A stochastic programming approach for Shelter location and evacuation planning

Shelter location and traffic allocation decisions are critical for an efficient evacuation plan. In this study, we propose a scenario-based two-stage stochastic evacuation planning model that optimally locates shelter sites and that assigns evacuees to nearest shelters and to shortest paths within a tolerance degree to minimize the expected total evacuation time. Our model considers the uncertainty in the evacuation demand and the disruption in the road network and shelter sites. We present a case study for a potential earthquake in Istanbul. We compare the performance of the stochastic programming solutions to solutions based on single scenarios and mean values.

[1]  Gilbert Laporte,et al.  A Tabu Search Heuristic for the Static Multi-Vehicle Dial-a-Ride Problem , 2002 .

[2]  Alexander Stepanov,et al.  Production , Manufacturing and Logistics Multi-objective evacuation routing in transportation networks , 2009 .

[3]  Yanfeng Ouyang,et al.  A continuum approximation approach to reliable facility location design under correlated probabilistic disruptions , 2010 .

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

[5]  Michel Gendreau,et al.  Location of facilities on a network subject to a single-edge failure , 1992, Networks.

[6]  Nilay Noyan,et al.  Risk-averse two-stage stochastic programming with an application to disaster management , 2012, Comput. Oper. Res..

[7]  Shaligram Pokharel,et al.  Optimization models in emergency logistics: A literature review , 2012 .

[8]  Carlos F. Daganzo,et al.  Managing Evacuation Routes , 2009 .

[9]  Andrzej Galat,et al.  Technical note , 2008, Comput. Biol. Chem..

[10]  Cheng Pan,et al.  A method for designing centralized emergency supply network to respond to large-scale natural disasters , 2014 .

[11]  Oded Berman,et al.  Locating mobile servers on a network with markovian properties , 1982, Networks.

[12]  Mark A. Turnquist,et al.  Pre-positioning of Emergency Supplies for Disaster Response , 2006, 2006 IEEE International Symposium on Technology and Society.

[13]  A. Odoni,et al.  Locations of Medians on Stochastic Networks , 1979 .

[14]  Zelda B. Zabinsky,et al.  Stochastic optimization of medical supply location and distribution in disaster management , 2010 .

[15]  Mark S. Daskin,et al.  A facility reliability problem: Formulation, properties, and algorithm , 2010 .

[16]  M J Lighthill,et al.  On kinematic waves II. A theory of traffic flow on long crowded roads , 1955, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[17]  Erhan Erkut,et al.  Optimal ambulance location with random delays and travel times , 2008, Health care management science.

[18]  Gilbert Laporte,et al.  Models and exact solutions for a class of stochastic location-routing problems , 1987 .

[19]  Antonio Alonso Ayuso,et al.  Introduction to Stochastic Programming , 2009 .

[20]  Ni-Bin Chang,et al.  A LOCATIONAL MODEL FOR THE SITE SELECTION OF SOLID WASTE MANAGEMENT FACILITIES WITH TRAFFIC CONGESTION CONSTRAINTS , 1995 .

[21]  Linda Luther.  Disaster Debris Removal After Hurricane Katrina: Status and Associated Issues [Updated April 2, 2008] , 2008 .

[22]  Gülay Barbarosoglu,et al.  A two-stage stochastic programming framework for transportation planning in disaster response , 2004, J. Oper. Res. Soc..

[23]  Mark S. Daskin,et al.  The α‐reliable mean‐excess regret model for stochastic facility location modeling , 2006 .

[24]  A. Mawson.  Understanding Mass Panic and Other Collective Responses to Threat and Disaster , 2005, Psychiatry.

[25]  Pamela Murray-Tuite,et al.  Evacuation transportation modeling: An overview of research, development, and practice , 2013 .

[26]  Luís Santos,et al.  A Multiobjective Approach to Locate Emergency Shelters and Identify Evacuation Routes in Urban Areas , 2009 .

[27]  Yupo Chan,et al.  A multiple-depot, multiple-vehicle, location-routing problem with stochastically processed demands , 2001, Comput. Oper. Res..

[28]  Michael S. Waterman,et al.  Technical Note - Determining All Optimal and Near-Optimal Solutions when Solving Shortest Path Problems by Dynamic Programming , 1984, Oper. Res..

[29]  Oded Berman,et al.  Locating capacitated facilities to maximize captured demand , 2007 .

[30]  Charles J. Colbourn,et al.  Locating A Broadcast Facility In An Unreliable Network , 1990 .

[31]  Serge P. Hoogendoorn,et al.  A review on travel behaviour modelling in dynamic traffic simulation models for evacuations , 2012 .

