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

2. ALTITUDE 2 coût (40) (10)(20) (30) 8 12 2427 (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

3. ALTITUDE 3 Étiquetage des sommets...

4. ALTITUDE 4 Plus court chemin avec fenêtres de temps

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

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

7. ALTITUDE 7 Des contraintes globales

8. ALTITUDE 8 Le problème maître

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

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

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

12. 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

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

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

17. 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

18. 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

19. 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

20. 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

21. ALTITUDE 21 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

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

23. ALTITUDE 23 SEQUENCES ON A MACHINE OPERATIONSJOB-SHOP PRODUCTION ROUTESTRAINSLOCO. ROUTING RAIL ROSTERSPAIRINGSROSTERING PAIRINGSFLIGHTSCREW PAIRING ROUTESFLIGHTSAIRCRAFT ROUTING AIRLINE ROSTERSSHIFTSROSTERING SHIFTSTRIP SEGMENTSDRIVER SCHEDULING ROUTESBUS TRIPSBUS ROUTING BUS PATHSTASKS Examples

24. 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 x same time schedules Minimize fleet size Maximize profit

25. 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

26. 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

27. ALTITUDE 27 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)

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

29. 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 synchronization new configuration of pairings & monthly schedules

30. 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

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

32. ALTITUDE 32 Integer Multi-Commodity Network Flow Structure

33. 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

34. ALTITUDE 34 Complements...

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

36. ALTITUDE 36 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

37. 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

38. ALTITUDE 38 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

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

40. ALTITUDE 40 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”

41. ALTITUDE 41 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

42. ALTITUDE 42 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

43. 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.column generation

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

45. 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)

46. ALTITUDE 46 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 R&D PARTNERSHIPS Award University-Industry Synergy (Vancouver, October 1997)

47. ALTITUDE 47 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

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

49. ALTITUDE 49 The Family of Products SCHOOLURBAN BUS DRIVER ADAPTED TRANSPORT RAIL CREW ROSTERING CREW PAIRING BUSAIRCRAFT PROTOTYPE DAYS-OPT PROTOTYPE GIROAD OPT GENCOL

50. ALTITUDE 50 Altitude - Ad Opt

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

52. ALTITUDE 52 Crew Pairing Air Canada FLIGHT ATTENDANTS DC-9 + A 320 2.0311914MONTHLY 1.392425WEEKLY 0.47430DAILY % FATFLIGHTS 5 BASES Savings vs Air Canada solution : 7.8 %  2.03 % TRANSAT, CAN. REGIONAL, NORTHWEST, U.P.S., DELTA, SABENA, SWISSAIR, FEDEX

53. ALTITUDE 53 Crew Rostering Air France Flight Attendant ORLY CDG PAIRINGS454*73000*5 PERSONS 240 840 SAVINGS 7.4% 7.6% A. C., TRANSAT, CAN. REGIONAL, TWA, DELTA, SABENA, SWISSAIR, AMERICA WEST

54. 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.

55. ALTITUDE 55 Fleet Assignment & Aircraft Routing Air France 51 AIRCRAFT, 6 TYPES, 44 STATIONS BASIC PROBLEM 6.5 %  10 MIN Time Windows11.2 %  10 MIN T.W. + FLEET OPTIMIZATION 21.9 % PROFIT IMPROVEMENT

56. ALTITUDE 56 Aircraft Routing & Scheduling Canadian Army (C-130) WEST CHALLENGE ( 19 city-pairs) 750 soldiers and equipment MAX 65 soldiers per flight 1 (33 %)20 HRS (34 %)SAVINGS 339 HRS GENCOL Optimizer 459 HRSManual solution NUMBER OF AIRCRAFT FLIGHT TIME

57. ALTITUDE 57 2000 – 3000 bus segments One- 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

58. ALTITUDE 58 Weekly problem 2000 Trains26 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

59. 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 VIA VIA Rail

60. 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.

61. ALTITUDE 61 Other Commercial Benefits... 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 …

62. ALTITUDE 62 Industrial Benefits

63. 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.

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

65. 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 ---> --->

66. ALTITUDE 66 Research Trends

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

68. ALTITUDE 68 Soutenance de Daniel V.