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
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Outline
o
Public transport scheduling
o
Optimisation issues
o
Discussion
2
Public transport service
Depot Operations
& management
The
Public
Routes Vehicle &
Driver
Timetables
Operations
Fares
Transport
Operator
Payroll
Planning &
Scheduling
3
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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Parties involved in UK train timetabling
Strategic Rail
Authority
Train Operating
Companies
Office of the Rail
Regulator
Health and Safety
Executive
Track Operator
UK Train
Timetables
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Train timetables generation
o
Three key types of decision variable
 Departure times
 Scheduled runtimes
 Resource options at a station
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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
Arrivals
Departures
FIFO for regular
steady service
FILO for end of peak
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Driver Scheduling
- Vehicle work to be covered
Piece of work
Vehicle 38
0600
0742
0935
1110
1304
G
S
H
H
S
Time
Location
( Relief opportunity )
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2-spell driver shift example
sign on at depot
Vehicle 1
meal break
sign off at depot
Vehicle 2
Vehicle 3
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More example potential shifts
Vehicle 1
Vehicle 2
Vehicle 3
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Some characteristics of vehicle
and driver scheduling
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
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Driver Rostering
o
To compile work packages for drivers
e.g. A one-week rota
Mon S46 Tue S46
Wed S46 Thu S07
Fri S14
0512 - 1357
0512 - 1357
1350 - 1815
0512 - 1357
1201 - 1846
Sat
REST
Sun
REST
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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Global optimisation?
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 offpeak service
 Sao Paolo: driver and vehicle tied schedules
 First (UK bus): “ferry bus” problems
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Better optimisation through intelligent
integration of the scheduling tasks
o
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
Needs good vision from the human scheduler –
rule-based expert system to integrate the
scheduling tasks?
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Scheduling for different service types
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
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Discussion
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