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ALTITUDE 1
Le partenariat Universités - Entreprises
Un problème générique
Plus court chemin avec fenêtres de temps
Un peu d’histoire ...
ALTITUDE 2
coût
(40)
(10)(20)
(30)
8
12
24 27
(48) (44) (42) (37)
temps, coût
5, 12
(6, 10)(4, 20)
(4, 30)
(5, 40)
5, 27
3, 8
2, 24
( 6, 44) ( 8, 48) ( 9, 42) (11, 37)
Figure 7.1. Étiquetage des sommets
Étiquetage des sommets
ALTITUDE 3
sinon. ,
si),},,(max{),(
jij
eiij
eiij
eije
ie
iijbtTcCtTa
CTF
Étiquetage des sommets ...
ALTITUDE 4
Plus court chemin avec fenêtres de temps
AjiTtTX
VibTa
AjiX
di
Ni
oi
XX
Xc
jijiij
iii
ij
Vjji
Vjij
Ajiijij
),(,0)(
,
),(binaire,
,1
,0
,1
: àsujet
Minimiser),(
ALTITUDE 5Figure 7.2. Quelques fonctions d'extension
Des fonctions d’extension
ALTITUDE 6
Figure 7.2. Une fonction de coût discontinue
3 7
Une fonction de coût discontinue
ALTITUDE 7
Coûts39 43 42 40 38 38 … 43 44 34 41 34 33 38 58 41
1 1 … 1 1 1 … = 1
2 1 1 1 … 1 1 1 1 1 … = 2
3 1 1 1 … 1 1 1 1 … = 1
4 1 1 1 1 … 1 1 1 1 1 … = 1
5 1 1 … 1 1 1 1 … = 2
6 1 1 1 … 1 1 1 1 … = 1
7 1 … 1 1 1 … = 1
8 1 1 1 … 1 1 1 1 … = 1
9 1 1 … 1 1 1 1 1 … = 1
Tâc
hes
10 1 1 1 … 1 1 1 … = 1
13 17 15 11 13 14 … … 25
… 12 18 13 12 9 10 14 24 13 … = 40
1 1 1 1 1 1 … … = 2
… 1 1 1 1 1 1 1 1 1 … = 4
Figure 7.3. Structure matricielle des contraintes globales
Des contraintes globales
ALTITUDE 8
KkY
dYD
bYB
Yc
k
kk
kk
kk
entières,0
: àsujet
Minimiser
Kk
Kk
Kk
Le problème maître
ALTITUDE 9
Mise en œuvre de la décomposition :
la génération de colonnes
et l’optimiseur GENCOL
ALTITUDEAn Optimization System for the Management of Operations in Air Transport
A University-Industry R&D Project (1993 -1998)
ALTITUDE 11
GOVERNMENTS
COMMERCIAL PARTNERS
AIRLINE COMPANIESAIRLINE COMPANIES
CREW MEMBERS
UNIVERSITIES
RESEARCH CENTERS
Professors & Researchers
STUDENTS & ANALYSTS
ALTITUDE 12
The Presentation
The Research Team
The Operations Phases in Air Transport
The Financial Support
The Structure of the Problems Solved
The Optimization Methods Utilized
Benefits of the Project
ALTITUDE 13
The Research Team
G. Desaulniers, M. Gamache & F. Soumis
Ecole Polytechnique & GERADJ. Desrosiers
Ecole des HEC & GERADM. M. Solomon
Northeastern University & GERAD
ALTITUDE 14
GERADan Operations Research center
that brings together ...
Ecole Polytechnique de Montréal Ecole des Hautes Etudes Commerciales McGill University Université du Québec à Montréal
ALTITUDE 15
GERAD
Few numbers...
30 professors / researchers 20 post-docs and computer science
analysts 120 graduate students
3M$ grants / year
ALTITUDE 16
The Research Team ...
Team manager
François SoumisEcole Polytechnique
de Montréal
Past director of GERAD (1992-96)
ALTITUDE 17
The Research Team ...
