Un peu dhistoire Le partenariat Universits Entreprises Un

Un peu d’histoire. . . Le partenariat Universités - Entreprises Un problème générique Plus court chemin avec fenêtres de temps 1

Étiquetage des sommets temps, coût (20) (4, 20) (10) 24 (6, 10) 27 2, 24 5, 27 (4, 30) (30) 5, 12 12 (40) 8 (48) (44) (42) (37) (5, 40) 3, 8 ( 6, 44) ( 8, 48) ( 9, 42) (11, 37) Figure 7. 1. Étiquetage des sommets 2

Étiquetage des sommets. . . 3

Plus court chemin avec fenêtres de temps 4

Des fonctions d’extension Figure 7. 2. Quelques fonctions d'extension 5

Une fonction de coût discontinue 3 7 Figure 7. 2. Une fonction de coût discontinue 6

Des contraintes globales 7

Le problème maître 8

Mise en œuvre de la décomposition : la génération de colonnes et l’optimiseur GENCOL 9

ALTITUDE An Optimization System for the Management of Operations in Air Transport A University-Industry R&D Project (1993 -1998)

UNIVERSITIES RESEARCH CENTERS Professors & Researchers STUDENTS & ANALYSTS GOVERNMENTS COMMERCIAL PARTNERS AIRLINE COMPANIES CREW MEMBERS 11

The Presentation The Research Team The Structure of the Problems Solved The Operations Phases in Air Transport The Optimization Methods Utilized The Financial Support Benefits of the Project 12

The Research Team G. Desaulniers, M. Gamache & F. Soumis Ecole Polytechnique & GERAD J. Desrosiers Ecole des HEC & GERAD M. M. Solomon Northeastern University & GERAD 13

GERAD an Operations Research center that brings together. . . Ecole Polytechnique de Montréal Ecole des Hautes Etudes Commerciales Mc. Gill University Université du Québec à Montréal 14

GERAD Few numbers. . . · 30 professors / researchers · 20 post-docs and computer science analysts · 120 graduate students · 3 M$ grants / year 15

The Research Team. . . Team manager François Soumis x. Ecole Polytechnique de Montréal x. Past director of GERAD (1992 -96) 16

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 17

University Collaborators Ecole des HEC P. Hansen F. Chauny Ecole Polytechnique B. Sanso B. Jaumard G. Savard Université de Montréal G. Lapalme Mc. Gill University J. -L. Goffin Université du Québec à Montréal O. Marcotte 18

Operations Phases in Air Transport Planning aircraft routes crew pairings employees monthly schedules Day-to-day operations rescheduling of aircraft routes & crew schedules 19

The Financial Support: CDN $ 5, 500, 000 Quebec Government $ 2. 5 M Research infrastructure provided by AD OPT Technologies & Cognologic $ 1. 5 M Natural Sciences and Engineering Research Council of Canada $ 1. 5 M GERAD 20

The Structure of the Problems Solved Tasks to be performed represented by nodes or arcs on time space networks Local constraints characterize a single path Global constraints Paths covering the tasks the required number of times on the path set composition Objective: context dependent 21

The Generic Problem TASK COVER AT MINIMUM COST A SET OF TASKS WITH FEASIBLE PATHS COMMODITY 22

Examples BUS ROUTING DRIVER SCHEDULING ROSTERING AIRLINE AIRCRAFT ROUTING CREW PAIRING ROSTERING RAIL LOCO. ROUTING TASKS PATHS BUS TRIP SEGMENTS SHIFTS ROUTES SHIFTS ROSTERS FLIGHTS PAIRINGS ROUTES PAIRINGS ROSTERS TRAINS ROUTES OPERATIONS SEQUENCES ON A MACHINE PRODUCTION JOB-SHOP 23

The Aircraft Routing Problem Tasks flight legs to be flown Paths Global constraints flight synchronization xsame time schedules aircraft routes Minimize Local constraints time windows on flights fleet size Maximize profit 24

The Crew Pairing Problem Tasks flight legs to cover Paths Global constraints number of crews per base crew travels Local constraints pilots & flight attendants work rules Minimize total crew costs 25

Employees Monthly Schedules Tasks pre-assignments & crew pairings Local constraints employees work rules annual vacations, training Paths sequence of tasks assigned to employees the number of employees required by a pairing sometimes exceeds 10 Global constraints ratios on full time / part time employees 26

Employees Monthly Schedules … Flight deck Flight attendants minimize costs incurred maximize an index of personnel satisfaction maximize rotation covering (uncovered tasks allocated to reserve personnel) balance work schedules 27

Day-to-Day Operations Schedule perturbations Cost optimization illness breakdowns lateness storm … vs Client satisfaction 28

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 29

The Optimization Methods Utilized Integer multi-commodity network flow problems Mathematical decomposition Dantzig-Wolfe with additional constraints decomposition (column generation) Lagrangian relaxation Benders decomposition 30

Resource Constrained Shortest Path Problem on G=(N, A) P(N, A) : 31

Integer Multi-Commodity Network Flow Structure 32

The Optimization Methods Utilized. . . Dynamic programming for efficient solution of shortest path problems embedding local constraints Sequential & Parallel implementations CPLEX software flexibility Network Primal & Dual Simplex Barrier column pricing DP algorithms 33

