An efficient algorithm for facility location in the presence of forbidden regions

Butt, Steven E.; Cavalier, Tom M.

doi:10.1016/0377-2217(94)00297-5

Cited by 77 publications

(54 citation statements)

References 17 publications

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“…IPOPT 3.11 is used to solve the formulation to optimality, yielding the solution (−1.186, 2.060) with an objective value of 48.257 as shown in Figure 10. This solution is better than the one found in Katz and Cooper (1981), and same with the solutions given in Butt and Cavalier (1996), Klamroth (2001), Bischoff and Klamroth (2007) and Klamroth (2004). The execution time is 0.234s.…”

Section: Barrier Instancessupporting

confidence: 57%

“…Aneja and Parlar (1994) use the concept of visibility and the Dijkstra algorithm to compute the shortest distance between customer sites and the location of the new facility, using polygons as barriers. Butt and Cavalier (1996) consider the restricted 1-median problem with convex polygonal forbidden regions. They use the Euclidean distance metric and describe an iterative solution procedure.…”

Section: Restricted Problems With Barriersmentioning

confidence: 99%

“…The distance metric is Euclidean. This instance is also studied in various papers, including Butt and Cavalier (1996), Klamroth (2001), Bischoff and Klamroth (2007) and Klamroth (2004).…”

Section: Barrier Instancesmentioning

confidence: 99%

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A modelling framework for solving restricted planar location problems using phi-objects

Oğuz

Bektaş

Bennell

et al. 2016

Journal of the Operational Research Society

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This paper presents a general modelling framework for restricted facility location problems with arbitrarily shaped forbidden regions or barriers, where regions are modelled using phi-objects. Phi-objects are an efficient tool in mathematical modelling of 2D and 3D geometric optimization problems, and are widely used in cutting and packing problems and covering problems. The paper shows that the proposed modelling framework can be applied to both median and centre facility location problems, either with barriers or forbidden regions. The resulting models are either mixed-integer linear or non-linear programming formulations, depending on the shape of the restricted region and the considered distance measure. Using the new framework, all instances from the existing literature for this class of problems are solved to optimality. The paper also introduces and optimally solves a realistic multifacility problem instance derived from an archipelago vulnerable to earthquakes. This problem instance is significantly more complex than any other instance described in the literature.

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Section: Barrier Instancessupporting

confidence: 57%

Section: Restricted Problems With Barriersmentioning

confidence: 99%

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A modelling framework for solving restricted planar location problems using phi-objects

Oğuz

Bektaş

Bennell

et al. 2016

Journal of the Operational Research Society

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“…The simplest convex programming problem is an unconstrained problem of the form Min imize ||Ax-b|| (6) where ARmxn and bRm are problem data, xRn is the variable, and . is a norm on R m .…”

Section: Preliminaries and Problem Setupmentioning

confidence: 99%

A Note on Convex Programming in Practical Problems

Osinuga

Agunbiade

2013

BSMaSS

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Abstract. In recent years, convex programming has become a sophisticated tool of central importance in engineering, finance, operations research, statistics etc. The goal of this paper is to emphasize modeling and present several convex programming problem formulations especially in optimal design and location theory. We build simple models to address this question, investigate their properties and apply a variant of the Weierstrass theorem to prove the existence of a solution. Our results extend and improve some other comparable results of the author [2,8,20,21,22,23,24,25].

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“…Aneja and Parlar [1] and Butt and Cavalier [3] developed heuristics for the 1-median problem in the presence of polygonal barriers under the l p distance metric. Though the center problem in R 2 without barriers has been extensively studied in the literature (e.g., books of Drezner [5], Love et al [11] and Francis et al [6]), very few references can be obtained for the corresponding problem in the presence of barriers.…”

Section: Introductionmentioning

confidence: 99%

Placing a finite size facility with a center objective on a rectangular plane with barriers

Sarkar

Batta

Nagi

2007

European Journal of Operational Research

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We study the problem when the facility orientation is known a priori. We obtain domination results when the facility is fully contained inside 1, 2 and 3-cornered cells. For full containment in a 4-cornered cell, we formulate the problem as a linear program. However, when the facility intersects gridlines, analytical representation of the distance functions becomes challenging. We study the difficulties of this case and formulate our problem as a linear or nonlinear program, depending on whether the feasible region is convex or nonconvex. An analysis of the solution complexity is presented along with an illustrative numerical example.

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An efficient algorithm for facility location in the presence of forbidden regions

Cited by 77 publications

References 17 publications

A modelling framework for solving restricted planar location problems using phi-objects

A modelling framework for solving restricted planar location problems using phi-objects

A Note on Convex Programming in Practical Problems

Placing a finite size facility with a center objective on a rectangular plane with barriers

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