ALTITUDE 1

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Un peu dhistoire ...

• Le partenariat Universités - Entreprises
• Un problème générique
• Plus court chemin avec fenêtres de temps

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Étiquetage des sommets
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Étiquetage des sommets ...
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Plus court chemin avec fenêtres de temps
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Des fonctions dextension
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Une fonction de coût discontinue
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Des contraintes globales
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Le problème maître
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Mise en œuvre de la décomposition la
génération de colonneset loptimiseur GENCOL
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ALTITUDEAn Optimization System for the
Management of Operations in Air Transport

• A University-Industry RD Project (1993 -1998)

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• GOVERNMENTS
• COMMERCIAL PARTNERS
• AIRLINE COMPANIES
• CREW MEMBERS

• UNIVERSITIES
• RESEARCH CENTERS
• Professors Researchers
• STUDENTS ANALYSTS

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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

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The Research Team

• G. Desaulniers, M. Gamache F. Soumis
• Ecole Polytechnique GERAD
• J. Desrosiers
• Ecole des HEC GERAD
• M. M. Solomon
• Northeastern University GERAD

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GERAD

• an Operations Research center
  that brings together ...
• Ecole Polytechnique de Montréal
• Ecole des Hautes Etudes Commerciales
• McGill University
• Université du Québec à Montréal

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GERAD

• Few numbers...
• 30 professors / researchers
• 20 post-docs and computer science analysts
• 120 graduate students
• 3M grants / year

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The Research Team ...

• Team manager
• François Soumis
• Ecole Polytechnique de Montréal
• Past director of GERAD (1992-96)

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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

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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

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Operations Phases in Air Transport

• Planning
• aircraft routes
• crew pairings
• employees monthly schedules

• Day-to-day operations
• rescheduling of
• aircraft routes crew schedules

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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

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The 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

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The Generic Problem

• COVER AT MINIMUM COST
• A SET OF TASKS
• WITH FEASIBLE PATHS

TASK
COMMODITY
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Examples
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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

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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

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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

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Employees 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)

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Day-to-Day Operations

• Schedule perturbations
  
• illness
• breakdowns
• lateness
• storm

• Cost optimization
• vs
• Client satisfaction

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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 synchronization
• new configuration of pairings monthly
  schedules

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The Optimization Methods Utilized

• Integer multi-commodity network flow problems
• with additional constraints

• Mathematical decomposition
• Dantzig-Wolfe decomposition (column generation)
• Lagrangian relaxation
• Benders decomposition

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Resource Constrained Shortest Path Problem on
G(N,A)
P(N, A)
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Integer Multi-Commodity Network Flow Structure
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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

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Complements...
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Benefits of the Project

• academic
• scientific
• commercial
• industrial
• and artistic

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Academic 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

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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

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Academic 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

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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 RD project 3 Ph. D. dissertations
• 4 master thesis 8 analysts

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Scientific 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

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Scientific 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

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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 strategies
• partial pricing for sub-problems
• primal perturbation dual stabilization for
  the master problem

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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.

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Prizes and Honors

• ECOLE POLYTECHNIQUE Research Prize (1992)
• François Soumis
• ECOLE des HEC Research Prize (1997)
• Jacques Desrosiers

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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)

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Prizes 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)

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Commercial 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

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Product Architecture
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The Family of Products
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Altitude - Ad Opt
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Computational Results

• Crew Pairing
• Crew Rostering
• Fleet Assignment and Aircraft Routing
• Aircraft Routing and Flight Scheduling
• Subway Driver Scheduling
• Locomotive Routing

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Crew 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
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Crew Rostering Air France

• Flight Attendant

ORLY CDG PAIRINGS 4547 30005 PERSONS
240 840
SAVINGS 7.4 7.6
A. C., TRANSAT, CAN. REGIONAL, TWA, DELTA,
SABENA, SWISSAIR, AMERICA WEST
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Fleet Assignment Aircraft Routing Air Canada

• 91 AIRCRAFT, 9 TYPES, 33 STATIONS
• FLEET REDUCTION
• WITH TIME WINDOWS ON FLIGHT SCHEDULE

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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
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Aircraft Routing Scheduling Canadian Army
(C-130)

• WEST CHALLENGE (19 city-pairs)
• 750 soldiers and equipment
• MAX 65 soldiers per flight

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Subway 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
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Locomotive 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
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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
• VIA Rail

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Commercial 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.

• Cognologic

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Other 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

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Industrial Benefits
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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.

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Common Goal Efforts

• Jean-Yves Blais
• President of GIRO
• Tom Ivaskiv
• President of Ad Opt
• Jacques Desrosiers
• Ecole des HEC
• François Soumis
• Ecole Polytechnique

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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 ---gt

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Research Trends
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• GOVERNMENTS
• COMMERCIAL PARTNERS
• AIRLINE COMPANIES
• CREW MEMBERS

• UNIVERSITIES
• RESEARCH CENTERS
• Professors Researchers
• STUDENTS ANALYSTS

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Soutenance de Daniel V.