30 people per year at GERAD for this project 3 to 6 post-doctoral researchers 15 master and Ph. D. students 5 to 7 full time programmers 7 university collaborators
+ + Personnel from commercial partners
ALTITUDE 18
University Collaborators
Ecole des HEC
P. Hansen F. Chauny
Ecole Polytechnique
B. Sanso B. Jaumard G. Savard
Université de Montréal
G. Lapalme
McGill University
J.-L. Goffin
Université du Québec à Montréal
O. Marcotte
ALTITUDE 19
Operations Phases in Air Transport
Planning
aircraft routes crew pairings employees monthly
schedules
Day-to-day operations
rescheduling of
aircraft routes & crew schedules
ALTITUDE 20
The Financial Support: CDN $ 5,500,000
Quebec Government $ 2.5 M
AD OPT Technologies
& Cognologic $ 1.5 M
Natural Sciences and Engineering Research Council of Canada $ 1.5 M
Research infrastructure provided by
GERAD
ALTITUDE 21
The Structure of the Problems Solved
Tasks to be performed represented
by nodes or arcs ontime space networks
Paths covering the tasks the required
number of times
Local constraintscharacterize a single path
Global constraints on the path set composition
Objective: context dependent
ALTITUDE 22
The Generic Problem
COVER AT MINIMUM COST
A SET OF TASKS
WITH FEASIBLE PATHS
COMMODITY
TASK
TASK
ALTITUDE 23
SEQUENCES ON A MACHINEOPERATIONSJOB-SHOP
PRODUCTION
ROUTESTRAINSLOCO. ROUTING
RAIL
ROSTERSPAIRINGSROSTERING
PAIRINGSFLIGHTSCREW PAIRING
ROUTESFLIGHTSAIRCRAFT ROUTING
AIRLINE
ROSTERSSHIFTSROSTERING
SHIFTSTRIP SEGMENTSDRIVER SCHEDULING
ROUTESBUS TRIPSBUS ROUTING
BUS
PATHSTASKS
Examples
ALTITUDE 24
The Aircraft Routing Problem
Tasks flight legs to be flown
Paths aircraft routes
Local constraints time windows
on flights
Global constraints flight synchronization
same time schedules
Minimize fleet size
Maximize profit
ALTITUDE 25
The Crew Pairing Problem
Tasks flight legs to cover
Paths crew travels
Local constraints
pilots &flight
attendants work rules
Global constraints
number of crews per base
Minimize total crew costs
ALTITUDE 26
Employees Monthly Schedules
Tasks pre-assignments & crew pairings
annual vacations, training
Paths sequence of tasks assigned to employees
the number of employees required by a pairing sometimes exceeds 10
Local constraints employees
work rules
Global constraints ratios on full time / part time employees
ALTITUDE 27
Employees Monthly Schedules …
Flight deck minimize
costs incurred
maximizean index of personnel satisfaction
balance work schedules
Flight attendants
maximizerotation covering
(uncovered tasks allocated to
reserve personnel)
ALTITUDE 28
Day-to-Day Operations
Schedule perturbations
illnessbreakdownslatenessstorm …
Cost optimization
vs
Client satisfaction
ALTITUDE 29
Day-to-Day Operations ...
Tasks scheduled & new flights
Paths aircraft & crew routes (modified or not)strong / weak interaction
Local constraints flight time windows
Local constraints crew work rules on pairings & monthly schedules
Global constraints fleet composition flight synchronizationnew configuration of pairings & monthly schedules
ALTITUDE 30
The Optimization Methods Utilized
Integer multi-commodity network flow problems
with additional constraints
Mathematical decomposition
Dantzig-Wolfe decomposition (column generation)Lagrangian relaxation Benders decomposition
ALTITUDE 31
Resource Constrained Shortest Path Problem on G=(N,A)
Ni Rr
rii
Ajiijij TxcMin
),(
doidioixxAijj
ijAjij
ij ,,0;,1;,1),(:),(:
RrAjiTTfx rjiijij ,),(,0))((
Ajix
RrNibxTax
ij
ri
Ajijij
ri
ri
Ajijij
),(,binary
,,)()(),(:),(:
P(N, A) :
ALTITUDE 32
Integer Multi-Commodity Network Flow Structure
Kk Ni Rr
kri
ki
Aji
kij
kij
kk
TxcMin )(),(
MmbTaxa
Nibx
mKk
kri
Ni
krim
Aji
kij
kijm
ki
Kk Ajij
kij
kk
k
,)(
,)(
,),(
,
),(:
KkANPTx kkkk ),,(),(
ALTITUDE 33
The Optimization Methods Utilized ...
Dynamic programming for efficient solution of shortest path problems embedding local constraints
Sequential & Parallel implementations
column pricing DP algorithms
CPLEX software flexibility
Network Primal & Dual Simplex Barrier
ALTITUDE 34
Complements...
ALTITUDE 35
Benefits of the Project
academic
scientific
commercial
industrial
… and artistic
ALTITUDE 36
Academic spin-offs
Aircraft RoutingDaily IanickWeekly Nicolas *Monthly LucienSchedule synchronization
Irina *
Pairing ConstructionDeadhead Selection
Gilles & Hatem
Regional Carrier Arielle
Crew Complement Bogdan
* Ph.D. students
ALTITUDE 37
Academic spin-offs ...
