuel Consumption and CO Emission . . . . . 11
2
2.4 Chance Constraints . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.5 Second Order Cone Programming . . . . . . . . . . . . . . . . . . 14
2.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
3 Problem Definition 16
3.1 Distribution of Non-cruise Times . . . . . . . . . . . . . . . . . . 20
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CONTENTS vii
3.1.1 Log-Laplace Distribution . . . . . . . . . . . . . . . . . . . 21
3.2 Fuel Cost . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
3.3 CO Emission Cost . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2
3.4 Service Level . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.5 Numerical Example . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
4 Problem Formulation 36
4.1 Mathematical Model . . . . . . . . . . . . . . . . . . . . . . . . . 37
4.1.1 Challenges for Solving the Model . . . . . . . . . . . . . . 40
4.2 Conic Reformulation of the Model . . . . . . . . . . . . . . . . . 40
4.2.1 Closed Form Expressions for the Chance Constraints . . . 40
4.2.2 Conic Representation of the Chance Constraints . . . . . . 42
4.2.3 Conic Representation of the Fuel and CO Emission Cost
2
Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
4.2.4 Conic Formulation of the Model . . . . . . . . . . . . . . . 48
4.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
5 Algorithm for Fleet Assignment and Robust Airline Scheduling 51
5.1 Proposed Two-Stage Algorithm . . . . . . . . . . . . . . . . . . . 52
5.2 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
6 Computational Results 59
CONTENTS viii
6.1 Analysis on the Schedule with 41 Flights . . . . . . . . . . . . . . 65
6.1.1 Computational Analysis on the Integrated Model . . . . . 66
6.1.2 Computational Analysis on Two-Stage Algorithm . . . . . 72
6.2 Analysis on the Schedule with 114 Flights . . . . . . . . . . . . . 73
6.2.1 Computational Analysis on the Two-Stage Algorithm . . . 74
6.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
7 Conclusions and Future Work 81
7.1 Summary of Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . 81
7.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
A Computational Results 90
A.1 Schedule with 41 flights . . . . . . . . . . . . . . . . . . . . . . . 90
A.2 Schedule with 114 flights . . . . . . . . . . . . . . . . . . . . . . . 96
List of Figures
3.1 Fuel Cost Function at Cruise Stage . . . . . . . . . . . . . . . . . 25
3.2 Idle Time versus Fuel and CO Emission Cost Functions . . . . . 27
2
3.3 Time Space Network for the Published Schedule . . . . . . . . . . 31
3.4 Time Space Network - After FA-RS . . . . . . . . . . . . . . . . . 32
6.1 What if Analysis on the Service Level . . . . . . . . . . . . . . . . 65
ix
List of Tables
3.1 Published Schedule . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.2 Cost Calculation for Published Schedule . . . . . . . . . . . . . . 33
3.3 Cost Calculation for FA-RS . . . . . . . . . . . . . . . . . . . . . 33
6.1 Factor Values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
6.2 Published Schedule . . . . . . . . . . . . . . . . . . . . . . . . . . 61
6.3 Aircraft Parameters . . . . . . . . . . . . . . . . . . . . . . . . . 62
6.4 Congestion Coefficients . . . . . . . . . . . . . . . . . . . . . . . . 63
6.5 Turnaround Time Study . . . . . . . . . . . . . . . . . . . . . . . 64
6.6 Original Aircraft Types . . . . . . . . . . . . . . . . . . . . . . . . 67
6.7 Comparison of Factor Effects . . . . . . . . . . . . . . . . . . . . 69
6.8 Factor Effects on the Percentage of Uncaptured Passengers . . . . 69
6.9 Cost Comparison for Different Replications . . . . . . . . . . . . . 70
6.10 Percentage of Uncaptured Passengers for Different Replications . . 70
6.11 CPU Time Analysis of the Integrated Model . . . . . . . . . . . . 71
x