problem on a tree network considering maximum distance constraint is presented. The first
objective function called centdian is a weighted mean of a minisum and a minimax criterion
and the second one is a maximal covering criterion. For the solution of the bi-objective
optimization problem, the problem is split in two sub problems: the selection of the best set of
locations, and a demand assignment problem to evaluate each selection of locations. We
propose a heuristic algorithm to characterize the efficient location point set on the network.
Finally, some numerical examples are presented to illustrate the effectiveness of the proposed
algorithm.
How to cite this paper
Hosseini, M & Ameli, M. (2011). A bi-objective model for emergency services location-allocation problem with maximum distance constraint.Management Science Letters , 1(2), 115-126.
Refrences
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Goldberg, J. and Paz, L. (1991) Locating emergency vehicle bases when service time depends on call location. Transportation Science, 25, 264–280.
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Halpern, J. (1976). The location of a center-median convex combination on an undirected tree. Journal of regional science, 16(2), 237-245.
Halpern, J. (1978). Finding minimal enter-median onvex ombination (Cent-Dian) of a Graph. Management Science, 24(5), 535-544.
Hooker, J. N., Garfinkel, R. S., & Chen, C. K. (1991). Finite ominating sets for network location problems. Operations Research, 39(1), 100-118.
Hochbaum, D. S., & Pathria, A. (1998). Locating centers in a dynamically changing network and related problems. Location Science, 6, 243–256.
Halpern, J. (1980). Duality in the ent-ian of a raph. Operations Research, 28(3), 722-735.
Jia, H., Ordonez, F., Dessouky, M. (2007). A modeling framework for facility location of medical services for large-scale emergencies. IIE Transactions, 39, 41-55.
Paluzzi, M. (2004). Testing a heuristic P-median location allocation model for siting emergency service facilities. presented at the Annual Meeting of the Association of American Geographers, Philadelphia, PA.
Perez-Brito, D., Moreno-Perez, J. A., & Rodriguez-Martin, I. (1997). Finite Dominating Set for the p-Facility Cent-Dian Network Location Problem. Studies in Location Analysis, 11, 27-40.
Perez-Brito, D., Moreno-Perez, J. A., & Rodriguez-Martin, I. (1998). The 2-facility centdian network problem. Location Science, 1998. 6, 369-381.
Mirchandani, P. B. (1987). Generalized hierarchical facility location. Transportation Science, 21, 123-125.
Mirchandani, P. B. (1980). Locational decisions on stochastic networks. Geographical Analysis, 12, 172-183.
ReVelle, C., & Hogan, K. (1989). The maximum availability location problem. Transportation Science, 23, 192–200.
Salcedo-Sanz, S., Portilla-Figueras, J. A., Ortiz-Garcıia, E. G., Peirez-Bellido, A. M., Thraves, C., Fernandez-Anta, A., & Yao, X. (2008). Optimal switch location in mobile communication networks using hybrid genetic algorithms. Applied Soft Computing, 8, 1486-1497.
Schilling, D.A. (1982). Strategic facility planning. the analysis of options. Decision Sciences, 13, 1-14.
Serra, D., & Marianov, V. (1999). The P-median problem in a changing network: the case of Barcelona, Location Science, 6(1), 383–394.
Storbeck, J. (1989). Slack, natural slack, and location coveting, Socio-Economic Planning Sciences 16(3).
Talwar, M. (2002). Location of rescue helicopters in South Tyrol, presented at the 37th Annual ORSNZ Conference, Auckland, New Zealand.
Tamir, A., Brito, D. P., & Moreno-Perez, J. A. (2003). A Polynomial Algorithm for the p-Centdian Problem on a Tree.
Tien, J. M., El-Tell, K., & Simons, G. (1983). Improved formulations to the hierarchical health facility location-allocation problem, IEEE Transactions in Systems Management and Cybernetics, 13, 1128– 1132.
Toregas, C., Swain, R., ReVelle, C., & Bergman, L. (1971). The location of emergency service facility. Operations Research, 19, 1363–1373.
Berman, O., &Yang, K. E. (1991). Medi-Centre Location Problems. The Journal of the Operational Research Society, 42(4), 313-322.
Bianchi,C., & Church, R. (1988). A hybrid FLEET model for emergency medical service system design. Social Sciences in Medicine, 26(1), 163–171.
Beraldi, P., & Ruszczynski, A. (2002). A branch and bound method for stochastic integer problems under probabilistic constraints. Optimization Methods and Software, 17, 359–382.
