Title: ALTITUDE 1
1Un peu dhistoire ...
- Le partenariat Universités - Entreprises
- Un problème générique
- Plus court chemin avec fenêtres de temps
2Étiquetage des sommets
3Étiquetage des sommets ...
4Plus court chemin avec fenêtres de temps
5Des fonctions dextension
6Une fonction de coût discontinue
7Des contraintes globales
8Le problème maître
9Mise en œuvre de la décomposition la
génération de colonneset loptimiseur GENCOL
10 ALTITUDEAn Optimization System for the
Management of Operations in Air Transport
- A University-Industry RD Project (1993 -1998)
11- GOVERNMENTS
- COMMERCIAL PARTNERS
- AIRLINE COMPANIES
- CREW MEMBERS
- UNIVERSITIES
- RESEARCH CENTERS
- Professors Researchers
- STUDENTS ANALYSTS
12The 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
13The Research Team
- G. Desaulniers, M. Gamache F. Soumis
- Ecole Polytechnique GERAD
- J. Desrosiers
- Ecole des HEC GERAD
- M. M. Solomon
- Northeastern University GERAD
14GERAD
- an Operations Research center
that brings together ... - Ecole Polytechnique de Montréal
- Ecole des Hautes Etudes Commerciales
- McGill University
- Université du Québec à Montréal
15GERAD
- Few numbers...
- 30 professors / researchers
- 20 post-docs and computer science analysts
- 120 graduate students
- 3M grants / year
16The Research Team ...
- Team manager
- François Soumis
- Ecole Polytechnique de Montréal
- Past director of GERAD (1992-96)
17The 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
18University 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
19Operations Phases in Air Transport
- Planning
- aircraft routes
- crew pairings
- employees monthly schedules
- Day-to-day operations
- rescheduling of
- aircraft routes crew schedules
20The 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
21The Structure of the Problems Solved
- Tasks to be performed
- represented by nodes or arcs on
- time space networks
- Paths covering the tasks
- the required number of times
- Local constraints
- characterize a single path
- Global constraints
- on the path set composition
- Objective context dependent
22The Generic Problem
- COVER AT MINIMUM COST
- A SET OF TASKS
- WITH FEASIBLE PATHS
TASK
COMMODITY
23Examples
24The 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
25The 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
26Employees 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
27Employees Monthly Schedules
- Flight deck
- minimize
- costs incurred
-
- maximize
- an index of personnel satisfaction
- balance
- work schedules
- Flight attendants
- maximize
- rotation covering
- (uncovered tasks allocated to reserve
personnel)
28Day-to-Day Operations
- Schedule perturbations
- illness
- breakdowns
- lateness
- storm
- Cost optimization
- vs
-
- Client satisfaction
29Day-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 synchronization
- new configuration of pairings monthly
schedules
30The Optimization Methods Utilized
- Integer multi-commodity network flow problems
- with additional constraints
- Mathematical decomposition
- Dantzig-Wolfe decomposition (column generation)
- Lagrangian relaxation
- Benders decomposition
31Resource Constrained Shortest Path Problem on
G(N,A)
P(N, A)
32Integer Multi-Commodity Network Flow Structure
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
34Complements...
35Benefits of the Project
- academic
- scientific
- commercial
- industrial
- and artistic
36Academic spin-offs
- Aircraft Routing
- Daily Ianick
- Weekly Nicolas
- Monthly Lucien
- Schedule synchronization Irina
- Pairing Construction
- Deadhead Selection Gilles Hatem
- Regional Carrier Arielle
- Crew Complement Bogdan
- Ph.D. students
37Academic 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
38Academic spin-offs ...
- Column Generation
- Sub-problem algorithms Irina Daniel Ma
nuel Sylvie - Master problem Norbert Daniel Eric
- Column Generation Stabilized Daniel Manuel
Viviane - Branch Bound François Eric Sylvie Nor
bert Ph.D. students
39Academic 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 RD project 3 Ph. D. dissertations
- 4 master thesis 8 analysts
40Scientific Advances
- 30 publications
- Management Science
- Operations Research
- Transportation Science
- Networks
- EJOR
- Handbooks in ORMS
- Fleet 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
41Scientific Advances ...