Complements. . . 34

Benefits of the Project academic scientific commercial industrial … and artistic 35

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 36

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 37

Academic spin-offs. . . Column Generation Sub-problem algorithms Irina* Daniel* Manuel Sylvie* Master problem Norbert Daniel* Eric Column Generation Stabilized Daniel* Manuel Viviane Branch & Bound François Eric Sylvie Norbert … * Ph. D. students 38

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 project 3 Ph. D. dissertations 4 master thesis 8 analysts 39

Scientific Advances 30 publications Management Science Operations Research Transportation Science Networks EJOR Handbooks in OR&MS 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” 40

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 41

Scientific Advances. . . Resource constrained shortest paths y non linear cost functions y non linear resource functions y 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 42

Scientific Advances. . . GENCOL 3. 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. 43

Prizes and Honors ECOLE POLYTECHNIQUE Research Prize (1992) François Soumis ECOLE des HEC Research Prize (1997) Jacques Desrosiers 44

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 TéléQuébec and RDI. (December 1996) 45

Prizes and Honors. . . ACFAS The CONFERENCE J. -Armand Bombardier Medal BOARD of Canada for Technological Innovation & NSERC (Montreal, May 1997) ADRIQ TRANSFERT Prize 1997 with Ad Opt Technologies (Montreal, November 1997) R&D PARTNERSHIPS Award University. Industry Synergy (Vancouver, October 1997) 46

Commercial Benefits Ad Opt Technologies Provided by the Universities: commercial licenses of GENCOL to Airline industry Rail industry Les Entreprises GIRO Urban transportation School busing Dial-a-Ride System 47

Product Architecture USER GRAPHICAL USER INTERFACE DATA BASE MODELING MODULE TASKS, NETWORKS PATHS GENCOL OPTIMIZER 48

The Family of Products PROTOTYPE DAYS-OPT RAIL AIRCRAFT CREW ROSTERING BUS PROTOTYPE CREW PAIRING SCHOOL AD OPT ADAPTED TRANSPORT URBAN BUS DRIVER GIRO GENCOL 49

Altitude - Ad Opt 50

Computational Results Crew Pairing Crew Rostering Fleet Assignment and Aircraft Routing and Flight Scheduling Subway Driver Scheduling Locomotive Routing 51

Crew Pairing Air Canada FLIGHT ATTENDANTS DC-9 + A 320 5 BASES FLIGHTS % FAT DAILY 430 0. 47 WEEKLY 2425 1. 39 MONTHLY 11914 2. 03 Savings vs Air Canada solution : 7. 8 % 2. 03 % TRANSAT, CAN. REGIONAL, NORTHWEST, U. P. S. , DELTA, SABENA, SWISSAIR, FEDEX 52

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 53

Aircraft Routing Air Canada 91 AIRCRAFT, 9 TYPES, 33 STATIONS SAVINGS T. W. 3. 8 % ± 10 MIN 8. 9 % ± 20 MIN 13. 9 % ± 30 MIN FLEET REDUCTION WITH TIME WINDOWS ON FLIGHT SCHEDULE 54

Aircraft Routing Air France 51 AIRCRAFT, 6 TYPES, 44 STATIONS BASIC PROBLEM 10 MIN Time Windows 6. 5 % 11. 2 % 10 MIN T. W. + FLEET OPTIMIZATION 21. 9 % PROFIT IMPROVEMENT 55

Aircraft Routing & Scheduling Canadian Army (C-130) WEST CHALLENGE (19 city-pairs) 750 soldiers and equipment MAX 65 soldiers per flight FLIGHT TIME NUMBER OF AIRCRAFT Manual solution 59 HRS 4 GENCOL Optimizer 39 HRS 3 SAVINGS 20 HRS (34 %) 1 (33 %) 56

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 57

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 58

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 Air Canada Northwest UPS Sabena Fed. Ex TWA Delta ………. RAIL-WAYS System VIA Rail 59

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. 60

Other Commercial Benefits. . . Les Entreprises GIRO 12 35 installations of CREW-OPT 150 cities using the HASTUS System for bus drivers The CREW-OPT version integrates GENCOL (Lyon) (Toulouse) Tokyo Vienna Singapore Barcelona Helsinki Oslo Perpignan Stockholm Valenciennes … 61

Industrial Benefits 62

Industrial Benefits. . . 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. 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. 63

Common Goal Efforts Jean-Yves Blais President of GIRO Tom Ivaskiv President of Ad Opt Jacques Desrosiers Ecole des HEC François Soumis Ecole Polytechnique 64

Commercial Benefits. . . Ad Opt Technologies Number of employees 5 55 Yearly revenues $ 300 K $ 5. 7 M … 75 . . . $ 12 M Toronto Stock Market (since June 17, 1999) AOP stock value : $ 62 M ---> 65

Research Trends 66

UNIVERSITIES RESEARCH CENTERS Professors & Researchers STUDENTS & ANALYSTS GOVERNMENTS COMMERCIAL PARTNERS AIRLINE COMPANIES CREW MEMBERS 67

Soutenance de Daniel V. 68