1. 1 Experience from designing transport scheduling algorithms Raymond Kwan School of Computing, University of Leeds R.S.Kwan @ leeds.ac.uk Open Issues in Grid Scheduling Workshop, Oct 21-22, 03

2. 2 oPublic transport scheduling Outline oOptimisation issues oDiscussion

3. 3 Vehicle & Driver Operations Transport Operator The Public Routes Timetables Fares Planning & Scheduling Depot Operations & management Payroll Public transport service

4. 4 Planning and scheduling oMinimise operating costs oOperator: one optimisation problem, all decisions are variables oSolution designer: Sequential tasks Some decisions are fixed by earlier tasks Some decisions are left open for later tasks

5. 5 Planning and scheduling tasks Service and Timetable Planning Vehicle Scheduling Crew Scheduling Crew Rostering

6. 6 Research & Development at Leeds oSpan over 40 years (22 years myself) oAlgorithmic approaches -hueristics -integer linear programming -rule-based/knowledge-based -evolutionary algorithms -tabu search -constraint – based methods -ant colony oNumerous users in the UK bus and train industries

7. 7 Track Operator UK Train Timetables Train Operating Companies Strategic Rail Authority Office of the Rail Regulator Health and Safety Executive Parties involved in UK train timetabling

8. 8 oThree key types of decision variable Departure times Scheduled runtimes Resource options at a station Train timetables generation

9. 9 Hard Constraints oHeadway: time gap between trains on the same track oJunction Margins: time gap between trains at a track crossing point oNo train collision! - On a track - At a platform

10. 10 Soft constraints o(TOCs) Commercial Objectives Preferred departure/arrival times Clockface times Passenger connections Even service Efficient train units schedule

11. 11 Bus Vehicle Scheduling oSelection and sequencing of trips to be covered by each bus oEach link may incur idling or deadrun time oMinimise fleet size, idling time, deadrun time oOther objectives: e.g. preferred block size, route mixing

12. 12 Bus Vehicle Scheduling - FIFO, FILO Departures Arrivals FIFO for regular steady service FILO for end of peak

13. 13 Driver Scheduling - Vehicle work to be covered Vehicle 38 S 13041110093507420600 HHSG ( Relief opportunity ) Location Time Piece of work

14. 14 2-spell driver shift example Vehicle 1 Vehicle 2 Vehicle 3 sign on at depot sign off at depot meal break

15. 15 Vehicle 1 Vehicle 2 Vehicle 3 More example potential shifts

16. 16 oJobs to be scheduled have precise starting and ending clock times oScheduling involves trying to get subsets of jobs to fit within their timings to be collectively served by a resource (vehicle or driver) oNot the type of problem where jobs are queued to be served by a designated resource Some characteristics of vehicle and driver scheduling

17. 17 Driver Rostering oTo compile work packages for drivers e.g. A one-week rota Sun REST Sat REST Fri S14 1350 - 1815 Thu S07 1201 - 1846 Wed S46 0512 - 1357 Tue S46 0512 - 1357 Mon S46 0512 - 1357 oRules on weekly rotas oDrivers may take the rotas in rotation oOptimise fairness across the packages subject to rules and standby requirements

18. 18 Multi-objectives – what is optimality? oOperators do not always try equally hard to achieve optimal operational efficiency Union rules Service reliability Problem at hand is not on the critical path

19. 19 oAutomatic global optimisation is obviously impractical oCombining two successive tasks for optimisation are sometimes desirable, e.g. Hong Kong: fixed size fleet, fixed peak time requirements, schedule buses & maximise off- peak service Sao Paolo: driver and vehicle tied schedules First (UK bus): ferry bus problems Global optimisation?

20. 20 oSometimes superior results could be simply obtained where powerful optimisation algorithms fail A more favourable scheduling condition could be achieved from the preceding scheduling task E.g. driver forced to take a break after a short work spell – swap in the vehicle schedule to lengthen the work spell Better optimisation through intelligent integration of the scheduling tasks oNeeds good vision from the human scheduler – rule-based expert system to integrate the scheduling tasks?

21. 21 oDifferent types of service may pose different levels of difficulty for scheduling (different algorithmic approaches?) Urban commuting: high frequency, many stops Sub-urban and rural: lower frequency, fewer stops Inter-city and provincial: long distance, few stops Some problems have to consider route and vehicle type compatibility Scheduling for different service types

22. 22 Discussion