Abstract
The solution of the Cooper location problem min ▪ where r i is the radial (Euclidean) distance between the ith given location ( a i , b i and the center ( x, y) to be located is further investigated. The iterative mehtod given by Cooper (which includes the well known Weiszfeld procedure for n = 1) was previously amended using semi-intuitive arguments. In the present work a better proof is offered for the results given before. Furthermore, using the same line of argument, a broader group of problems previously mentioned by Katz and others can be efficiently solved. These are the problems min ▪ where ψ i are non-decreasing functions of the Euclidean distances. The method is also extended to solve similar problems in E K with K> 2. Apart from the theoretical account, computational experience is reported for the three dimensional Cooper problem with differet values of n. Computational results of the min ▪ which is a different member of the Katz class of problems, are also presented.
Published Version
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