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Facility location models for distribution system design
, 2004
"... The design of the distribution system is a strategic issue for almost every company. The problem of locating facilities and allocating customers covers the core topics of distribution system design. Model formulations and solution algorithms which address the issue vary widely in terms of fundamenta ..."
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Cited by 33 (0 self)
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The design of the distribution system is a strategic issue for almost every company. The problem of locating facilities and allocating customers covers the core topics of distribution system design. Model formulations and solution algorithms which address the issue vary widely in terms of fundamental assumptions, mathematical complexity and computational performance. This paper reviews some of the contributions to the current stateoftheart. In particular, continuous location models, network location models, mixedinteger programming models, and applications are summarized.
Discrete Facility Location and Routing of Obnoxious Activities
, 2000
"... The problem of simultaneously locating obnoxious facilities and routing obnoxious materials between a set of builtup areas and the facilities is addressed. Obnoxious facilities are those facilities which cause nuisance to people as well as to the environment i.e. dump sites, chemical industrial pla ..."
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Cited by 15 (2 self)
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The problem of simultaneously locating obnoxious facilities and routing obnoxious materials between a set of builtup areas and the facilities is addressed. Obnoxious facilities are those facilities which cause nuisance to people as well as to the environment i.e. dump sites, chemical industrial plants, electric power supplier networks, nuclear reactors and so on. A discrete combined locationrouting model, which we refer to as Obnoxious Facility Location and Routing model (OFLR), is defined. OFLR is a NPhard problem for which a Lagrangean heuristic approach is presented. The Lagrangean relaxation proposed allows to decompose OFLR into a Location subproblem and a Routing subproblem; such subproblems are then strenghtened by adding suitable inequalities. Based on this Lagrangean relaxation two simple Lagrangean heuristics are provided. An effective Branch and Bound algorithm is then presented, which aims at reducing the gap between the above mentioned lower and upper bounds. Our Bran...
A Survey on Obnoxious Facility Location Problems
, 1999
"... Obnoxious location models are models in which customers no longer consider the facility desirable and try to have it as close as possible to their own location, but instead avoid the facility and stay away from it. Typical applications are optimal locations of nuclear reactors, garbage dumps, or wa ..."
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Cited by 13 (0 self)
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Obnoxious location models are models in which customers no longer consider the facility desirable and try to have it as close as possible to their own location, but instead avoid the facility and stay away from it. Typical applications are optimal locations of nuclear reactors, garbage dumps, or water purication plants. This work presents a survey of mathematical models for undesirable location problems in the plane and particularly on networks; solution procedures are briey described. A brief review of extensive (obnoxious) facility location problems in networks is also given. Finally critical aspects of existing models are identied and some directions for future search are suggested. Keywords: survey, obnoxious, undesirable, location. Dipartimento di Elettronica ed Informazione, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milano, Italy 1 1 Introduction One of the main objectives we attempt to achieve with this survey on Undesirable Facilities Location is ...
Approximation Algorithms for Dispersion Problems
, 2001
"... Dispersion problems involve arranging a set of points as far away from each other as possible. They have numerous applications in the location of facilities and in management decision science. We suggest a simple formalism which lets us describe different dispersal problems in a uniform way. We p ..."
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Cited by 9 (0 self)
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Dispersion problems involve arranging a set of points as far away from each other as possible. They have numerous applications in the location of facilities and in management decision science. We suggest a simple formalism which lets us describe different dispersal problems in a uniform way. We present several algorithms and hardness results for dispersion problems using different natural measures of remoteness, some of which have been studied previously in the literature and others which we introduce; in particular, we give the rst algorithm with a nontrivial performance guarantee for the problem of locating a set of points such that the sum of their distances to their nearest neighbor in the set is maximized.
Compact Location Problems
 Th. Comp. Sci
, 1996
"... We consider the problem of placing a specified number (p) of facilities on the nodes of a network so as to minimize some measure of the distances between facilities. This type of problem models a number of problems arising in facility location, statistical clustering, pattern recognition, and pro ..."
