Results 1  10
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21
A general approximation technique for constrained forest problems
 SIAM J. COMPUT.
, 1995
"... We present a general approximation technique for a large class of graph problems. Our technique mostly applies to problems of covering, at minimum cost, the vertices of a graph with trees, cycles, or paths satisfying certain requirements. In particular, many basic combinatorial optimization proble ..."
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Cited by 353 (21 self)
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We present a general approximation technique for a large class of graph problems. Our technique mostly applies to problems of covering, at minimum cost, the vertices of a graph with trees, cycles, or paths satisfying certain requirements. In particular, many basic combinatorial optimization problems fit in this framework, including the shortest path, minimumcost spanning tree, minimumweight perfect matching, traveling salesman, and Steiner tree problems. Our technique produces approximation algorithms that run in O(n log n) time and come within a factor of 2 of optimal for most of these problems. For instance, we obtain a 2approximation algorithm for the minimumweight perfect matching problem under the triangle inequality. Our running time of O(n log n) time compares favorably with the best strongly polynomial exact algorithms running in O(n 3) time for dense graphs. A similar result is obtained for the 2matching problem and its variants. We also derive the first approximation algorithms for many NPcomplete problems, including the nonfixed pointtopoint connection problem, the exact path partitioning problem, and complex locationdesign problems. Moreover, for the prizecollecting traveling salesman or Steiner tree problems, we obtain 2approximation algorithms, therefore improving the previously bestknown performance guarantees of 2.5 and 3, respectively [Math. Programming, 59 (1993), pp. 413420].
THE PRIMALDUAL METHOD FOR APPROXIMATION ALGORITHMS AND ITS APPLICATION TO NETWORK DESIGN PROBLEMS
"... The primaldual method is a standard tool in the design of algorithms for combinatorial optimization problems. This chapter shows how the primaldual method can be modified to provide good approximation algorithms for a wide variety of NPhard problems. We concentrate on results from recent researc ..."
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Cited by 120 (7 self)
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The primaldual method is a standard tool in the design of algorithms for combinatorial optimization problems. This chapter shows how the primaldual method can be modified to provide good approximation algorithms for a wide variety of NPhard problems. We concentrate on results from recent research applying the primaldual method to problems in network design.
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.
Branch and infer: a unifying framework for integer and finite domain constraint programming
 INFORMS J. Comput
, 1998
"... We introduce branch and infer, a unifying framework for integer linear programming and finite domain constraint programming. We use this framework to compare the two approaches with respect to their modeling and solving capabilities, to introduce symbolic constraint abstractions into integer program ..."
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Cited by 26 (2 self)
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We introduce branch and infer, a unifying framework for integer linear programming and finite domain constraint programming. We use this framework to compare the two approaches with respect to their modeling and solving capabilities, to introduce symbolic constraint abstractions into integer programming, and to discuss possible combinations of the two approaches. C ombinatorial problems are ubiquitous in many real world applications like scheduling, planning, transportation, assignment, and many others. Besides special purpose algorithms to compute exact or approximate solutions, there exist also general approaches to solve this kind of problem. We are interested here in two such approaches: • Integer linear programming (ILP) • Finite domain constraint programming (CP(FD)) Integer linear programming has a long tradition in operations research and has produced a large number of impressive results during the last 40 years, see for example [37, 30]. Finite domain constraint programming is a promising new approach for solving complex combinatorial problems, which combines recent progress in programming language design, like constraint logic programming[29] or concurrent constraint programming,[42] with efficient constraint solving techniques from mathematics, artificial intelligence, and operations research, see for example [49, 50]. The aim of this paper is to develop a unifying framework for integer linear programming and finite domain constraint programming. On the one hand, we want to clarify the relationship between these two approaches and identify (some of) their strengths and weaknesses. On the other hand, we want to show how each of the two approaches may profit from the other and indicate possible ways towards their integration. This continues our previous work in
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...
Distribution Network Design: New Problems and Related Models
 European Journal of Operational Research
, 2001
"... We study some complex distribution network design problems, which involve facility location, warehousing, transportation and inventory decisions. Several realistic scenarios are investigated. Two kinds of mathematical programming formulations are proposed for all the introduced problems, togethe ..."
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Cited by 14 (0 self)
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We study some complex distribution network design problems, which involve facility location, warehousing, transportation and inventory decisions. Several realistic scenarios are investigated. Two kinds of mathematical programming formulations are proposed for all the introduced problems, together with a proof of their correctness. Some formulations extend models proposed by Perl and Daskin (1985) for some warehouse locationrouting problems; other formulations are based on ow variables and constraints. 1
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 ...
Locationrouting: Issues, models and methods
, 2006
"... This paper is a survey of locationrouting: a relatively new branch of locational analysis that takes into account vehicle routing aspects. We propose a classification scheme and look at a number of problem variants. Both exact and heuristic algorithms are investigated. Finally, some suggestions for ..."
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Cited by 9 (0 self)
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This paper is a survey of locationrouting: a relatively new branch of locational analysis that takes into account vehicle routing aspects. We propose a classification scheme and look at a number of problem variants. Both exact and heuristic algorithms are investigated. Finally, some suggestions for future research are presented.
Strategic, Tactical and Operational Decisions in Multinational Logistics Networks: A Review and Discussion of Modeling Issues
 International Journal of Production Research
, 2000
"... The rapidly developing, worldwide marketplace is leading to the geographical dispersion of production, assembly and distribution operations. This paper deals with three aspects of international logistics networks: strategic, tactical and operational. The strategic level designs the logistics networ ..."
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Cited by 7 (0 self)
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The rapidly developing, worldwide marketplace is leading to the geographical dispersion of production, assembly and distribution operations. This paper deals with three aspects of international logistics networks: strategic, tactical and operational. The strategic level designs the logistics network, including prescribing facility locations, production technologies and plant capacities. The tactical level prescribes material flow management policies, including production levels at all plants, assembly policy, inventory levels, and lot sizes. The operational level schedules operations to assure intime delivery of final products to customers. This paper reviews the literature that deals with strategic, tactical and operational levels and discusses relevant modeling issues.
Facility Location in SUpply Chain Design
, 2003
"... In this chapter we outline the importance of facility location decisions in supply chain design. We begin with a review of classical models including the traditional fixed charge facility location problem. We then summarize more recent research aimed at expanding the context of facility location ..."
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Cited by 5 (2 self)
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In this chapter we outline the importance of facility location decisions in supply chain design. We begin with a review of classical models including the traditional fixed charge facility location problem. We then summarize more recent research aimed at expanding the context of facility location decisions to incorporate additional features of a supply chain including LTL vehicle routing, inventory management, robustness, and reliability.