Vehicle Routing & Vehicle Routing & Job Shop Scheduling: Job Shop Scheduling: What’s the Difference?What’s the Difference?

ICAPS’03, June 13, 2003

J. Christopher Beck, Patrick Prosser, & Evgeny SelenskyJ. Christopher Beck, Patrick Prosser, & Evgeny Selensky

Dept. of Computing ScienceDept. of Computing Science

University of Glasgow University of Glasgow

{pat,evgeny}@dcs.gla.ac.uk{pat,evgeny}@dcs.gla.ac.uk

Cork Constraint Computation CentreCork Constraint Computation Centre

University College Cork University College Cork

c.beck@4c.ucc.iec.beck@4c.ucc.ie

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Old Solutions for New ProblemsOld Solutions for New Problems

We have strong techniques to solve hard problems

Use them! – use existing problem models and solution

techniques to solve a new problemCommon approach in research and in

practice– SAT, IP, CP, etc

If you have a hammer, …

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A Nice Idea, ButA Nice Idea, But

New problems don’t fit exactly the old models

New problems look “strange”– Scheduling with 0 duration activities– Routing with 0 travel time

How will solution techniques work?

… is the problem really a nail?

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Get the Picture?Get the Picture?

ExistingProblemModels

Real-WorldProblem

+ ?

?

5

This PaperThis Paper

Basic Question– How does existing solution technology cope with

changed characteristics?Basic Approach

– Create problems “between” JSP & VRP– Compare the relative performance of routing and

scheduling solution techniques– What problem characteristics are important to the

solution techniques?More in talk than in the paper

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Vehicle Routing ProblemVehicle Routing Problem

T1

T2T3

Make a set of deliveries (visits) with a set of vehicles– Vehicles have limited

capacity– Visits have time

windows– Minimize total

distance traveled

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R1

R0

R1

R0 R2

R2 R0

R1 R2

R1

R2

R0

R2

R1 R1

R0 R0 R0

R1

R2R2

makespan

Job Shop Scheduling Problem (JSP)Job Shop Scheduling Problem (JSP)

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Off-the-Shelf Solution TechnologyOff-the-Shelf Solution Technology

VRP: ILOG Dispatcher– First Solution: Savings Heuristic– Improvement: Guided Local Search

JSP: ILOG Scheduler– Constructive CP tree-search

• Slack-based heuristics

– Strong constraint propagation• Edge-finding, precedence graph

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Evaluating the TechnologyEvaluating the Technology

Cx: cost of solution found by technology x with fixed time limit (10 minutes)

> 1: routing technology is better < 1: scheduling technology is better

rout

sched

C

C

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JSP JSP VRP Transformation VRP Transformation

[Beck et al. 2002] We can transform JSPs to VRPs

and vice versaScheduling technology is poor

on reformulated VRPsRouting technology is poor on

reformulated JSPs– Can’t find first solutions due to

precedence constraints!

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CharacteristicsCharacteristics

What are the problem characteristics that lead to this difference?Ideas:

– Alternative resources– Optimization criteria– Precedence constraints– (3 more not really discussed here)

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From VRPFrom VRP

VRP

?

?

?

?

14

From JSPFrom JSP

JSP

+

?

?

?

?

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Alternative ResourcesAlternative Resources

VRP: many (e.g., 25)JSP: few (1, 4, 8)

Savings can’t solve ~70% of problems with 2 alternatives– Only problems solved by

both are included

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Alternative Resources: VRPAlternative Resources: VRP

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Alternative Resources: JSPAlternative Resources: JSP

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Optimization CriteriaOptimization Criteria

VRP: total travelJSP: makespan

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Optimisation Criteria: VRPOptimisation Criteria: VRP

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Optimisation Criteria: JSPOptimisation Criteria: JSP

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Precedence ConstraintsPrecedence Constraints

VRP: noneJSP: paths of totally

ordered activities

Savings can’t find first solution– Start with scheduling

solution

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Precedence Constraints: VRPPrecedence Constraints: VRP

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Precedence Constraints: JSPPrecedence Constraints: JSP

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Experimental SummaryExperimental Summary

VRP JSP

Alt Res Alt Res

Precedence Cts Precedence Cts

Opt. Makespan Opt. Total Travel

scheduling performance

routing performance

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Other CharacteristicsOther Characteristics

Smaller impactTemporal Slack

slack = scheduling performanceVehicle Resource Capacity

– Like alternative resourcesActivity duration to transition time ratio

– VRP: ratio = routing performance– JSP: ratio = scheduling performance

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ConclusionsConclusions

Try scheduling technology on VRP with– makespan minimization (strong propagation?)– complex temporal constraints

Try routing technology on JSP with– total time minimization (weak propagation?)– few temporal constraints (open shop?)

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ConclusionsConclusions

Even isolated changes in problem characteristics change the best choice of off-the-shelf problem model

Understanding this is important to extending the scope of optimisation techniques to– new problems – new people

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Alternative ResourcesAlternative Resources