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

ICAPS’03, June 13, 2003. Vehicle Routing & Job Shop Scheduling: What’s the Difference?. J. Christopher Beck, Patrick Prosser, & Evgeny Selensky. Cork Constraint Computation Centre University College Cork c.beck@4c.ucc.ie. Dept. of Computing Science University of Glasgow

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

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  1. ICAPS’03, June 13, 2003 Vehicle Routing & Job Shop Scheduling: What’s the Difference? J. Christopher Beck, Patrick Prosser, & Evgeny Selensky Cork Constraint Computation Centre University College Cork c.beck@4c.ucc.ie Dept. of Computing Science University of Glasgow {pat,evgeny}@dcs.gla.ac.uk

  2. 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, …

  3. A 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?

  4. ? + ?  Real-World Problem Get the Picture? Existing Problem Models

  5. 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

  6. 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

  7. makespan R0 R0 R0 R0 R1 R1 R1 R1 R2 R2 R2 R2 Job Shop Scheduling Problem (JSP) R1 R0 R2 R1 R2 R0 R0 R1 R2

  8. 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

  9. Evaluating 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

  10. 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 • Can’t find first solutions due to precedence constraints!

  11. Characteristics • What are the problem characteristics that lead to this difference? • Ideas: • Alternative resources • Optimization criteria • Precedence constraints • (3 more not really discussed here)

  12. ? ? ? From VRP ? VRP

  13. + ? ? ? From JSP ? JSP

  14. Alternative 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

  15. Alternative Resources: VRP

  16. Alternative Resources: JSP

  17. Optimization Criteria • VRP: total travel • JSP: makespan

  18. Optimisation Criteria: VRP

  19. Optimisation Criteria: JSP

  20. Precedence Constraints • VRP: none • JSP: paths of totally ordered activities • Savings can’t find first solution • Start with scheduling solution

  21. Precedence Constraints: VRP

  22. Precedence Constraints: JSP

  23. Experimental Summary JSP VRP  Alt Res   Alt Res   Precedence Cts   Precedence Cts  Opt. Makespan Opt. Total Travel  scheduling performance  routing performance

  24. 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

  25. 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?)

  26. 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

  27. Alternative Resources

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