Facility location under demand uncertainty: Response to a large-scale bio-terror attack

In the event of a catastrophic bio-terror attack, major urban centers need to efficiently distribute large amounts of medicine to the population. In this paper, we consider a facility location problem to determine the points in a large city where medicine should be handed out to the population. We consider locating capacitated facilities in order to maximize coverage, taking into account a distance-dependent coverage function and demand uncertainty. We formulate a special case of the maximal covering location problem (MCLP) with a loss function, to account for the distance-sensitive demand, and chance-constraints to address the demand uncertainty. This model decides the locations to open, and the supplies and demand assigned to each location. We solve this problem with a locate-allocate heuristic. We illustrate the use of the model by solving a case study of locating facilities to address a large-scale emergency of a hypothetical anthrax attack in Los Angeles County.

[1]  Robert J. Elliott,et al.  On risk minimizing portfolios under a Markovian regime-switching Black-Scholes economy , 2010, Ann. Oper. Res..

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

[3]  Mark S. Daskin,et al.  Stochastic p-robust location problems , 2006 .

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

[5]  Éric D. Taillard,et al.  Heuristic Methods for Large Centroid Clustering Problems , 2003, J. Heuristics.

[6]  Mark A. Turnquist,et al.  Pre-positioning of emergency supplies for disaster response , 2010 .

[7]  L V Snyder,et al.  STOCHASTIC PROBUST LOCATION PROBLEMS , 2006 .

[8]  Zvi Drezner,et al.  Location of congested capacitated facilities with distance-sensitive demand , 2006 .

[9]  Zvi Drezner,et al.  The variable radius covering problem , 2009, Eur. J. Oper. Res..

[10]  R. T. Wong,et al.  `Multidimensional' extensions and a nested dual approach for the m-median problem , 1985 .

[11]  Xiangtong Qi,et al.  A logistics scheduling model: scheduling and transshipment for two processing centers , 2006 .

[12]  Michel Gendreau,et al.  The maximal expected coverage relocation problem for emergency vehicles , 2006, J. Oper. Res. Soc..

[13]  Zvi Drezner,et al.  The p-median problem under uncertainty , 2008, Eur. J. Oper. Res..

[14]  Oded Berman,et al.  Flow intercepting spatial interaction model: a new approach to optimal location of competitive facilities , 1998 .

[15]  M. John Hodgson,et al.  A hierarchical location-allocation model with travel based on expected referral distances , 2009, Ann. Oper. Res..

[16]  Oded Berman,et al.  Location of terror response facilities: A game between state and terrorist , 2007, Eur. J. Oper. Res..

[17]  James V. Jucker,et al.  The Simple Plant-Location Problem under Uncertainty , 1976, Oper. Res..

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

[19]  François V. Louveaux,et al.  A Dual-Based Procedure for Stochastic Facility Location , 1992, Oper. Res..

[20]  Eric Sheppard,et al.  A Conceptual Framework for Dynamic Location—Allocation Analysis , 1974 .

[21]  V. Balachandran,et al.  Optimal Facility Location under Random Demand with General Cost Structure , 1976 .

[22]  Oded Berman,et al.  Competitive facility location and design problem , 2007, Eur. J. Oper. Res..

[23]  Paul J. Densham,et al.  DESIGNING AND IMPLEMENTING STRATEGIES FOR SOLVING LARGE LOCATION-ALLOCATION PROBLEMS WITH HEURISTIC METHODS _ , 2009 .

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

[25]  M. Cemal Dincer,et al.  A multifactor model for international plant location and financing under uncertainty , 1986, Comput. Oper. Res..

[26]  Maged Dessouky,et al.  A modeling framework for facility location of medical services for large-scale emergencies , 2007 .

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

[28]  R. Church,et al.  The maximal covering location problem , 1974 .

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

[30]  R. Church,et al.  Computational Procedures for Location Problems on Stochastic Networks , 1983 .

[31]  Lawrence V. Snyder,et al.  Facility location under uncertainty: a review , 2006 .

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

[33]  Oded Berman,et al.  The generalized maximal covering location problem , 2002, Comput. Oper. Res..

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

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

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

[37]  Zvi Drezner,et al.  The gradual covering decay location problem on a network , 2003, Eur. J. Oper. Res..

[38]  Robert Carbone,et al.  Public Facilities Location Under Stochastic Demand , 1974 .

[39]  Charles S. ReVelle,et al.  The Location of Emergency Service Facilities , 1971, Oper. Res..

[40]  Leon Cooper,et al.  Heuristic Methods for Location-Allocation Problems , 1964 .

[41]  Maged M. Dessouky,et al.  Solution approaches for facility location of medical supplies for large-scale emergencies , 2007, Comput. Ind. Eng..

[42]  M. Brandeau,et al.  Reducing mortality from anthrax bioterrorism: strategies for stockpiling and dispensing medical and pharmaceutical supplies. , 2006, Biosecurity and bioterrorism : biodefense strategy, practice, and science.