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Un peu d’histoire ...

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

  2. coût temps, coût (20) (10) (4, 20) (6, 10) 24 27 2, 24 5, 27 (30) (4, 30) 5, 12 12 (40) (48) (44) (42) (37) (5, 40) ( 6, 44) ( 8, 48) ( 9, 42) (11, 37) 3, 8 8 Figure 7.1. Étiquetage des sommets Étiquetage des sommets

  3. Étiquetage des sommets ...

  4. Plus court chemin avec fenêtres de temps

  5. Figure 7.2. Quelques fonctions d'extension Des fonctions d’extension

  6. 3 7 Figure 7.2. Une fonction de coût discontinue Une fonction de coût discontinue

  7. Des contraintes globales

  8. Le problème maître

  9. Mise en œuvre de la décomposition :la génération de colonneset l’optimiseur GENCOL

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

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

  12. 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 The Presentation

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

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

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

  16. The Research Team ... • Team manager • François Soumis • Ecole Polytechnique de Montréal • Past director ofGERAD (1992-96)

  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

  18. 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 University Collaborators

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

  20. 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 The Financial Support: CDN $5,500,000

  21. 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 The Structure of the Problems Solved

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

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

  24. 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 The Aircraft Routing Problem

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

  26. 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 Employees Monthly Schedules

  27. 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) Employees Monthly Schedules…

  28. Schedule perturbations illness breakdowns lateness storm … Cost optimization vs Clientsatisfaction Day-to-Day Operations

  29. 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 Day-to-Day Operations ...

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

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

  32. Integer Multi-Commodity Network Flow Structure

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

  34. Complements...

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

  36. 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 Academic spin-offs

  37. 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 Academic spin-offs ...

  38. 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 Academic spin-offs ...

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

  40. 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” Scientific Advances

  41. IP Column Generation Basis of a theory on branching methods and cutting planes, hence resolving difficulties faced for several decades. Equivalence betweenDantzig-WolfeDecomposition & Column Generation Branching rules on Network Flow Supplementary & Resource variables Cutting Planes at Master & Sub-problem levels Scientific Advances ...

  42. 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 Scientific Advances ...

  43. Scientific Advances ... • GENCOL3.0 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.

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

  45. CORS Best Application "A Column Generation Approach for Large ScaleAircrew RosteringProblems"collaboration with Air France(Montréal, May 1994) " ThePreferential BiddingProblem 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) Prizes and Honors ...

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

  47. Provided by the Universities: commerciallicensesof GENCOL to Ad OptTechnologies Airline industry Rail industry Les Entreprises GIRO Urban transportation School busing Dial-a-Ride System Commercial Benefits

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

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

  50. Altitude - Ad Opt