×

The location of ambivalent facilities: Use of a quadratic zero-one programming algorithm. (English) Zbl 0828.90070

Summary: Ambivalent facilities are defined here as facilities that have undesirable or obnoxious properties, such as the generation of noise or pollution, in addition to the desirable properties for which they were chosen. The problem studied is that of finding the site or sites on a discrete set of rectangular grid positions for a small number of these facilities (which need not all be of the same type) among other facilities that are sensitive to the undesirable properties. The criterion used is that of maximizing the minimum Euclidean distance between any ambivalent-sensitive pair. The existence of exclusion zones and the possible requirement of a minimum tolerable distance between facilities are easily modelled. An original, data-structural computer implementation of Hansen’s quadratic zero-one programming algorithm has successfully been used to solve a series of test problems containing up to 100-200 sensitive locations with grid resolutions up to \(1023\times 1023\). The results are reported here.

MSC:

90B80 Discrete location and assignment
90C09 Boolean programming

Software:

QUAD01
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Erkut, E.; Neuman, S., Analytical models for locating undesirable facilities, Eur. J. Opl. Res., 40, 3, 275-291 (1989) · Zbl 0668.90025
[2] Melachrinoudis, E., Determining an optimum location for an undesirable facility in a workroom environment, Appl. Math. Modelling, 9, 5, 365-369 (1985) · Zbl 0605.90047
[3] Mehrez, A.; Sinauny-Stern, Z.; Stulman, A., J. Opl. Res. Soc., 43, 4, 373-374 (1992), Minor corrections by the authors in
[4] Appa, G.; Giannikos, I., A good enhancement with logical weaknesses, J. Opl. Res. Soc., 44, 1, 103-106 (1993), [Commenting on Ref. 3]
[5] Moon, I. D.; Papayanopoulos, L., Minimax location of two facilities with minimum separation: interactive graphical solutions, J. Opl. Res. Soc., 42, 8, 685-694 (1991) · Zbl 0737.90038
[6] Karkazis, J.; Papadimitriou, C., A branch-and-bound algorithm for the location of facilities causing atmospheric pollution, Eur. J. Opl. Res., 58, 3, 363-373 (1992) · Zbl 0760.90066
[7] Hansen, P., Quadratic zero-one programming by implicit enumeration, (Lootsma, F. A., Numerical Methods for Non-Linear Optimization (1972), Academic Press: Academic Press London), 265-278
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.