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 Natural disasters  Wildfires  Floods  Hurricanes  …

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

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)

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

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

Related Research Prize-collecting arc routing  Feillet, Dejax, Gendreau (2005)  Aráoz, Fernández, Franquesa (2009)  Corberán, Fernández, Franquesa, Sanchis (2011) Prize-collecting node routing  Orienteering / TSP or VRP with profits Tsiligirides (1984) Golden, Levy, Vohra (1987) Balas (1989) Chao, Golden, Wasil (1996) …  Team orienteering Butt, Ryan (1999) Tang, Miller-Hooks (2005) Archetti, Hertz, Speranza (2007) Boussier, Feillet, Gendreau (2007) …

Solution Approach 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 Rural Postman Problem (RPP) Vehicle Routing

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

(8,5) (3,3) (9,--) (7,--) (6,3) (6,4) (5,3) (8,--) (6,5) (4,--) (7,6) (6,--) (5,--) (4,4) (4,--) (7,--) (2,3) RPP Solution Euler tour 59 min Subpaths at capacity Vehicle 1 60 min Vehicle 2 68 min Best solution

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

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

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