Facility Location Problems in the presence of Two-Circular Forbidden Regions with Euclidean Distance Norm (original) (raw)

Improved algorithms for placing undesirable facilities

Computers & Operations Research, 2002

We improve several existing algorithms for determining the location of one or more undesirable facilities amidst a set P of n demand points, under various constraints and distance functions. We assume that the demand points reside within some given bounded region R. Applying concepts and techniques from Computational Geometry, we provide e cient algorithms for the following problems:

Nonlinear Programming Model for the Facility Location Problem in the Presence of Arc-Shaped Barrier

In this paper we consider the single facility location problem with respect to a given set of existing facilities in the presence of an arc-shaped barrier. A barrier is considered a region where neither facility location nor travelling is permitted. We present a mixed-integer nonlinear programming model for this single facility location problem. The objective of this problem is to locate this single facility such that the sum of the rectilinear distances from the facility to the demand points is minimized. Test problems are presented to illustrate the applicability of the proposed model.

Obstacle Avoidance and Travel Path Determination in Facility Location Planning

2009

This research finds a solution methodology for determining optimal travel path to and from existing facilities and corresponding location of a new facility having physical flow interaction between them in different degrees translated into associated weights, in presence of barriers impeding the shortest flow-path involving straight-line distance metric. The proposed methodology considers all types of quadrilateral barriers or forbidden region configurations to generalize, to bypass these obstacles, and adopts a scheme of searching through the vertices of these quadrilaterals to determine the alternative shortest flow-path for optimal location of facilities based on weighted-distance computation algorithm with minimum summation or mini-sum objective. Congruence testing has been carried out for reconfiguring complex obstacle geometry as an equivalent quadrilateral. This procedure of obstacle avoidance is completely new. Software, DANSORK, has been developed to facilitate computations for the new search algorithm and test results have been presented based on computations using this software.

The single facility location problem with minimum distance constraints

Location Science, 1997

We consider the problem of locating a single facility (server) in the plane, where the location of the facility is restricted to be outside a specified forbidden region (neighborhood) around each demand point. Two models are discussed. In the restricted l-median model, the objective is to minimize the sum of the weighted rectilinear distances from the n customers to the facility. We present an O(n log n) algorithm for this model, improving upon the O(n") complexity bound of the algorithm by Brimberg and Wesolowsky (1995). In the restricted l-center model the objective is to minimize the maximum of the weighted rectilinear distances between the customers and the serving facility. We present an O(n logn) algorithm for finding an optimal i-center. We also discuss some related models, involving the Euclidean norm.

A general model for the undesirable single facility location problem

2006

In this paper, a finite set in which an optimal solution for a general Euclidean problem of locating an undesirable facility in a polygonal region, is determined and can be found in polynomial time. The general problem we propose leads us, among others, to several well-known problems such as the maxisum, maximin, anticentdian or r-anticentrum problem.

On a specific method to solve semi-obnoxious continuous facility location problems

2010

Locating a semi-obnoxious facility, like an airport or correctional center is typically a bi-criterion problem combining a convex objective function representing minimum transportation cost with a multi-extremal objective function representing the non-desirable part of the facility. Generic one or bi-objective heuristic methods can be applied to generate efficient locations for the problem. We consider the location of one facility in the plane and show that a simple random or grid search with filtering already provides a very good picture of the trade-off between the two objectives. Moreover, we argue that instead of using bi-criterion meta-heuristics, one could better exploit the convex-nonconvex structure of the problem applying the constraint method. We show how to evaluate the methods systematically using several heuristics from literature.

Optimal Facility Location Under Various Distance Functions

International Journal of Computational Geometry & Applications, 2000

We present efficient algorithms for two problems of facility location. In both problems we want to determine the location of a single facility with respect to n given sites. In the first we seek a location that maximizes a weighted distance function between the facility and the sites, and in the second we find a location that minimizes the sum (or sum of the squares) of the distances of k of the sites from the facility.

A Stable Algorithm for Solving the Multifacility Location Problem Involving Euclidean Distances

SIAM Journal on Scientific and Statistical Computing, 1980

There is a rapidly growing interdisciplinary interest in the application of location models to real life problems. Unfortunately, the current methods used to solve the most popular minisum and minimax location problems are computationally inadequate. A more unified and numerically stable approach for solving these problems is proposed. Detailed analysis is done for the linearly constrained Euclidean distance minisum problem for facilities located in a plane. Preliminary computational experience suggests that this approach compares favourably with other methods. Key words, continuous location problems, nonsmooth optimization, numerical linear algebra *Received by the editors March 24, 1980. This work was supported in part by NSERC Grant No. A8639. This paper was typeset at the University of Waterloo using the Troff software developed for the Unix operating system. Final copy was produced on a Photon Econosetter.

Solving multifacility location problems involving Euclidean distances

Naval Research Logistics …, 1980

This paper considers the problem of locating multiple new facilities in order to minimize a total cost function consisting of the sum of weighted Euclidean distances among the new facilities and between the new and existing facilities, the locations of which are known. A new ...