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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 Cork Constraint Computation Centre University College Cork

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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, …

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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?

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

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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

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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

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

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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

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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

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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!

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11 Base Case: Pure Problems

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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)

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13 From VRP VRP ? ? ? ?

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14 From JSP JSP + ? ? ? ?

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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

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16 Alternative Resources: VRP

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17 Alternative Resources: JSP

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18 Optimization Criteria VRP: total travel JSP: makespan

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19 Optimisation Criteria: VRP

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20 Optimisation Criteria: JSP

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

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22 Precedence Constraints: VRP

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23 Precedence Constraints: JSP

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

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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

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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?)

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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

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28 Alternative Resources

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