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Extensions to emergency vehicle location models. (English) Zbl 1086.90034
Summary: This paper is concerned with extending models for the maximal covering location problem in two ways. First, the usual 0-1 coverage definition is replaced by the probability of covering a demand within the target time. Second, once the locations are determined, the minimum number of vehicles at each location that satisfies the required performance levels is determined. Thus, the problem of identifying the optimal locations of a pre-specified number of emergency medical service stations is addressed by goal programming. The first goal is to locate these stations so that the maximum expected demand can be reached within a pre-specified target time. Then, the second goal is to ensure that any demand arising located within the service area of the station will find at least one vehicle, such as an ambulance, available. Erlang’s loss formula is used to identify the arrival rates when it is necessary to add an ambulance in order to maintain the performance level for the availability of ambulances. The model developed has been used to evaluate locations for the Saudi Arabian Red Crescent Society, Riyadh City, Saudi Arabia.

90B85 Continuous location
90B90 Case-oriented studies in operations research
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[1] Church, R.L.; ReVelle, C.S., The maximal covering location problem, Papers of the regional science association, 32, 101-118, (1974)
[2] Marianov, V.; ReVelle, C.S., Siting emergency services, (), 199-223
[3] Brotcorne, L.; Laporte, G.; Semet, F., Ambulance location and relocation models, European journal of operational research, 147, 451-463, (2003) · Zbl 1037.90554
[4] Charnes, A.; Storbeck, J., A goal programming model for the siting of multilevel EMS systems, Socio-economic planning sciences, 14, 383-389, (1980)
[5] Ball, M.O.; Lin, F.L., A reliability model applied to emergency service vehicle location, Operations research, 41, 18-36, (1993) · Zbl 0775.90264
[6] Marianov, V.; ReVelle, C.S., The queueing maximal availability location problem: a model for siting of emergency vehicles, European journal of operational research, 93, 110-120, (1996) · Zbl 0912.90195
[7] Daskin, M., A maximal expected covering location model: formulation, properties, and heuristic solution, Transportation science, 17, 48-69, (1983)
[8] ReVelle, C.S.; Hogan, K., A reliability-constrained siting model with local estimates of busy fractions, Environment and planning B: planning and design, 15, 143-152, (1988)
[9] ReVelle, C.S.; Hogan, K., The maximum availability location problem, Transportation science, 23, 192-199, (1989) · Zbl 0681.90036
[10] Eaton, D.J.; Church, R.L.; Bennett, V.L.; Hamon, B.L.; Lopez, L.G.V., On deployment of health resources in rural valle del cauca, Colombia, TIMS studies in the management sciences, 17, 331-359, (1981)
[11] Eaton, D.J.; Daskin, M.S.; Simmons, D.; Bulloch, B.; Jansma, G., Determining emergency medical service vehicle deployment in Austin, Texas, Interfaces, 15, 1, 96-108, (1985)
[12] Eaton, D.J.; Sanchez, H.M.L.; Lantigua, R.R.; Morgan, J., Determining ambulance deployment in santo domingo, dominican republic, Journal of the operational research society, 37, 113-126, (1986)
[13] Fujiwara, M.; Makjamroen, T.; Gupta, K., Ambulance deployment analysis: a case study of Bangkok, European journal of operational research, 31, 9-18, (1987)
[14] Fujiwara, M.T.; Kachenchai, K.; Makjamroen, T.; Gupta, K., An efficient scheme for deployment of ambulances in metropolitan Bangkok, (), 730-741
[15] Aly, A.A.; White, J.A., Probabilistic formulation of the emergency service location problem, Journal of the operational research society, 29, 1167-1179, (1987) · Zbl 0388.90047
[16] Daskin, M.S.; Haghani, A.E.; Khanal, M.; Malandraki, C., Aggregation effects in maximum covering models, Annals of operations research, 18, 115-140, (1989) · Zbl 0707.90067
[17] Current, J.R.; Schilling, D.A., Analysis of errors due to demand data aggregation in the set covering and maximal covering location problem, Geographical analysis, 22, 1, 116-126, (1990)
[18] Benveniste, R., Solving the combined zoning and location problem for several emergency units, Journal of the operational research society, 36, 433-450, (1985) · Zbl 0577.90020
[19] Fitzsimmons, J.A., A methodology for emergency ambulance deployment, Management science, 19, 627-636, (1973)
[20] Kolesar, P.; Walker, W.; Hausner, J., Determining the relation between fire engine travel times and travel distances in New York city, Operations research, 23, 614-627, (1975)
[21] Perez CE. Regional planning of emergency medical resources. PhD thesis. University of Pittsburgh, 1982.
[22] Goldberg, J.; Dietrich, R.; Chen, J.; Mitwasi, M.; Valenzuela, T.; Criss, E., Validating and applying a model for locating emergency medical vehicles in Tucson, AZ, European journal of operational research, 49, 308-324, (1990)
[23] Goldberg, J.; Dietrich, R.; Chen, J.; Mitwasi, M.; Valenzuela, T.; Criss, E., A simulation model for evaluating a set of emergency vehicle base location: development, validation, and usage, Socio-economic planning sciences, 24, 125-141, (1990)
[24] Goldberg, J.R.; Paz, L., Locating emergency vehicle bases when service time depends on call location, Transportation science, 25, 264-280, (1991) · Zbl 0825.90649
[25] Papacostas, C.S.; Prevedouros, P.D., Transportation engineering and planning, (2001), NJ Prentice-Hall Englewood Cliffs
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