×

US coast guard air station location with respect to distress calls: a spatial statistics and optimization based methodology. (English) Zbl 1176.90370

Summary: We study the problem of suitably locating US Coast Guard air stations to respond to emergency distress calls. Our goal is to identify robust locations in the presence of uncertainty in distress call locations. Our analysis differs from the literature primarily in the way we model this uncertainty. In our optimization and simulation based methodology, we develop a statistical model and demonstrate our procedure using a real data set of distress calls. In addition to guiding strategic decisions of placement of various stations, our methodology is also able to provide guidance on how the resources should be allocated across stations.

MSC:

90B90 Case-oriented studies in operations research

Software:

bootstrap
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Amaldi, E.; Capone, A.; Malucelli, F., Planning UMTS base station location: Optimization models with power control and algorithms, IEEE Transactions on Wireless and Communication, 2, 939-952 (2003)
[2] Bechhofer, R. E.; Elmaghraby, S.; Morse, N., A single-sample multiple decision procedure for selecting the multinomial event which has the highest probability, Annals of Mathematical Statistics, 30, 102-119 (1959) · Zbl 0218.62064
[3] Belardo, S.; Harrald, W. A.; Ward, J., A partial covering approach to siting response resources for major maritime oil spills, Management Science, 30, 10, 1184-1196 (1984)
[4] Carbone, R., Public facilities under stochastic demand, INFOR, 12, 3, 261-270 (1974) · Zbl 0288.90031
[5] Cooper, L., A random locational equilibrium problem, Journal of Regional Science, 14, 1, 47-54 (1974)
[6] Cooper, L., Bounds on the Weber problem solution under conditions of uncertainty, Journal of Regional Science, 18, 1, 87-92 (1978)
[7] Cuzick, J.; Edwards, R., Spatial clustering for inhomogeneous populations, Journal of the Royal Statistical Society, Series B, 52, 73-104 (1990) · Zbl 0703.62069
[8] Daskin, M. S., Application of an expected covering location model to emergency medical service system design, Decision Sciences, 13, 3, 416-439 (1982)
[9] Daskin, M. S., A maximum expected covering location model: Formulation properties and heuristic solution, Transportation Science, 17, 1, 48-70 (1983)
[10] Daskin, M. S.; Hesse, S. M.; ReVelle, C. S., \(α\)-Reliable \(p\)-minimax regret: A new model for strategic facility location modeling, Location Science, 5, 4, 227-246 (1997) · Zbl 0917.90231
[11] Diggle, P. J., A kernel method for smoothing point process data, Applied Statistics, 34, 138-147 (1985) · Zbl 0584.62140
[12] Diggle, P. J., Statistical Analysis of Spatial Point Patterns (2003), Oxford University Press Inc.: Oxford University Press Inc. New York · Zbl 1021.62076
[13] Efron, B.; Tibshirani, R., An Introduction to the Bootstrap (1993), Chapman and Hall: Chapman and Hall New York · Zbl 0835.62038
[14] Fitzsimmons, J., 1971. An emergency medical systems simulation model. In: Proceedings of the 1971 Winter Simulation Conference, New York, pp. 18-25.; Fitzsimmons, J., 1971. An emergency medical systems simulation model. In: Proceedings of the 1971 Winter Simulation Conference, New York, pp. 18-25.
[15] Francis, R. L.; Lowe, T. J.; Tamir, A., On aggregation error bounds for a class of location models, Operations Research, 48, 2, 294-307 (2000) · Zbl 1106.90355
[16] Gendreau, M.; Laporte, G.; Semet, F., The covering tour problem, Operations Research, 45, 4, 568-576 (1997) · Zbl 0887.90122
[17] (Gilks, W. R.; Richardson, S.; Spiegelhalter, D. J., Markov chain Monte Carlo in practice (1996), Chapman & Hall: Chapman & Hall London, New York) · Zbl 0832.00018
[18] Goldsman, D., Nelson, R.L., 2001. Statistical selection of the best system. In: Proceedings of the 2001 Winter Simulation Conference, pp. 139-146.; Goldsman, D., Nelson, R.L., 2001. Statistical selection of the best system. In: Proceedings of the 2001 Winter Simulation Conference, pp. 139-146.
