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Transit Vehicle Routing Methods for Large-Scale Evacuation

Transit Vehicle Routing Methods for Large-Scale Evacuation. Mark Hickman and Moshe Dror University of Arizona INFORMS November 15, 2011. Outline. Motivation Problem definition Solution approach Case study. Motivation. Evacuation context: short-notice, departure from home to shelters

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Transit Vehicle Routing Methods for Large-Scale Evacuation

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  1. Transit Vehicle Routing Methods forLarge-Scale Evacuation Mark Hickman and Moshe Dror University of Arizona INFORMS November 15, 2011

  2. Outline • Motivation • Problem definition • Solution approach • Case study

  3. Motivation • Evacuation context: short-notice, departure from home to shelters • Natural disasters • Wildfires • Floods • Hurricanes • … http://disastersafety.typepad.com/disaster_safety_blog/2008/11/index.html

  4. Evacuation Concept • Use transit, school, other public buses • Drive through areas to be evacuated • Pick up persons / families / households in these neighborhoods needing assistance to evacuate • Transport these persons to emergency shelters • Complete the evacuation as quickly as possible

  5. Problem Characteristics • Rural postman problem (RPP) • Undirected edges • Some edges do not need to be visited • Any connected set of served edges (clusters) must served as a whole • Possible precedence on components • Multiple vehicle routing • Capacitated vehicles • Capacitated shelters (depots)

  6. Problem Characteristics • m-vehicle capacitated arc routing problem • Formulation of objective • Min-max problem Minimize completion time / maximum time of any single vehicle Assumes there is sufficient time to evacuate all persons • Maximize the number of persons evacuated in a period of time Insufficient time to evacuate all persons • Min-max or Minimum cost with precedence relationships Phasing based on characteristics of disaster

  7. Problem Definition Objective: Minimize the time for a (possibly phased) evacuation Decision: Itinerary (routing) of each vehicle, through neighborhoods to shelters Inputs: • Fleet of vehicles with initial locations and capacities • Neighborhoods to be evacuated and road network • Estimate of persons to be evacuated along each street (possibly zero) • Estimate of travel times on streets and to / from shelters • Shelter capacities

  8. Transform RPP to GTSP (Dror and Langevin, 1997) Transform GTSP to TSP(Noon and Bean, 1993) Solve TSP (Concorde) Break Euler tour into sub-paths at vehicle capacity Route using insertion heuristic Post-optimization Solution Approach Rural Postman Problem(RPP) Vehicle Routing

  9. (8,5) (7,--) (6,4) (4,4) (5,3) (6,3) (3,3) (9,--) (5,--) (4,--) (8,--) (4,--) (6,--) (7,--) (7,6) Link w/ persons Shelter Vehicle 1 Vehicle 2 (2,3) (6,5) Example • Network with persons on some arcs (RPP) • 36 total persons • 2 shelter nodes • Capacity of 25 • 2 vehicles • Capacity of 8 (travel time, persons)

  10. (8,5) (7,--) (6,4) (4,4) (5,3) (6,3) (3,3) (9,--) (5,--) (4,--) RPP SolutionEuler tour59 min (8,--) (4,--) (6,--) (7,--) (7,6) (2,3) (6,5) Subpathsat capacity Vehicle 160 min Vehicle 268 min Best solution

  11. Case Study • Witch Fire, October 2007 • San Diego County, CA • Mandatory evacuations of hundreds of thousands of persons • Large network size, with effective heuristics • Precedence relationships • Large bus fleet

  12. Problem size 1313 buses 53 shelters ~24 hours total for evacuation ~38,000 served edges in mandatory evacuation zone ~3500 clusters

  13. Next Steps • Case study investigation and results • Problem size? • Effective partitioning and precedence • Investigation of other post-optimization heuristics • “Prize-collecting” with strict time bounds

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