- IP Column Generation
- Basis of a theory on branching methods and
cutting planes, hence resolving difficulties
faced for several decades. - Equivalence between Dantzig-Wolfe Decomposition
Column Generation
- Branching rules on
- Network Flow
- Supplementary
- Resource variables
- Cutting Planes at
- Master
- Sub-problem levels
42Scientific Advances ...
- Resource constrained shortest paths
- non linear cost functions
- non linear resource functions
- linear cost on resource
variables
- Acceleration techniques
- early and multiple branching strategies
- partial pricing for sub-problems
- primal perturbation dual stabilization for
the master problem
43Scientific 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.
44Prizes and Honors
- ECOLE POLYTECHNIQUE Research Prize (1992)
- François Soumis
- ECOLE des HEC Research Prize (1997)
- Jacques Desrosiers
45Prizes 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)
46Prizes and Honors ...
- ACFAS
- J.-Armand Bombardier Medal for Technological
Innovation (Montreal, May 1997) - ADRIQ
- TRANSFERT Prize 1997 with Ad Opt Technologies
(Montreal, November 1997)
- The CONFERENCE BOARD of Canada NSERC
- RD PARTNERSHIPS Award University-Industry
Synergy (Vancouver, October 1997)
47Commercial Benefits
- Provided by the Universities commercial
licenses of GENCOL to
- Ad Opt Technologies
- Airline industry
- Rail industry
- Les Entreprises GIRO
- Urban transportation
- School busing
- Dial-a-Ride System
48Product Architecture
49The Family of Products
50Altitude - Ad Opt
51Computational Results
- Crew Pairing
- Crew Rostering
- Fleet Assignment and Aircraft Routing
- Aircraft Routing and Flight Scheduling
- Subway Driver Scheduling
- Locomotive Routing
52Crew Pairing Air Canada
- FLIGHT ATTENDANTS DC-9 A 320
Savings vs Air Canada solution 7.8 ? 2.03
TRANSAT, CAN. REGIONAL, NORTHWEST, U.P.S., DELTA,
SABENA, SWISSAIR, FEDEX
53Crew Rostering Air France
ORLY CDG PAIRINGS 4547 30005 PERSONS
240 840
SAVINGS 7.4 7.6
A. C., TRANSAT, CAN. REGIONAL, TWA, DELTA,
SABENA, SWISSAIR, AMERICA WEST
54Fleet Assignment Aircraft Routing Air Canada
- 91 AIRCRAFT, 9 TYPES, 33 STATIONS
- FLEET REDUCTION
- WITH TIME WINDOWS ON FLIGHT SCHEDULE
55Fleet 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
56Aircraft Routing Scheduling Canadian Army
(C-130)
- WEST CHALLENGE (19 city-pairs)
- 750 soldiers and equipment
- MAX 65 soldiers per flight
57Subway Driver Scheduling Tokyo
- 2000 3000 bus segments
- One- or two-day shifts
- Collective agreement rules
- SAVINGS ? 15
- GIRO contract US 1,500,000
Stockholm, Helsinky, Singapore, Barcelone, New
York, Chicago 35 cities
58Locomotive Routing Canadian National
- 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 )
Via Rail
59Commercial 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
- VIA Rail
60Commercial Benefits ...
- 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.
61Other CommercialBenefits ...
- Les Entreprises GIRO
- 150 cities using the HASTUS System for bus
drivers - The CREW-OPT version integrates GENCOL
- 12 35 installations of CREW-OPT
- (Lyon) (Toulouse)
- Tokyo Vienna
- Singapore Barcelona
- Helsinki Oslo
- Perpignan Stockholm
- Valenciennes
62Industrial Benefits
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.
64Common Goal Efforts
- Jean-Yves Blais
- President of GIRO
- Tom Ivaskiv
- President of Ad Opt
- Jacques Desrosiers
- Ecole des HEC
- François Soumis
- Ecole Polytechnique
65Commercial 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 ---gt
66Research Trends
67- GOVERNMENTS
- COMMERCIAL PARTNERS
- AIRLINE COMPANIES
- CREW MEMBERS
- UNIVERSITIES
- RESEARCH CENTERS
- Professors Researchers
- STUDENTS ANALYSTS
68Soutenance de Daniel V.