TY - JOUR
TI - Noniterative Solution of Some Fermat-Weber Location Problems
VL - 2011
PY - 2011
DA - 2011/07/18
DO - 10.1155/2011/379505
UR - https://doi.org/10.1155/2011/379505
AB - 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.
JF - Advances in Operations Research
SN - 1687-9147
PB - Hindawi Publishing Corporation
SP - 379505
KW -
A2 - Averbakh, I. L.
AU - Chen, Reuven
ER -