Robust Shelter Locations for Evacuation Planning with Demand Uncertainty

This article presents a robust approach for determining optimal locations of public shelters and their capacities, from a given set of potential sites during evacuation planning under demand uncertainty. Demand uncertainty in the article refers to the uncertainty associated with the number of people using the public shelters during evacuation. It is assumed that a planning authority determines the number of shelters, their locations, and capacities whereas evacuees choose a shelter to evacuate and the routes to access it. The proposed model is formulated as a mathematical program with complementarity constraints and is solved by a cutting-plane scheme. A numerical example on the Sioux Falls network demonstrates that robust plans are able to achieve nearly the same level of performance with a significant lower cost as compared to a conservative plan, which assumes the highest demand of each origin node.

[1]  Anthony Chen,et al.  Shelter location-allocation model for flood evacuation planning , 2005 .

[2]  F. Benjamin Zhan,et al.  Agent-based modelling and simulation of urban evacuation: relative effectiveness of simultaneous and staged evacuation strategies , 2008, J. Oper. Res. Soc..

[3]  Brian Wolshon,et al.  Alternative Methods to Increase the Effectiveness of Freeway Contraflow Evacuation , 2004 .

[4]  Stefan Scholtes,et al.  Mathematical Programs with Complementarity Constraints: Stationarity, Optimality, and Sensitivity , 2000, Math. Oper. Res..

[5]  Melvyn Sim,et al.  Robust discrete optimization and network flows , 2003, Math. Program..

[6]  Larry J. LeBlanc,et al.  AN EFFICIENT APPROACH TO SOLVING THE ROAD NETWORK EQUILIBRIUM TRAFFIC ASSIGNMENT PROBLEM. IN: THE AUTOMOBILE , 1975 .

[7]  Arkadi Nemirovski,et al.  Robust optimization – methodology and applications , 2002, Math. Program..

[8]  Sven Leyffer,et al.  Solving mathematical programs with complementarity constraints as nonlinear programs , 2004, Optim. Methods Softw..

[9]  S. Travis Waller,et al.  A Hybrid Bilevel Model for the Optimal Shelter Assignment in Emergency Evacuations , 2010, Comput. Aided Civ. Infrastructure Eng..

[10]  Kaan Ozbay,et al.  Evacuation Modelling in the United States: Does the Demand Model Choice Matter? , 2008 .

[11]  Earl J. Baker,et al.  Hurricane Evacuation Behavior , 1991, International Journal of Mass Emergencies & Disasters.

[12]  Chester G. Wilmot,et al.  Sequential Logit Dynamic Travel Demand Model for Hurricane Evacuation , 2004 .

[13]  Marc L. Levitan,et al.  National Review of Hurricane Evacuation Plans and Policies , 2001 .

[14]  Linet Özdamar,et al.  A dynamic logistics coordination model for evacuation and support in disaster response activities , 2007, Eur. J. Oper. Res..

[15]  Bethany L. Nicholson,et al.  Mathematical Programs with Equilibrium Constraints , 2021, Pyomo — Optimization Modeling in Python.

[16]  Arne Stolbjerg Drud,et al.  CONOPT - A Large-Scale GRG Code , 1994, INFORMS J. Comput..

[17]  Hani S. Mahmassani,et al.  Optimal Scheduling of Evacuation Operations , 2006 .

[18]  Yafeng Yin,et al.  Robust Approach to Discrete Network Designs with Demand Uncertainty , 2009 .

[19]  Donald W. Hearn,et al.  An MPEC approach to second-best toll pricing , 2004, Math. Program..

[20]  Therese P. McAllister,et al.  Design Guidelines for Community Shelters for Extreme Wind Events , 2002 .

[21]  Yafeng Yin,et al.  Robust congestion pricing under boundedly rational user equilibrium , 2010 .

[22]  Yafeng Yin,et al.  An Active-set Algorithm for Discrete Network Design Problems , 2009 .

[23]  Todd Litman,et al.  Lessons From Katrina and Rita: What Major Disasters Can Teach Transportation Planners , 2006 .

[24]  Bob Edwards,et al.  Heading for higher ground: factors affecting real and hypothetical hurricane evacuation behavior , 2000 .

[25]  D. Zeigler,et al.  Modelling evacuation behavior during the three mile island reactor crisis , 1986 .

[26]  Brian Wolshon,et al.  "One-way-out": contraflow freeway operation for hurricane evacuation , 2001 .

[27]  Antoine G. Hobeika,et al.  A LOCATION-ALLOCATION MODEL AND ALGORITHM FOR EVACUATION PLANNING UNDER HURRICANE/FLOOD CONDITIONS , 1991 .

[28]  David Kendrick,et al.  GAMS, a user's guide , 1988, SGNM.

[29]  Katta G. Murty,et al.  Nonlinear Programming Theory and Algorithms , 2007, Technometrics.

[30]  Elise Miller-Hooks,et al.  traffic signal timing for urban evacuation , 2007 .