The three-dimensional Fermat-Weber problem with Tchebychev distances
نویسندگان
چکیده
The three-dimensional Fermat-Weber facility location problem with Tchebychev distances is investigated. Expanding on previous research for the analogous two-dimensional problem, this study presents a new algorithm for solving the elusive three-dimensional case. The algorithm presented herein finds near optimal solutions in practical computational times. Some experimental results are also conveyed. AMS Mathematics Subject Classification: 90B85
منابع مشابه
The Fermat-Torricelli problem in normed planes and spaces
The famous Fermat-Torricelli problem (in Location Science also called the Steiner-Weber problem) asks for the unique point x minimizing the sum of distances to arbitrarily given points x1, . . . ,xn in Euclidean d-dimensional space R. In the present paper, we will consider the extension of this problem to d-dimensional real normed spaces (= Minkowski spaces), where we investigate mainly, but no...
متن کاملA projected Weiszfeld algorithm for the box-constrained Weber location problem
The Fermat-Weber problem consists in finding a point in R that minimizes the weighted sum of distances from m points in R that are not collinear. An application that motivated this problem is the optimal location of industries in the 2-dimensional case. The Weber problem is a generalization of the well-known Fermat problem. An usual method to solve the Weber problem, proposed by Weiszfeld in 19...
متن کاملAdaptation of the Probability Changing Method for Weber Problem with an Arbitrary Metric
Fermat-Weber problem in its simple form (unconstrained, single facility, Euclidean metric) is well investigated. Lot of algorithms are also developed for more complicated cases. But the generalized multi-facility problem with barriers, restricted zones and an arbitrary metric has no well-known algorithm for its solving. In this paper, we consider the planar multi-facility Weber problem with res...
متن کاملA Heuristic Algorithm for Constrain Single-Source Problem with Constrained Customers
The Fermat-Weber location problem is to find a point in R that minimizes the sum of the weighted Euclidean distances from m given points in R. In this paper we consider the Fermat-Weber problem of one new facilitiy with respect to n unknown customers in order to minimizing the sum of transportation costs between this facility and the customers. We assumed that each customer is located in a none...
متن کاملar X iv : c s . C G / 0 31 00 27 v 1 1 5 O ct 2 00 3 On the Continuous Fermat - Weber Problem ∗
We give the first exact algorithmic study of facility location problems that deal with finding a median for a continuum of demand points. In particular, we consider versions of the “continuous k-median (Fermat-Weber) problem” where the goal is to select one or more center points that minimize the average distance to a set of points in a demand region. In such problems, the average is computed a...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2006