Maximizing the minimum cover probability by emergency facilities

In this paper we propose a stochastic model for the location of emergency facilities. The model is formulated and analyzed. The location of one facility in the plane is optimally solved. Optimal algorithms are proposed for the location of multiple facilities on a network. Computational experiments illustrate the effectiveness of these solution procedures.

[1]  Reza Barkhi,et al.  A REVIEW OF COVERING PROBLEMS IN FACILITY LOCATION. , 1993 .

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

[3]  Charles S. ReVelle,et al.  The Maximum Availability Location Problem , 1989, Transp. Sci..

[4]  C. Revelle.  Facility siting and integer-friendly programming , 1993 .

[5]  Zvi Drezner,et al.  Production , Manufacturing and Logistics Location with acceleration – deceleration distance , 2009 .

[6]  E. Minieka.  The m-Center Problem , 1970 .

[7]  John E. Beasley,et al.  OR-Library: Distributing Test Problems by Electronic Mail , 1990 .

[8]  Zvi Drezner,et al.  The Big Triangle Small Triangle Method for the Solution of Nonconvex Facility Location Problems , 2004, Oper. Res..

[9]  Zvi Drezner,et al.  Finding the optimal solution to the Huff based competitive location model , 2004, Comput. Manag. Sci..

[10]  Said Salhi,et al.  Facility Location: A Survey of Applications and Methods , 1996 .

[11]  Armann Ingolfsson,et al.  Empirical Analysis of Ambulance Travel Times: The Case of Calgary Emergency Medical Services , 2010, Manag. Sci..

[12]  Kazuo Murota,et al.  IMPROVEMENTS OF THE INCREMENTAL METHOD FOR THE VORONOI DIAGRAM WITH COMPUTATIONAL COMPARISON OF VARIOUS ALGORITHMS , 1984 .

[13]  Vladimir Marianov,et al.  The Queueing Maximal availability location problem: A model for the siting of emergency vehicles , 1996 .

[14]  Zvi Drezner,et al.  A new formulation for the conditional p-median and p-center problems , 2008, Oper. Res. Lett..

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

[16]  D. T. Lee,et al.  Two algorithms for constructing a Delaunay triangulation , 1980, International Journal of Computer & Information Sciences.

[17]  Z. Drezner.  On the rectangular p‐center problem , 1987 .

[18]  J. P. Jarvis,et al.  Approximating the Equilibrium Behavior of Multi-Server Loss Systems , 1985 .

[19]  Zvi Drezner.  Conditional p-Center Problems , 1989, Transp. Sci..

[20]  Charles ReVelle,et al.  A perspective on location science , 1997 .

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

[22]  John J. Bernardo,et al.  Developing and validating a decision support system for locating emergency medical vehicles in Louisville, Kentucky , 1994 .

[23]  S. L. Hakimi,et al.  Optimum Locations of Switching Centers and the Absolute Centers and Medians of a Graph , 1964 .

[24]  S. Kataoka.  A Stochastic Programming Model , 1963 .

[25]  Zvi Drezner,et al.  Locating service facilities whose reliability is distance dependent , 2003, Comput. Oper. Res..

[26]  Edward Minieka,et al.  Conditional centers and medians of a graph , 1980, Networks.

[27]  Reuven Chen,et al.  Conditional Minisum and Minimax Location-Allocation Problems in Euclidean Space , 1988, Transp. Sci..

[28]  Zvi Drezner,et al.  Generalized coverage: New developments in covering location models , 2010, Comput. Oper. Res..

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

[30]  James Vijay,et al.  An Algorithm for the p-Center Problem in the Plane , 1985, Transp. Sci..

[31]  J. Pell,et al.  Effect of reducing ambulance response times on deaths from out of hospital cardiac arrest: cohort study , 2001, BMJ : British Medical Journal.

[32]  Zvi Drezner,et al.  The p-Centre Problem—Heuristic and Optimal Algorithms , 1984 .

[33]  Zvi Drezner,et al.  Facility location - applications and theory , 2001 .

[34]  Z. Drezner.  The weighted minimax location problem with set-up costs and extensions , 1991 .

[35]  Mark S. Daskin,et al.  Network and Discrete Location: Models, Algorithms and Applications , 1995 .

[36]  Bhaba R. Sarker,et al.  Discrete location theory , 1991 .

[37]  L Price,et al.  Treating the clock and not the patient: ambulance response times and risk , 2006, Quality and Safety in Health Care.

[38]  Mark S. Daskin,et al.  A Maximum Expected Covering Location Model: Formulation, Properties and Heuristic Solution , 1983 .

[39]  Zvi Drezner,et al.  Equity Models in Planar Location , 2006, Comput. Manag. Sci..

[40]  Reuven Chen,et al.  The conditional p‐center problem in the plane , 1993 .

[41]  Zvi Drezner,et al.  The Facility Location Problem with Limited Distances , 1991, Transp. Sci..

[42]  D. Hearn,et al.  Geometrical Solutions for Some Minimax Location Problems , 1972 .

[43]  Zvi Drezner,et al.  A General Global Optimization Approach for Solving Location Problems in the Plane , 2007, J. Glob. Optim..

[44]  H. Frank,et al.  Letter to the Editor - A Note on a Graph Theoretic Game of Hakimi's , 1967, Oper. Res..

[45]  Gilbert Laporte,et al.  Ambulance location and relocation models , 2000, Eur. J. Oper. Res..

[46]  Robert Dietrich,et al.  Validating and applying a model for locating emergency medical vehicles in Tuczon, AZ , 1990 .

[47]  Richard L. Church,et al.  The maximal covering location problem , 1974 .

[48]  Richard C. Larson,et al.  Approximating the Performance of Urban Emergency Service Systems , 1975, Oper. Res..

[49]  Kokichi Sugihara,et al.  A robust Topology-Oriented Incremental algorithm for Voronoi diagrams , 1994, Int. J. Comput. Geom. Appl..

[50]  Vladimir Marianov,et al.  Trading off Species Protection and Timber Production in Forests Managed for Multiple Objectives , 2004 .

[51]  Martine Labbé,et al.  p-Center Problems , 2015 .

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

[53]  H. Frank,et al.  Letter to the Editor - Optimum Locations on Graphs with Correlated Normal Demands , 1967, Oper. Res..