Vehicle Routing

1
Vehicle Routing Job Shop Scheduling Whats
the Difference?
ICAPS03, June 13, 2003
J. Christopher Beck, Patrick Prosser, Evgeny
Selensky
Dept. of Computing Science University of Glasgow
pat,evgeny_at_dcs.gla.ac.uk
Cork Constraint Computation Centre University
College Cork c.beck_at_4c.ucc.ie
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Old 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 problem
• Common approach in research and in practice
• SAT, IP, CP, etc
• If you have a hammer,

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A Nice Idea, But

• New problems dont 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?
Existing Problem Models
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This 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 Problem

• Make a set of deliveries (visits) with a set of
  vehicles
• Vehicles have limited capacity
• Visits have time windows
• Minimize total distance traveled

T1
T3
T2
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Job Shop Scheduling Problem (JSP)
R1
R0
R2
R1
R2
R0
R0
R1
R2
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Off-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 Technology

• Cx cost of solution found by technology x with
  fixed time limit (10 minutes)
• ? gt 1 routing technology is better
• ? lt 1 scheduling technology is better

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JSP ? VRP Transformation

• Beck et al. 2002
• We can transform JSPs to VRPs and vice versa
• Scheduling technology is poor on reformulated
  VRPs
• Routing technology is poor on reformulated JSPs
• Cant find first solutions due to precedence
  constraints!

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Base Case Pure Problems
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Characteristics

• 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 VRP
??
VRP
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From JSP
??
JSP
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Alternative Resources

• VRP many (e.g., 25)
• JSP few (1, 4, 8)
• Savings cant solve 70 of problems with 2
  alternatives
• Only problems solved by both are included

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Alternative Resources VRP
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Alternative Resources JSP
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Optimization Criteria

• VRP total travel
• JSP makespan

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Optimisation Criteria VRP
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Optimisation Criteria JSP
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Precedence Constraints

• VRP none
• JSP paths of totally ordered activities
• Savings cant find first solution
• Start with scheduling solution

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Precedence Constraints VRP
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Precedence Constraints JSP
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Experimental Summary
JSP
VRP
? Alt Res ?
? Alt Res ?
? Precedence Cts ?
? Precedence Cts ?
Opt. Makespan
Opt. Total Travel
? scheduling performance
? routing performance
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Other Characteristics

• Smaller impact
• Temporal Slack
• ? slack ? scheduling performance
• Vehicle Resource Capacity
• Like alternative resources
• Activity duration to transition time ratio
• VRP ? ratio ? routing performance
• JSP ? ratio ? scheduling performance

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Conclusions

• 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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Conclusions

• 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 Resources