×

Public facility location using dispersion, population, and equity criteria. (English) Zbl 1304.90119

Summary: From a practical perspective, the paper demonstrates that the appropriate use of dispersion, population, and equity criteria can lead to fairly good solutions with respect to the \(p\)-median objective. The only stipulation is that the decision maker verifies (through simple constraint checks) that the chosen locations meet the dispersion, population, and equity criteria. An empirical investigation is conducted to obtain appropriate values for these parameters. From a location science perspective, a new location model that accounts for equity and efficiency simultaneously is studied and analyzed. Specifically, the \(p\)-maxian problem with side constraints on dispersion, population, and equity is developed, its NP-completeness established, and valid inequalities and bounds derived. Computational tests show encouraging results.

MSC:

90B80 Discrete location and assignment
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Antunes, A. P., Location analysis helps manage solid waste in central Portugal, Interfaces, 29, 4, 32-43 (1999)
[2] Avella, P.; Benati, S.; Martinez, L. C.; Dalby, K., Some personal views of the current state and the future of locational analysis, European Journal of Operational Research, 104, 2, 269-287 (1998) · Zbl 0955.90061
[3] Batta, R.; Leifer, L. A., On the accuracy of demand point solutions to the planar, manhattan metric, p-median problem, with and without barriers to travel, Computers & Operations Research, 15, 3, 253-262 (1988) · Zbl 0638.90033
[4] Berman, O.; Huang, R., The minimum weighted covering location problem with distance constraints, Computers & Operations Research, 35, 2, 356-372 (2008) · Zbl 1141.90022
[6] Brandeau, M. L.; Chiu, S. S., An overview of representative problems in location research, Management Science, 31, 6, 645-674 (1989) · Zbl 0669.90040
[7] Burkey, M. L.; Bhadury, J.; Eiselt, H. A., A location-based comparison of health care services in four US states with efficiency and equity, Socio-Economic Planning Sciences, 46, 2, 157-163 (2012)
[8] Carling, K.; Han, M.; Hakansson, J., Does euclidean distance work well when the p-median model is applied in rural areas?, Annals of Operations Research, 201, 83-97 (2012) · Zbl 1260.90120
[9] Carson, Y. M.; Batta, R., Locating an ambulance on the amherst campus of the state University of New York at Buffalo, Interfaces, 20, 5, 43-49 (1990)
[10] Cheng, Y.; Kang, L., The p-maxian problem on interval graphs, Discrete Applied Mathematics, 158, 18, 1986-1993 (2010) · Zbl 1215.05182
[11] Church, R. L., The planar maximal covering location problem, Journal of Regional Science, 24, 185-201 (1984)
[12] Church, R. L.; Garfinkel, R. S., Locating an obnoxious facility on a network, Transportation Science, 12, 107-118 (1978)
[13] Church, R. L.; Meadows, M. E., Location modeling using maximum service distance criteria, Geographical Analysis, 11, 358-373 (1979)
[14] Church, R. L.; ReVelle, C., The maximal covering location problem, Papers in Regional Science Association, 32, 101-118 (1974)
[15] Daskin, M. S., What you should know about location modeling, Naval Research Logistics, 55, 283-294 (2008) · Zbl 1153.90482
[16] Dearing, P. M.; Francis, R. L.; Lowe, T. J., Convex location problems on tree networks, Operations Research, 24, 628-642 (1976) · Zbl 0341.90042
[18] Eaton, D. J.; Daskin, M. S.; Simmons, D. S.; Bulloch, B.; Jansma, G., Determining emergency medical service vehicle deployment in Austin, Texas, Interfaces, 15, 1, 96-108 (1985)
[19] Erdemir, E. T.; Batta, R.; Spielman, S.; Rogerson, P.; Blatt, A.; Flanigan, M., Evaluating the performance of aeromedical base locations of New Mexico by considering nodal and path demand, Accident Analysis and Prevention, 40, 1105-1114 (2008)
[20] Erkut, E.; Baptie, T.; Hohenbalken, B. V., The discrete p-maxian location problem, Computers & Operations Research, 17, 51-61 (1990) · Zbl 0682.90038
[21] Erkut, E.; Francis, R. L.; Lowe, T. J., A multimedian problem with interdistance constraints, Environment and Planning B: Planning and Design, 15, 181-190 (1988)
[22] Erkut, E.; Francis, R. L.; Tamir, A., Distance-constrained multifacility minimax location problems on tree networks, Networks, 22, 37-54 (1992) · Zbl 0751.90043
[23] Erkut, E.; Neuman, S., Analytical models for locating undesirable facilities, European Journal of Operational Research, 40, 275-291 (1989) · Zbl 0668.90025