[19] Green, L.; Kolesar, P., Improving emergency responsiveness with management science, Management Science, 50, 8, 1001-1014 (2004)
[20] Hakimi, S. L., Optimum location of switching centers and the absolute centers and medians of a graph, Operations Research, 12, 450-459 (1964) · Zbl 0123.00305
[21] Hillsman, E. L.; Rhoda, R., Errors in measuring distances from populations to service centers, Annals of the Regional Science Association, 12, 74 (1978)
[22] Hodgson, M. J., Stability of solutions to the \(p\)-median problem under induced data error, INFOR Canadian Journal of Operations Research and Information Processing, 29, 167-183 (1991) · Zbl 0732.90046
[23] Kim, S., Nelson, B.L., 2002. Selecting the best system: Theory and methods. In: 2003 Winter Simulation Conference Proceedings, pp. 101-112.; Kim, S., Nelson, B.L., 2002. Selecting the best system: Theory and methods. In: 2003 Winter Simulation Conference Proceedings, pp. 101-112.
[24] Lewis, P. A.W.; Shedler, G. S., Simulation of nonhomogeneous Poisson processes by thinning, Naval Research Logistics Quarterly, 26, 403-414 (1979) · Zbl 0497.60003
[25] Louveaux, F. V., Discrete stochastic location models, Annals of Operations Research, 6, 23-34 (1986)
[26] Mathar, R.; Niessen, T., Optimum positioning of base stations for cellular radio networks, Wireless Networks, 6, 421-428 (2000) · Zbl 1012.68927
[27] Mirchandani, P.; Odoni, A., Locations of medians on stochastic networks, Transportation Science, 13, 2, 85-97 (1979)
[28] Mirchandani, P.; Oudjit, A.; Wong, R. T., ‘Multidimensional’ extensions and a nested dual approach for the \(m\)-median problem, European Journal of Operational Research, 21, 1, 121-137 (1985) · Zbl 0587.90037
[29] Ntaimo, L.; Sen, S., The million-variable march for stochastic combinatorial optimization, Journal of Global Optimization, 32, 3 (2005) · Zbl 1098.90045
[30] Owen, S. H.; Daskin, M., Strategic facility location: A review, European Journal of Operational Research, 111, 423-447 (1998) · Zbl 0938.90048
[31] Pichitlamken, J.; Nelson, B. L., A Combined Procedure for Optimization via Simulation, 2003, ACM Transactions on Modeling and Computer Simulation, 13, 2, 155-179 (2003) · Zbl 1390.65024
[32] Psaraftis, H.; Tharakan, G.; Ceder, A., Optimal response to oil spills: The strategic decision case, Operations Research, 34, 203-217 (1986)
[33] Serra, D.; Marianov, V., The \(p\)-median problem in a changing network: The case of Barcelona, Location Science, 6, 383-394 (1998)
[34] Silverman, B. W., Density Estimation for Statistics and Data Analysis (1986), Chapman and Hall: Chapman and Hall New York · Zbl 0617.62042
[35] Snyder, L., Facility location under uncertainty: A review, IIE Transactions, 38, 547-564 (2006)
[36] United States Coast Guard, FY 2003. 2004 Report.; United States Coast Guard, FY 2003. 2004 Report.
[37] Weaver, J. R.; Church, R. L., Computational procedures for location problems on stochastic networks, Transportation Science, 17, 2, 168-180 (1983)
[38] Weaver, J. R.; Church, R. L., A median location problem with nonclosest facility service, Transportation Science, 19, 1, 58-74 (1985)
[39] Weber, A., 1909. Uber den Standort der Industrien. (in German), Tubingen; English Translation: Theory of the Location of Industries (C.J. Friedrich, Ed. and Trans.), Chicago University Press, 1929.; Weber, A., 1909. Uber den Standort der Industrien. (in German), Tubingen; English Translation: Theory of the Location of Industries (C.J. Friedrich, Ed. and Trans.), Chicago University Press, 1929.
[40] Zhuang, J.; Ogata, Y.; Vere-Jones, D., Stochastic declustering of space-time earthquake occurrences, Journal of the American Statistical Association, 97, 369-380 (2002) · Zbl 1073.62558
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.