The obnoxious facilities planar p-median problem (original) (raw)
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Results of a New Approach to Solving the p-Median Problem with Maximum Distance Constraints
Geographical Analysis, 2010
Results of a New Approach to Solving the p-Median Problem with Maximum Distance Constraints Considerable interest has been directed in the past to developing approaches for solving the p-median problem with maximum distance Constraints. All culrent solution techniques consider potential facilities to be located only at nodes of the network. This paper deals with the solution of this problem under the condition where facility placement is not restricted to nodes. The examples given show that improvement in weighted distance can be obtained by solving the unrestricted site problem. In addition, feasible solutions can be obtained for smaller numbers of facilities than possible by all nodal facility placement.
Obnoxious Facility Location: The Case of Weighted Demand Points
Journal of the Operations Research Society of Japan
The problem considered in this paper is the weighted obnoxious facility location in the convex hull of demand points. The objective function is to maximize the smallest weighted distance between a facility and a set of demand points. Three new global optimal solution approaches are proposed. Two variants of the "Big Triangle Small Triangle" global optimization method, and a procedure based on intersection points between Apollonius circles. We also compared the results with a multi-start approach using the non-linear multipurpose software SNOPT. Problems with 1,000 demand points are exactly solved in a fraction of a second of computer time.
Improved starting solutions for the planar p-median problem
Yugoslav Journal of Operations Research, 2020
In this paper we present two new approaches for finding good starting solutions to the planar p-median problem. Both methods rely on a discrete approximation of the continuous model that restricts the facility locations to the given set of demand points. The first method adapts the first phase of a greedy random construction algorithm proposed for the minimum sum of squares clustering problem. The second one implements a simple descent procedure based on vertex exchange. The resulting solution is then used as a starting point in a local search heuristic that iterates between the well-known Cooper?s alternating locate-allocate method and a transfer follow-up step with a new and more effective selection rule. Extensive computational experiments show that (1) using good starting solutions can significantly improve the performance of local search, and (2) using a hybrid algorithm that combines good starting solutions with a \deep" local search can be an effective strategy for solvi...
Journal of the Operations Research Society of Japan, 2007
The criteria used in location analysis have to be chosen according to the character ofthe facllity, The single facility location models addressed ln this paper accommodate simultaneous multiple criteria in a continuous space in the framework of ordered median problems, which generate and unify many standard location problems. We demonstrate that too]s of computational geometry such as Vbronoi diagrams and arrangements of eurves and lines, enable us to identify the entire set of Pareto-optimal locations, when the squared Euclidean distances between the facility and affected inhabitants are used. For two objectives this works for any type of ordered mediall objectives and any polygonally bounded feasible region. When more than two criteria are present the objectives and the feasible Tegion have to be convex. For the analysis of this last case we extend several recent st･ructural results for unconstrained convex vector optimization to a convex and compact constraint, Our findings are iUustrated by seveTal exarnples.
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:
Journal of Automation, Mobile Robotics and Intelligent Systems, 2014
The paper introduces the bi-partial version of the well known p-median or p-center facility location problem. The bi-partial approach, developed by the author, primarily to deal with the clustering problems, is shown here to work for a problem that does not possess some of the essential properties, inherent to the bi-partial formulations. It is demonstrated that the classical objective function of the problem can be correctly interpreted in terms of the bi-partial approach, that it possesses the essential properties that are at the core of the bi-partial approach, and, finally, that the general algorithmic precepts of the bi-partial approach can also be applied to this problem. It is proposed that the use of bi-partial approach for similar problems can be beneficial from the point of view of flexibility and interpretation.
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.
Dynamic facility location: The progressive p-median problem
Location Science, 1995
A dynamic p-median problem is considered. Demand is changing over a given time horizon and the facilities are built one at a time at given times. Once a new facility is built, some of the customers will use its services and some of the customers will patronize an existing facility. At any given time, customers patronize the closest facility. The problem is to find the best locations for the new facilities. The problem is formulated and the two facilities case is solved by a special algorithm. The general problem is solved using the standard mathematical programming code AMPL.
A branch-and-price approach to p-median location problems
2005
This paper describes a branch-and-price algorithm for the p-median location problem. The objective is to locate p facilities (medians) such as the sum of the distances from each demand point to its nearest facility is minimized. The traditional column generation process is compared with a stabilized approach that combines the column generation and Lagrangean/surrogate relaxation. The Lagrangean/surrogate multiplier modies the reduced cost criterion, providing the selection of new productive columns at the search tree. Computational experiments are conducted considering especially dicult instances to the traditional column generation and also with some large-scale instances.