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Cited by 5 (1 self)
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We consider the problem of placing a specified number (p) of facilities on the nodes of a network so as to minimize some measure of the distances between facilities. This type of problem models a number of problems arising in facility location, statistical clustering, pattern recognition, and processor allocation problems in multiprocessor systems. We consider the problem under three different objectives, namely minimizing the diameter, minimizing the average distance, and minimizing the variance. We observe that in general, the problem is NPhard under any of the objectives. Further, even obtaining a constant factor approximation for any of the objectives is NPhard. We present a general framework for obtaining nearoptimal solutions to the compact location problems for the above measures, when the distances satisfy the triangle inequality. We show that this framework can be extended to the case when there are also node weights. Further, we investigate the complexity and ap...
Facility Dispersion and Remote Subgraphs
"... Dispersion problems involve arranging a set of points as far away from each other as possible. They have numerous applications in the location of facilities and in management decision science. We present several algorithms and hardness results for dispersion problems using different natural measures ..."
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Cited by 4 (0 self)
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Dispersion problems involve arranging a set of points as far away from each other as possible. They have numerous applications in the location of facilities and in management decision science. We present several algorithms and hardness results for dispersion problems using different natural measures of remoteness, some of which have been studied previously in the literature and others which we introduce; in particular, we give the first algorithm with a nontrivial performance guarantee for the problem of locating a set of points such that the sum of their distances to their nearest neighbor in the set is maximized.
Finding Subsets Maximizing Minimum Structures
, 1995
"... We consider the problem of finding a set of k vertices in a graph that are in some sense remote, stated more formally: "Given a graph G and an integer k, and a set P of k vertices for which the total weight of a minimum structure on P is maximized." In particular, we are interested in three problems ..."
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Cited by 3 (1 self)
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We consider the problem of finding a set of k vertices in a graph that are in some sense remote, stated more formally: "Given a graph G and an integer k, and a set P of k vertices for which the total weight of a minimum structure on P is maximized." In particular, we are interested in three problems of this type, where the structure to be minimized is a Spanning Tree (RemoteMST), Steiner Tree (RemoteST), or Traveling Salesperson tour (RemoteTSP). We give a natural greedy approximation algorithm that simultaneously approximates all three problems on metric graphs. For instance, its performance ratio for RemoteMST is exactly 4, while it is NP hard to approximate within a factor of less than 2. We also show a better approximation for graphs induced by Euclidean points in the plane, give an exact algorithm for graphs whose distances correspond to shortestpath distances in a tree, and give hardness and approximability results for general nonmetric graphs.
Embedding a Bundle Method in a Branch and Bound Framework: an ApplicationOriented Development
, 2000
"... An eective Branch and Bound algorithm based on Lagrangean heuristic is presented, which aims at reducing the gap between the lower and upper bounds. The Branch and Bound method proposed exploits the information gathered while going down in the enumeration tree in order to solve eciently the subprobl ..."
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Cited by 2 (1 self)
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An eective Branch and Bound algorithm based on Lagrangean heuristic is presented, which aims at reducing the gap between the lower and upper bounds. The Branch and Bound method proposed exploits the information gathered while going down in the enumeration tree in order to solve eciently the subproblems related to other nodes. This is accomplished by using a bundle method to solve at each node the Lagrangean dual. A discrete combined locationrouting model, which we refer to as Obnoxious Facility Location and Routing model (OFLR), is used as a benchmark to validate the eciency of the method proposed. Such model simultaneously locates obnoxious facilities and routes obnoxious materials between a set of builtup areas and the facilities. Obnoxious facilities are those facilities which cause nuisance to people as well as to the environment i.e. dump sites, chemical industrial plants, electric power supplier networks, nuclear reactors and so on. OFLR is a particular case of the Obnoxious...
Discrete Location Problems With PushPull Objectives
, 1999
"... The models within Operational Research concerned with locational decisions mostly either consider only the positive effects, pulling the facilities towards demand, or only negative eects, pushing the facilities away from the places affected by the facilities nearness. In real world situations both o ..."
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Cited by 2 (0 self)
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The models within Operational Research concerned with locational decisions mostly either consider only the positive effects, pulling the facilities towards demand, or only negative eects, pushing the facilities away from the places affected by the facilities nearness. In real world situations both of these opposing forces are at work. We give an overview of a number of pushpull models, yielding alternative ways to incorporate both types of eects simultaneously. The discussion is restricted to models of combinatorial optimisation and includes indications of reduction to standard models and/or algorithmic approaches where possible.