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Experience from designing transport scheduling algorithms
Raymond Kwan
School of Computing, University of LeedsR.S.Kwan @ leeds.ac.uk
Open Issues in Grid Scheduling Workshop, Oct 21-22, 03
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o Public transport scheduling
Outline
o Optimisation issues
o Discussion
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Vehicle & Driver Operations
Transport Operator
The Public
Routes
Timetables
Fares
Planning & Scheduling
Depot Operations & management
Payroll
Public transport service
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Planning and scheduling
o Minimise operating costs
o Operator: one optimisation problem, all decisions are variables
o Solution designer:
Sequential tasks
Some decisions are fixed by earlier tasks
Some decisions are left open for later tasks
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Planning and scheduling tasks
Service and Timetable Planning
Vehicle Scheduling
Crew Scheduling
Crew Rostering
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Research & Development at Leeds
o Span over 40 years (22 years myself)
o Algorithmic approaches- hueristics- integer linear programming- rule-based/knowledge-based- evolutionary algorithms- tabu search- constraint – based methods- ant colony
o Numerous users in the UK bus and train industries
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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
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o Three key types of decision variable
Departure times
Scheduled runtimes
Resource options at a station
Train timetables generation
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Hard Constraints
o Headway: time gap between trains on the same track
o Junction Margins: time gap between trains at a track crossing point
o No train collision!
- On a track
- At a platform
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Soft constraints
o (TOCs) Commercial Objectives
Preferred departure/arrival times
Clockface times
Passenger connections
Even service
Efficient train units schedule
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Bus Vehicle Scheduling
o Selection and sequencing of trips to be covered by each bus
o Each link may incur idling or deadrun time
o Minimise fleet size, idling time, deadrun time
o Other objectives: e.g. preferred block size, route mixing
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Bus Vehicle Scheduling - FIFO, FILO
Departures
Arrivals
FIFO for regular steady service
FILO for end of peak
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Driver Scheduling - Vehicle work to be covered
Vehicle 38S
13041110093507420600
HHSG
( Relief opportunity )
Location
Time
Piece of work
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2-spell driver shift example
Vehicle 1
Vehicle 2
Vehicle 3
sign on at depot
sign off at depotmeal break
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Vehicle 1
Vehicle 2
Vehicle 3
More example potential shifts
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o Jobs to be scheduled have precise starting and ending clock times
o Scheduling involves trying to get subsets of jobs to fit within their timings to be collectively served by a resource (vehicle or driver)
o Not the type of problem where jobs are queued to be served by a designated resource
Some characteristics of vehicle and driver scheduling
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Driver Rostering
o To compile work packages for driverse.g. A one-week rota
Sun REST
Sat REST
Fri S141350 - 1815
Thu S071201 - 1846
Wed S460512 - 1357
Tue S460512 - 1357
Mon S460512 - 1357
o Rules on weekly rotas
o Drivers may take the rotas in rotation
o Optimise fairness across the packages subject to rules and standby requirements
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Multi-objectives – what is optimality?
o Operators do not always try equally hard to achieve optimal operational efficiency
Union rules
Service reliability
Problem at hand is not on the “critical path”
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o Automatic global optimisation is obviously impractical
o Combining 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?
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o Sometimes 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
o Needs good vision from the human scheduler – rule-based expert system to integrate the scheduling tasks?
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o Different 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
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Discussion