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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