Monthly Schedules
Rostering (crew cabin) Michel *Rostering (flight attendants) Michel *Preferential Bidding
Michel *
Day-of-Operations
Crew members Mirela *Aircraft schedules Goran *
(Strong interaction) **
* Ph.D. students
ALTITUDE 38
Academic spin-offs ...
Column GenerationSub-problem algorithms Irina*
Daniel*ManuelSylvie*
Master problemNorbertDaniel*Eric
Column Generation Stabilized Daniel*Manuel VivianeBranch & BoundFrançois Eric SylvieNorbert … * Ph.D. students
ALTITUDE 39
Academic spin-offs ...
7 post-doctoral researchers for periods of one to three years.
5 residencies
23 analysts
6 Ph. D. dissertations
14 master thesis
• New RAIL R&D project3 Ph. D. dissertations
4 master thesis8 analysts
ALTITUDE 40
Scientific Advances
30 publications
Management Science Operations ResearchTransportation Science Networks EJOR
Handbooks in ORHandbooks in OR&&MSMSFleet Management & Logistics ...
3 survey papers
“Time Constrained Routing and Scheduling”
“A Unified Framework for Deterministic Vehicle Routing and Crew Scheduling Problems”
“Crew Scheduling in Air Transportation”
ALTITUDE 41
Scientific Advances ...
IP Column GenerationBasis of a theory on branching methods and cutting planes, hence resolving difficulties faced for several decades.
Equivalence betweenDantzig-Wolfe Decomposition & Column Generation
Branching rules on Network Flow
Supplementary & Resource variables
Cutting Planes at Master & Sub-problem levels
ALTITUDE 42
Scientific Advances ...
Resource constrained shortest paths
non linear cost functions non linear resource functions linear cost on resource variables
Acceleration techniques
early and multiple branching
strategiespartial pricing
for sub-problemsprimal perturbation &
dual stabilization for the master problem
ALTITUDE 43
Scientific Advances ...
GENCOL 3.0 4.0 4.1 4.2
This optimizer integrates the majority of the scientific advances made on column generation to solve very large scale vehicle routing & crew scheduling problems.
ALTITUDE 44
Prizes and Honors
ECOLE POLYTECHNIQUEResearch Prize (1992)
François Soumis
ECOLE des HEC Research Prize (1997)
Jacques Desrosiers
ALTITUDE 45
Prizes and Honors ...
CORS Best Application "A Column Generation Approach for Large Scale Aircrew Rostering Problems" collaboration with Air France (Montréal, May 1994)
" The Preferential Bidding Problem at Air Canada " (Vancouver, July 1996)
TV show "Option Education"
The research of professors J. Desrosiers and F. Soumis has been the subject of a segment televised by Télé-Québec and RDI .
(December 1996)
ALTITUDE 46
Prizes and Honors ...
ACFASJ.-Armand Bombardier Medal for Technological Innovation (Montreal, May 1997)
ADRIQTRANSFERT Prize 1997 with Ad Opt Technologies (Montreal, November 1997)
The CONFERENCE BOARD of Canada
& NSERC
R&D PARTNERSHIPS Award University-Industry Synergy (Vancouver, October 1997)
ALTITUDE 47
Commercial Benefits
Provided by the Universities:
commercial licenses of
GENCOL to
Ad Opt Technologies
Airline industryRail industry
Les Entreprises GIROUrban transportation
School busingDial-a-Ride System
ALTITUDE 48
Product Architecture
GENCOL OPTIMIZER
MODELING MODULE
GRAPHICAL USER INTERFACE
USER
DATA BASE
TASKS, NETWORKS PATHS
ALTITUDE 49
The Family of Products
SCHOOLURBAN
BU
S D
RIV
ER
AD
AP
TE
DT
RA
NS
PO
RT
RA
IL
CR
EW
RO
ST
ER
ING
CR
EW
PA
IRIN
G
BUS AIRCRAFT
PROTOTYPE
DAYS-OPT
PROTOTYPE
GIRO AD OPT
GENCOL
ALTITUDE 50
Altitude - Ad Opt
ALTITUDE 51
Computational Results
Crew Pairing
Crew Rostering
Fleet Assignment and Aircraft Routing
Aircraft Routing and Flight Scheduling
Subway Driver Scheduling
Locomotive Routing
ALTITUDE 52
Crew Pairing Air Canada
FLIGHT ATTENDANTS DC-9 + A 320
2.0311914MONTHLY
1.392425WEEKLY
0.47430DAILY
% FATFLIGHTS5 BASES
Savings vs Air Canada solution : 7.8 % 2.03 %
TRANSAT, CAN. REGIONAL, NORTHWEST, U.P.S., DELTA, SABENA, SWISSAIR, FEDEX
ALTITUDE 53
Crew Rostering Air France
Flight Attendant
ORLY CDG
PAIRINGS 454*7 3000*5
PERSONS 240 840
SAVINGS 7.4% 7.6%
A. C., TRANSAT, CAN. REGIONAL, TWA, DELTA, SABENA, SWISSAIR, AMERICA WEST
ALTITUDE 54
Fleet Assignment & Aircraft Routing Air Canada
91 AIRCRAFT, 9 TYPES, 33 STATIONS
FLEET REDUCTION WITH TIME WINDOWS ON FLIGHT SCHEDULE
13.9 %
± 30 MIN
8.9 %
± 20 MIN
3.8 %
±10 MIN
SAVINGS
T.W.
