Allocation of Mobile Units in an Urban Emergency Service System

In an urban area the location allocation of emergency
services mobile units, such as ambulances, police patrol cars must be
designed so as to achieve a prompt response to demand locations.
In this paper the partition of a given urban network into distinct
sub-networks is performed such that the vertices in each component
are close and simultaneously the sums of the corresponding
population in the sub-networks are almost uniform. The objective
here is to position appropriately in each sub-network a mobile
emergency unit in order to reduce the response time to the demands.
A mathematical model in framework of graph theory is developed.
In order to clarify the corresponding method a relevant numerical
example is presented on a small network.


Authors:



References:
[1] Alsalloum, O.I., Rand, G.K., Extensions to emergency vehicle location
models, Computers& Operations Research, 33, p2725-2743, 2006.
[2] Andersson, T., Värband P., Decision support tools for ambulance
dispatch and relocation, Journal of the Operational Research Society
(2007) 58, 195–2007.
[3] Burwell, T.H., Jarvis, J.P., McKnew, M.A., An application of a spatially
distributed queuing model to an ambulance system, Socio-Economic
Planning Sciences, Volume 26, Issue 4, p289-300,1992.
[4] Christofides N, Graph Theory an Algorithmic Approach, Academic
Press, 1975.
[5] Floyd R.W., Algorithm 97: Shortest Paths, Communication of the ACM
5 (6), 1962, p 345.
[6] Gendreau, M., Laporte, G., Semet, F., The Maximal Expected Coverage
Relocation Problem for Emergency Vehicles, Jour. of the Operational
Research Society, 92006) 57, p 22-28.
[7] Goldberg J, Dietrich R, Chen J, Mitwasi M, Valenzuela T and Criss
E,Validating and applying a model for locating emergency medical
vehicles in Tucson, AZ. European Journal of Operational Research, 49:
308-324, (1990).
[8] Goldberg J, Dietrich R, Chen J, Mitwasi M, Valenzuela T and Criss E
(1990). A simulation model for evaluating a set of emergency vehicle
base location: Development, validation, and usage. Socio-Econ Plan Sci,
24: 125-141.
[9] Harary Frank, Graph Theory, Addison Wesley, 1969.
[10] Henderson, S.G., and A.J. Mason. Ambulance service planning:
simulation and data visualisation. In M.L. Brandeau, F. Sainfort and
W.P. Pierskalla, eds, Operations Research and Health Care: A Handbook
of Methods and Applications, 77-102. Kluwer Academic, Boston, 2004.
[11] Jia, Hongzhong, Ordóñez, Fernando; Dessouky, Maged, A modeling
framework for facility location of medical services for large-scale
emergencies, IIE Transactions, 39:1, p41-55, 2007.
[12] Paluzzi, M. (2004). Testing a heuristic P-median location allocation
model for siting emergency service facilities. Paper Presented at the
Annual Meeting of Association of American Geographers, Philadelphia,
PA.
[13] Uyeno, Dean H., and C. Seeberg, A practical methodology for
ambulance location, Simulation, Vol. 43, No. 2, 79-87 (1984), DOI:
10.1177/003754978404300202.