×

On the conditional \(p\)-median problem. (English) Zbl 0830.90070

Summary: We investigate the conditional \(p\)-median problem. Optimal algorithms for the Euclidean case in the 1-median with several existing facilities are proposed. A general heuristic algorithm for any metric or environment (network or continuous space) is presented. The algorithm is based on solving several \(p\)-median problems.

MSC:

90B35 Deterministic scheduling theory in operations research

Software:

AMPL
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Francis, R. L.; White, J., Facility Layout and Location (1974), Prentice-Hall: Prentice-Hall Englewood Cliffs, NJ
[2] Love, R. F.; Morris, J. G.; Wesolowsky, G. O., Facilities Location, Models and Methods (1988), North-Holland: North-Holland Amsterdam · Zbl 0685.90036
[3] Berman, O., The \(p\) maximal cover—\(p\) partial center problem on networks, Eur. J. Opl Res., 72, 432-442 (1993) · Zbl 0809.90092
[4] Berman, O.; Handler, G.; Einva, D., The zone constrained location problem on a network, Eur. J. Opl Res., 53, 14-24 (1991) · Zbl 0732.90048
[5] Berman, O.; Simchi-Levi, D., Conditional location problems on networks, Transportation Sci., 24, 77-78 (1990) · Zbl 0703.90056
[6] Chen, R., Conditional minimum and minimax location-allocation problems in Euclidean space, Transportation Sci., 22, 157-160 (1988)
[7] Chen, R.; Handler, G. Y., The conditonal p-center in the plane, (Working Paper No. 889/86 (1986), The Israel Institute of Business Research), 14
[8] Drezner, Z., The \(p\)-center problem—heuristic and optimal algorithms, J. Opt Res. Soc., 35, 741-748 (1984) · Zbl 0544.90024
[9] Minieka, E., Conditional centers and medians on a graphs, Networks, 10, 265-272 (1980)
[10] Drezner, Z., Competitive location strategies for two facilities, Regional Sci. Urban Econom., 23, 485-493 (1982)
[11] Drezner, Z.; Zemel, E., Competitive location in the plane, Ann. Ops Res., 40, 173-193 (1992) · Zbl 0787.90044
[12] Hakimi, S. L., On locating new facilities in a competitive environment, Eur. J. Opl Res., 12, 29-35 (1983) · Zbl 0499.90026
[13] Drezner, Z., On the modified one-center model, Mgmt Sci., 27, 848-851 (1981) · Zbl 0462.90027
[14] Drezner, Z., The \(p\)-cover problem, Eur. J. Opl Res., 26, 312-313 (1986) · Zbl 0597.90028
[15] Watson-Gandy, C. D.T., Heuristic procedures for the \(m\)-partial cover problem on the plane, Eur. J. Opl Res., 11, 149-157 (1982) · Zbl 0495.52009
[16] Domschke, W.; Drexl, A., Location and Layout Planning, Lecture notes in Economics and Mathematical Systems, No. 238, 134 (1985)
[17] Drezner, Z., On the conditional \(p\)-center problem, Transportation Sci., 23, 51-53 (1989) · Zbl 0675.90025
[18] Drezner, Z., The planar two-center and two-median problems, Transportation Sci., 18, 351-361 (1984)
[19] Elzinga, D. J.; Hearn, D. W., On stopping rules for facilities location algorithms, IIE Trans., 15, 81-83 (1983)
[20] Weiszfeld, E., Sur le point pour lequel la somme des distances de \(n\) points donnes est minimum, Tohoku Math. J., 43, 335-386 (1937) · Zbl 0017.18007
[21] Drezner, Z., A note on the Weber location problem, Ann. Ops Res., 40, 153-161 (1992) · Zbl 0787.90042
[22] Love, R. F.; Yeong, W. Y., A stopping rule for facilities location algorithms, AIIE Trans., 13, 357-362 (1981)
[23] Jeul, H., On a rational stopping rule for facilities location algorithms, Naval Res. logist. Q., 31, 9-11 (1984)
[24] Dowling, P. D.; Love, R. F., Bounding methods for facilities location algorithms, Naval Res. logist. Q., 33, 775-787 (1986) · Zbl 0614.90052
[25] Love, R. F.; Dowling, P. D., A new bounding method for single facility location models, (Presented at the ISOLDE IV Conference. Presented at the ISOLDE IV Conference, Namur, Belgium (1987)) · Zbl 0707.90069
[26] Okabe, A.; Boots, B.; Sugihara, K., Spatial Tessellations—Concepts and Applications of Voronoi Diagrams (1992), John Wiley & Sons: John Wiley & Sons Chichester, U.K · Zbl 0877.52010
[27] Fourer, R.; Gay, D. M.; Kernighan, B. W., AMPL A Modeling Language for Mathematical Programming (1993), The Scientific Press: The Scientific Press South San Francisco
[28] Drezner, T., Locating a single new facility among existing, unequally attractive facilities, J. Regional Sci., 34, 237-252 (1994)
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.