[32]  R. Rosenfeld.  Confidence , 2007, Otolaryngology--head and neck surgery : official journal of American Academy of Otolaryngology-Head and Neck Surgery.

[33]  Yanfeng Ouyang,et al.  Reliable Facility Location Design Under the Risk of Disruptions , 2010, Oper. Res..

[34]  Hande Yaman,et al.  Compromising system and user interests in shelter location and evacuation planning , 2015 .

[35]  Zhi-Hua Hu,et al.  Post-disaster evacuation and temporary resettlement considering panic and panic spread , 2014, Transportation Research Part B: Methodological.

[36]  Benita M. Beamon,et al.  Facility location in humanitarian relief , 2008 .

[37]  H. W. Hamacher,et al.  Mathematical Modelling of Evacuation Problems: A State of Art , 2001 .

[38]  D. R. Fulkerson,et al.  Constructing Maximal Dynamic Flows from Static Flows , 1958 .

[39]  Ronald W. Perry,et al.  Evacuation Decision-Making in Natural Disasters , 1979 .

[40]  Athanasios K. Ziliaskopoulos,et al.  A Linear Programming Model for the Single Destination System Optimum Dynamic Traffic Assignment Problem , 2000, Transp. Sci..

[41]  Kaan Ozbay,et al.  Evacuation Network Modeling via Dynamic Traffic Assignment with Probabilistic Demand and Capacity Constraints , 2010 .

[42]  Michael K. Lindell,et al.  Critical Behavioral Assumptions in Evacuation Time Estimate Analysis for Private Vehicles: Examples from Hurricane Research and Planning , 2007 .

[43]  Sarah Bretschneider.  Mathematical Models for Evacuation Planning in Urban Areas , 2012 .

[44]  Andrew Lim,et al.  Reliable logistics networks design with facility disruptions , 2011 .

[45]  Siamak Ardekani,et al.  Logistics problems in the aftermath of the 1985 Mexico City earthquake , 1988 .

[46]  Seokjin Kim,et al.  Facility location for large-scale emergencies , 2010, Ann. Oper. Res..

[47]  Lawrence V. Snyder,et al.  Reliability Models for Facility Location: The Expected Failure Cost Case , 2005, Transp. Sci..

[48]  Serge P. Hoogendoorn,et al.  Optimization of Evacuation Measures Under Uncertainty , 2010 .

[49]  John R. Birge,et al.  Introduction to Stochastic Programming , 1997 .

[50]  William H. K. Lam,et al.  Transportation Research, Part A: Policy and Practice , 1997 .

[51]  Luís Alçada-Almeida,et al.  Solving a location-routing problem with a multiobjective approach: the design of urban evacuation plans , 2012 .

[52]  Vedat Bayram,et al.  Optimization models for large scale network evacuation planning and management: A literature review , 2016 .

[53]  H. Frank,et al.  Optimum Locations on a Graph with Probabilistic Demands , 1966, Oper. Res..

[54]  Takeo Yamada,et al.  A network flow approach to a city emergency evacuation planning , 1996, Int. J. Syst. Sci..

[55]  Leon Cooper,et al.  A RANDOM LOCATIONAL EQUILIBRIUM PROBLEM , 1974 .

[56]  Li Zhang,et al.  Optimum Transit Operations during the Emergency Evacuations , 2009 .

[57]  F. Sibel Salman,et al.  Assessing the reliability and the expected performance of a network under disaster risk , 2011, OR Spectr..

[58]  Zuo-Jun Max Shen,et al.  Modeling Transportation Networks During Disruptions and Emergency Evacuations , 2008 .

[59]  Pinar Keskinocak,et al.  Pre-Positioning of Emergency Items for CARE International , 2011, Interfaces.

[60]  Hong Zheng,et al.  Modeling no-notice mass evacuation using a dynamic traffic flow optimization model , 2007 .

[61]  Carlos F. Daganzo,et al.  The Cell Transmission Model. Part I: A Simple Dynamic Representation Of Highway Traffic , 1992 .

[62]  S. Travis Waller,et al.  A dynamic evacuation network optimization problem with lane reversal and crossing elimination strategies , 2010 .

[63]  Mark S. Daskin,et al.  Planning for Disruptions in Supply Chain Networks , 2006 .

[64]  Di Wu,et al.  Robust Shelter Locations for Evacuation Planning with Demand Uncertainty , 2011 .

[65]  Oded Berman,et al.  Facility Reliability Issues in Network p-Median Problems: Strategic Centralization and Co-Location Effects , 2007, Oper. Res..

[66]  D. Thurston,et al.  Modeling Robust and Reliable Supply Chains , 2003 .

[67]  Mei-Shiang Chang,et al.  A scenario planning approach for the flood emergency logistics preparation problem under uncertainty , 2007 .