Calvo, A. H., & Marks, H. (1973). Location of health care facilities: an analytical approach. Socio-Economic Planning Sciences, 7, 407–422.
Carbone, R. (1974). Public facility location under stochastic demand. INFOR, 12, 261–270.
Colebrook, M., & Sicilia, J. (2007). A polynomial algorithm for the multicriteria cent-dian location problem. European Journal of Operational Research, 179, 1008-1024.
Colebrook, M., & Sicilia, J. (2006). An O(mn) algorithm for the anti-cent-dian problem. Applied Mathematics and Computation, 183, 350–364.
Daskin, M. S. (2008). What You Should Know About Location Modeling. Naval Research Logistics, 55, 283-294.
Daskin, M. S. & Stern, E. H. (1981). A hierarchical objective set covering model for emergency medical service vehicle deployment. Transportation Science, 15(2), 137–152.
Garfinkel, R. S., Neebe, A. W., & Rao, M. R. (1977). The m-center problem: minimax facility location. Management Science, 23, 1133–1142.
Goldberg, J. and Paz, L. (1991) Locating emergency vehicle bases when service time depends on call location. Transportation Science, 25, 264–280.
Hakimi, S. L. (1964). Optimum Locations of Switching Centers and the Absolute Centers and Medians of a Graph. Operations Research, 12(3), 450-459.
Halpern, J. (1976). The location of a center-median convex combination on an undirected tree. Journal of regional science, 16(2), 237-245.
Halpern, J. (1978). Finding minimal enter-median onvex ombination (Cent-Dian) of a Graph. Management Science, 24(5), 535-544.
Hooker, J. N., Garfinkel, R. S., & Chen, C. K. (1991). Finite ominating sets for network location problems. Operations Research, 39(1), 100-118.
Hochbaum, D. S., & Pathria, A. (1998). Locating centers in a dynamically changing network and related problems. Location Science, 6, 243–256.
Halpern, J. (1980). Duality in the ent-ian of a raph. Operations Research, 28(3), 722-735.
Jia, H., Ordonez, F., Dessouky, M. (2007). A modeling framework for facility location of medical services for large-scale emergencies. IIE Transactions, 39, 41-55.
Paluzzi, M. (2004). Testing a heuristic P-median location allocation model for siting emergency service facilities. presented at the Annual Meeting of the Association of American Geographers, Philadelphia, PA.
Perez-Brito, D., Moreno-Perez, J. A., & Rodriguez-Martin, I. (1997). Finite Dominating Set for the p-Facility Cent-Dian Network Location Problem. Studies in Location Analysis, 11, 27-40.
Perez-Brito, D., Moreno-Perez, J. A., & Rodriguez-Martin, I. (1998). The 2-facility centdian network problem. Location Science, 1998. 6, 369-381.
Mirchandani, P. B. (1987). Generalized hierarchical facility location. Transportation Science, 21, 123-125.
Mirchandani, P. B. (1980). Locational decisions on stochastic networks. Geographical Analysis, 12, 172-183.
ReVelle, C., & Hogan, K. (1989). The maximum availability location problem. Transportation Science, 23, 192–200.
Salcedo-Sanz, S., Portilla-Figueras, J. A., Ortiz-Garcıia, E. G., Peirez-Bellido, A. M., Thraves, C., Fernandez-Anta, A., & Yao, X. (2008). Optimal switch location in mobile communication networks using hybrid genetic algorithms. Applied Soft Computing, 8, 1486-1497.
Schilling, D.A. (1982). Strategic facility planning. the analysis of options. Decision Sciences, 13, 1-14.
Serra, D., & Marianov, V. (1999). The P-median problem in a changing network: the case of Barcelona, Location Science, 6(1), 383–394.
Storbeck, J. (1989). Slack, natural slack, and location coveting, Socio-Economic Planning Sciences 16(3).
Talwar, M. (2002). Location of rescue helicopters in South Tyrol, presented at the 37th Annual ORSNZ Conference, Auckland, New Zealand.
Tamir, A., Brito, D. P., & Moreno-Perez, J. A. (2003). A Polynomial Algorithm for the p-Centdian Problem on a Tree.
Tien, J. M., El-Tell, K., & Simons, G. (1983). Improved formulations to the hierarchical health facility location-allocation problem, IEEE Transactions in Systems Management and Cybernetics, 13, 1128– 1132.
Toregas, C., Swain, R., ReVelle, C., & Bergman, L. (1971). The location of emergency service facility. Operations Research, 19, 1363–1373.