Solution of location problems with radial cost functions

✍ Scribed by Reuven Chen

• Publisher: Elsevier Science
• Year: 1984
• Tongue: English
• Weight: 588 KB
• Volume: 10
• Category: Article
• ISSN: 0898-1221
• DOI: 10.1016/0898-1221(84)90089-0

✦ Synopsis

The solution of the Cooper location problem min 2 w,r," where r, is the radial (Euclidean) distance between the ith given location (a,, hi) and the center (x, y) to be located is further investigated. The iterative method 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 ; +XrJ where 4i are non-decreasing functions of the Euclidean distances. The method is also extended to solve similar problems in EK 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 rn$ ,g,exp(awy,-C)

which is a different member of the Katz class of problems, are also presented.