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}@dcs.gla.ac.uk Cork Constraint Computation Centre University College Cork c.beck@4c.ucc.ie

2. 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. 3 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?

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

5. 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. 6 Vehicle Routing Problem T1 T2 T3 Make a set of deliveries (visits) with a set of vehicles –Vehicles have limited capacity –Visits have time windows –Minimize total distance traveled

7. 7 R1 R0 R1 R0R2 R0 R1R2 R1 R2 R0 R2 R1 R0 R1 R2 makespan Job Shop Scheduling Problem (JSP)

8. 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. 9 Evaluating the Technology C x : cost of solution found by technology x with fixed time limit (10 minutes) > 1: routing technology is better < 1: scheduling technology is better

10. 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 –Cant find first solutions due to precedence constraints!

11. 11 Base Case: Pure Problems

12. 12 Characteristics What are the problem characteristics that lead to this difference? Ideas: –Alternative resources –Optimization criteria –Precedence constraints –(3 more not really discussed here)

13. 13 From VRP VRP ? ? ? ?

14. 14 From JSP JSP + ? ? ? ?

15. 15 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

16. 16 Alternative Resources: VRP

17. 17 Alternative Resources: JSP

18. 18 Optimization Criteria VRP: total travel JSP: makespan

19. 19 Optimisation Criteria: VRP

20. 20 Optimisation Criteria: JSP

21. 21 Precedence Constraints VRP: none JSP: paths of totally ordered activities Savings cant find first solution –Start with scheduling solution

22. 22 Precedence Constraints: VRP

23. 23 Precedence Constraints: JSP

24. 24 Experimental Summary VRP JSP Alt Res Precedence Cts Opt. MakespanOpt. Total Travel scheduling performance routing performance

25. 25 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

26. 26 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?)

27. 27 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

28. 28 Alternative Resources