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.