[68]  A. Madansky.  Inequalities for Stochastic Linear Programming Problems , 1960 .

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

[70]  François V. Louveaux,et al.  Discrete stochastic location models , 1986 .

[71]  Arkadi Nemirovski,et al.  Lectures on modern convex optimization - analysis, algorithms, and engineering applications , 2001, MPS-SIAM series on optimization.

[72]  Hanif D. Sherali,et al.  Optimal evacuation planning using staging and routing , 2014, J. Oper. Res. Soc..

[73]  Nancy P Humphrey,et al.  New TRB Special Report: The Role of Transit in Emergency Evacuation , 2008 .

[74]  Rolf H. Möhring,et al.  System-optimal Routing of Traffic Flows with User Constraints in Networks with Congestion System-optimal Routing of Traffic Flows with User Constraints in Networks with Congestion , 2022 .

[75]  Oya Ekin Karasan,et al.  Solution methodologies for debris removal in disaster response , 2016, EURO J. Comput. Optim..

[76]  S. Sen.  Algorithms for Stochastic Mixed-Integer Programming Models , 2005 .

[77]  Srinivas Peeta,et al.  Planning for Evacuation : Insights from an Efficient Network Design Model , 2009 .

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

[79]  Rajan Batta,et al.  Review of recent developments in OR/MS research in disaster operations management , 2013, Eur. J. Oper. Res..

[80]  Alf Kimms,et al.  A basic mathematical model for evacuation problems in urban areas , 2011 .

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

[82]  Carlos F. Daganzo,et al.  THE CELL TRANSMISSION MODEL, PART II: NETWORK TRAFFIC , 1995 .

[83]  Rachel A. Davidson,et al.  Shelter location and transportation planning under hurricane conditions , 2012 .

[84]  Oded Berman,et al.  Facility Location Problems with Stochastic Demands and Congestion , 2002 .

[85]  Hande Yaman,et al.  Shelter Location and Evacuation Route Assignment Under Uncertainty: A Benders Decomposition Approach , 2017, Transp. Sci..

[86]  M. Lindell,et al.  Preparedness for emergency response: guidelines for the emergency planning process. , 2003, Disasters.

[87]  Hediye Tuydesʹ.  Network traffic management under disaster conditions , 2005 .

[88]  S. Travis Waller,et al.  Reliable evacuation planning via demand inflation and supply deflation , 2010 .

[89]  James E. Ward,et al.  A Partial Covering Approach to Siting Response Resources for Major Maritime Oil Spills , 1984 .

[90]  Wilbert E. Wilhelm,et al.  A Strategic, Area-wide Contingency Planning Model for Oil Spill Cleanup Operations with Application Demonstrated to the Galveston Bay Area* , 1996 .

[91]  Yosef Sheffi,et al.  Urban Transportation Networks: Equilibrium Analysis With Mathematical Programming Methods , 1985 .

[92]  Pitu B. Mirchandani,et al.  Localizing 2-medians on probabilistic and deterministic tree networks , 1980, Networks.

[93]  Thomas J. Cova,et al.  A network flow model for lane-based evacuation routing , 2003 .

[94]  D. Wald,et al.  Global earthquake casualties due to secondary effects: a quantitative analysis for improving rapid loss analyses , 2010 .

[95]  Tao Yao,et al.  Evacuation Transportation Planning Under Uncertainty: A Robust Optimization Approach , 2009 .

[96]  Seong Soo Oh,et al.  Confidence, knowledge, and compliance with emergency evacuation , 2015 .

[97]  Harilaos N. Psaraftis,et al.  Optimal Response to Oil Spills: The Strategic Decision Case , 1986, Oper. Res..

[98]  P. I. Richards.  Shock Waves on the Highway , 1956 .

[99]  Oded Berman,et al.  Locating Facilities in the Presence of Disruptions and Incomplete Information , 2009, Decis. Sci..

[100]  Hairong Dong,et al.  State-of-the-Art Pedestrian and Evacuation Dynamics , 2020, IEEE Transactions on Intelligent Transportation Systems.

[101]  F. Sibel Salman,et al.  Locating disaster response facilities in Istanbul , 2011, J. Oper. Res. Soc..

[102]  Nicole Dash,et al.  Evacuation Decision Making and Behavioral Responses: Individual and Household , 2007 .

[103]  Melih Celik,et al.  The Post-Disaster Debris Clearance Problem Under Incomplete Information , 2015, Oper. Res..

[104]  Zuo-Jun Max Shen,et al.  An Inventory-Location Model: Formulation, Solution Algorithm and Computational Results , 2002, Ann. Oper. Res..

[105]  Mark S. Daskin,et al.  Models for Reliable Supply Chain Network Design , 2007 .