[24] Farahani, R. Z.; Seifi, M. S.; Asgari, N., Multiple criteria facility location problems: A survey, Applied Mathematical Modelling, 34, 7, 1689-1709 (2010) · Zbl 1193.90143
[25] Francis, R. L.; Lowe, T. J.; Ratliff, H. D., Distance constraints for tree network multifacility location problems, Operations Research, 26, 570-596 (1978) · Zbl 0385.90112
[26] Francis, R. L.; Lowe, T. J.; Tamir, A., Demand point aggregation for location models, (Drezner, Z.; Hamacher, H., Facility location: Application and theory (2004), Springer Verlag) · Zbl 1065.90053
[27] Hakimi, S. L., Optimum distribution of switching centers and the absolute centers and medians of a graph, Operations Research, 12, 450-459 (1964) · Zbl 0123.00305
[28] Hale, T. S.; Maberg, C. R., Location science research: A review, Annals of Operations Research, 123, 21-35 (2003) · Zbl 1137.90598
[29] Hansen, P.; Moon, D., Dispersing Facilities on a Network, RRR #52-88, RUTCOR (1988), Rutgers University
[30] Kuby, M. J., Programming models for facility dispersion: The p-dispersion and maxisum dispersion problems, Geographical Analysis, 19, 315-329 (1987)
[31] Kuby, M.; Lim, S.; Upchurch, C., Dispersion of nodes added to a network, Geographical Analysis, 37, 383-409 (2005)
[32] Larson, R. C., A hypercube queuing model for facility location and redistricting in urban emergency services, Computers & Operations Research, 1, 67-95 (1974)
[33] Larson, R. C.; Odoni, A. R., Urban operations research (1981), Prentice-Hall: Prentice-Hall Englewood Cliffs, NJ
[34] Larson, R. C.; Stevenson, K. A., On insensitivities in urban redistricting and facility location, Operations Research, 20, 595-612 (1972) · Zbl 0238.60088
[35] Love, R. F.; Walker, J., An empirical comparison of block and round norms for modeling actual distances, Location Science, 2, 21-43 (1994) · Zbl 0926.90056
[36] McAllister, D. A., Equity and efficiency in public facility location, Geographical Analysis, 8, 47-63 (1976)
[37] Mehrez, A.; Sinuany-Stern, Z.; Arad-Geva, T.; Binyamin, S., On the implementation of quantitative facility location models: The case of a hospital in a rural region, The Journal of the Operational Research Society, 47, 612-625 (1996)
[38] Minieka, E., Anticenters and antimedians of a network, Networks, 13, 359-364 (1983)
[39] Moon, I. D.; Chaudhry, S. S., An analysis of network location problems with distance constraints, Management Science, 30, 290-307 (1984) · Zbl 0553.90034
[40] Murray, A. T.; Church, R. L.; Gerrard, R. A.; Tsui, W., Impact models for siting undesirable facilities, Papers in Regional Science, 77, 19-36 (1999)
[42] Owen, S.; Daskin, M. S., Strategic facility location: A review, European Journal of Operational Research, 111, 423-447 (1998) · Zbl 0938.90048
[43] Price, W. L.; Turcotte, M., Relocation of the red cross blood donor clinic and transfusion center in quebec city, Interfaces, 16, 17-26 (1986)
[44] Rawls, C. G.; Turnquist, M. A., Pre-positioning of emergency supplies for disaster response, Transportation Research Part B: Methodological, 44, 4, 521-534 (2010)
[45] ReVelle, C. S.; Eiselt, H. A., Location analysis: A synthesis and survey, European Journal of Operational Research, 165, 1-19 (2005) · Zbl 1112.90362
[46] Rosing, K. E.; Hodgson, M. J., Heuristic concentration for the p-median: An example demonstrating how and why it works, Computers & Operations Research, 29, 10, 1317-1330 (2002) · Zbl 0994.90113
[47] Rosing, K. E.; ReVelle, C. S., Heuristic concentration: Two stage solution construction, European Journal of Operational Research, 97, 1, 75-86 (1997) · Zbl 0923.90107
[48] Schobel, A.; Hamacher, H. W.; Liebers, A.; Wagner, D., The continuous stop location problem in public transportation networks, Asia-Pacific Journal of Operational Research, 26, 13-30 (2009) · Zbl 1177.90253
[50] Tamir, A., Obnoxious facility location on graphs, SIAM Journal on Discrete Mathematics, 4, 550-567 (1991) · Zbl 0737.05063
[51] Teitz, M. B.; Bart, P., Heuristic methods for estimating the generalized vertex median of a weighted graph, Operations Research, 16, 955-961 (1968) · Zbl 0165.22804
[52] Ting, S. S., A linear time algorithm for maxisum facility location on tree networks, Transportation Science, 18, 76-84 (1984)
[53] Toregas, C.; ReVelle, C., Optimal location under time or distance constraints, Papers of the Regional Science Association, 28, 133-144 (1972)
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.