Transit Vehicle Routing Methods forLarge-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 …

http://disastersafety.typepad.com/disaster_safety_blog/2008/11/index.html

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 timeInsufficient time to evacuate all persons

Min-max or Minimum cost with precedence relationshipsPhasing 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

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 SolutionEuler tour

59 min

Subpathsat capacity

Vehicle 160 min

Vehicle 268 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