ALTITUDE 55
Fleet Assignment & Aircraft Routing Air France
51 AIRCRAFT, 6 TYPES, 44 STATIONS
BASIC PROBLEM 6.5 % 10 MIN Time Windows 11.2 %
10 MIN T.W. + FLEET OPTIMIZATION 21.9 %
PROFIT IMPROVEMENT
ALTITUDE 56
Aircraft Routing & Scheduling Canadian Army (C-130)
WEST CHALLENGE (19 city-pairs)750 soldiers and equipmentMAX 65 soldiers per flight
1 (33 %)20 HRS (34 %)SAVINGS
339 HRSGENCOL Optimizer
459 HRSManual solution
NUMBER
OF AIRCRAFT
FLIGHT
TIME
ALTITUDE 57
2000 – 3000 bus segmentsOne- or two-day shifts
Collective agreement rules
SAVINGS 15 %
GIRO contract : US $1,500,000
Subway Driver Scheduling
Tokyo
Stockholm, Helsinky, Singapore, Barcelone, New York, Chicago… 35 cities
ALTITUDE 58
Weekly problem
2000 Trains 26 Locomotive types
Maintenance constraints
Minimal demand for each train : nb. of locos & hp
SAVINGS : 100 locos over 1090 (9.17 %)
Locomotive Routing Canadian National
Via Rail
ALTITUDE 59
Commercial Benefits ...
Ad Opt Technologies
Number of employees
5 55 Hiring of 30 O.R. students
Yearly revenues
$ 300 K $ 5.7 M
ALTITUDE System
Air Transat UPS Air Canada TWA Northwest Delta
Sabena FedEx……….
RAIL-WAYS System
VIAVIA Rail
ALTITUDE 60
Commercial Benefits ...
Cognologic
had the role to design the graphical interfaces of the ALTITUDE system.
This 5-year project has permitted the company to consolidate its position in this market in Montreal.
ALTITUDE 61
Other CommercialBenefits ...
Les Entreprises GIRO
150 cities using the HASTUS Systemfor bus drivers
The CREW-OPT version
integrates GENCOL
12 35 installations of CREW-OPT
(Lyon) (Toulouse)Tokyo Vienna
Singapore BarcelonaHelsinki OsloPerpignan StockholmValenciennes …
ALTITUDE 62
Industrial Benefits
ALTITUDE 63
Industrial Benefits ...
The financial impact for the Aircraft Fleet is at least as large, if not larger, than that of the two preceding modules.
The DAYOPS module has a $$ impact on the entire system operated by any airline company.
Savings of several tens of millions of dollars for the Crew Pairing module.
Savings of same order are realized for the Monthly Schedules.
$AVING$ are additive.
ALTITUDE 64
Common Goal Efforts
Jean-Yves Blais
President of GIROTom Ivaskiv
President of Ad OptJacques Desrosiers
Ecole des HEC
François SoumisEcole Polytechnique
ALTITUDE 65
Commercial Benefits ...
Ad Opt Technologies
Number of employees
5 55 … 75
Yearly revenues
$ 300 K $ 5.7 M ... $ 12 M
Toronto Stock Market (since June 17, 1999)
AOP stock value : $ 62 M --->
ALTITUDE 66
Research Trends
ALTITUDE 67
GOVERNMENTS
COMMERCIAL PARTNERS
AIRLINE COMPANIESAIRLINE COMPANIES
CREW MEMBERS
UNIVERSITIES
RESEARCH CENTERS
Professors & Researchers
STUDENTS & ANALYSTS
ALTITUDE 68
Soutenance de Daniel V.