![](/images/graphics-bg.png)
Noniterative Solution of Some Fermat-Weber Location Problems
Author
Source
Advances in Operations Research
Issue
Vol. 2011, Issue 2011 (31 Dec. 2011), pp.1-10, 10 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2011-07-18
Country of Publication
Egypt
No. of Pages
10
Main Subjects
Information Technology and Computer Science
Abstract EN
The Fermat-Weber problem of optimally locating a service facility in the Euclidean continuous two-dimensional space is usually solved by the iterative process first suggested by Weiszfeld or by later versions thereof.
The methods are usually rather efficient, but exceptional problems are described in the literature in which the iterative solution is exceedingly long.
These problems are such that the solution either coincides with one of the demand points or nearly coincides with it.
We describe a noniterative direct alternative, based on the insight that the gradient components of the individual demand points can be considered as pooling forces with respect to the solution point.
It is demonstrated that symmetrical problems can thus be optimally solved with no iterations, in analogy to finding the equilibrium point in statics.
These include a well-known ill-conditioned problem and its variants, which can now be easily solved to optimality using geometrical considerations.
American Psychological Association (APA)
Chen, Reuven. 2011. Noniterative Solution of Some Fermat-Weber Location Problems. Advances in Operations Research،Vol. 2011, no. 2011, pp.1-10.
https://search.emarefa.net/detail/BIM-467413
Modern Language Association (MLA)
Chen, Reuven. Noniterative Solution of Some Fermat-Weber Location Problems. Advances in Operations Research No. 2011 (2011), pp.1-10.
https://search.emarefa.net/detail/BIM-467413
American Medical Association (AMA)
Chen, Reuven. Noniterative Solution of Some Fermat-Weber Location Problems. Advances in Operations Research. 2011. Vol. 2011, no. 2011, pp.1-10.
https://search.emarefa.net/detail/BIM-467413
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-467413