THE GENERAL ONE-CENTER LOCATION PROBLEM

• 成果类型: Article
• 署名作者: DURIER, R
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.20.2.400
• 发表日期: 1995
• 页码: 400-414
• 关键词: fermat-weber problem

摘要

The general one center location problem deals with the location of a point in a real normed space X in order to minimize an objective function G which depends on the distances to a finite number of centers and on initial costs. The function G is defined by G(x) = gamma(c(1) + w(1) parallel to x - a(1) parallel to,...,c(n) + w(n) parallel to x - a(n) parallel to), where a(1),...,a(n) are n given points in X, W-1,...,W-n are positive numbers, c(1),..., c(n) are nonnegative initial costs and gamma is a monotone norm on R(n). A geometrical description of the set of optimal solutions to the problem min(x is an element of X)G(x) is provided. The peculiar role of the minisum problem, where gamma is the l(1)-norm, is emphasized and the minimax problem, where gamma is the l(x)-norm, is used to illustrate the general geometrical description.