Facility location in the presence of forbidden regions, I: Formulation and the case of Euclidean distance with one forbidden circle

Katz, Irving; Cooper, Leon N.

doi:10.1016/0377-2217(81)90203-4

Cited by 111 publications

(53 citation statements)

References 12 publications

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“…Katz and Cooper (1981) instances. In the first instance, the barrier is a circle with a radius of two, with its centre located at (0, 0).…”

Section: Barrier Instancesmentioning

confidence: 98%

“…Restricted planar location problems with barriers, to the best of our knowledge, are first presented by Katz and Cooper (1981), where the barrier is a single circular region and the distance metric is Euclidean. In this paper, an algorithm is described to compute the shortest distance following which the modified objective function with the shortest distance is converted into a sequence of unconstrained minimization problems.…”

Section: Restricted Problems With Barriersmentioning

confidence: 99%

“…In this paper, an algorithm is described to compute the shortest distance following which the modified objective function with the shortest distance is converted into a sequence of unconstrained minimization problems. Klamroth (2004) presents new structural results for the problem described by Katz and Cooper (1981). Larson and Sadiq (1983) solve a p-median problem in a case of rectilinear distance.…”

Section: Restricted Problems With Barriersmentioning

confidence: 99%

“…The first two instances are first presented in Katz and Cooper (1981), for which the parameters use the following values: J max = 100, V = 0.01m/s and t max = 0.2s. The third instance is first presented in Aneja and Parlar (1994), for which the parameters are J max = 100, V = 0.01m/s and t max =0.2 s. These values are decided by considering the performance of the solvers at hand and the instances that are solved.…”

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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“…Katz and Cooper (1981) instances. In the first instance, the barrier is a circle with a radius of two, with its centre located at (0, 0).…”

Section: Barrier Instancesmentioning

confidence: 98%

Section: Restricted Problems With Barriersmentioning

confidence: 99%

Section: Restricted Problems With Barriersmentioning

confidence: 99%

Section: Barrier Instancesmentioning

confidence: 99%

See 2 more Smart Citations

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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“…Examples of barriers would be impassable areas on the shop floor like machines, subassembly areas, input-output docks, etc. The available literature on location problems in the presence of barriers can be classified according to the following criteria: In one the earliest facility location papers dealing with barriers, Katz and Cooper [8] investigated a problem with a circular barrier considering the median objective and the Euclidean distance metric. Larson and Li [9] developed an efficient algorithm for determining the shortest feasible rectangular path between two points in the presence of polygonal 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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Introduction to Facility Location

Snyder

2011

Wiley Encyclopedia of Operations Research and Management Science

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This article provides a broad overview of facility location problems, one of the oldest and most widely studied fields of applied optimization. The article presents a standard taxonomy of location models and discusses key dimensions along which they are classified. Mathematical programming formulations and common solution methods for several classical models are described. A variety of extensions that build upon these models and their application to richer and more complex settings are also discussed. The article covers discrete and network location problems and, to a lesser extent, continuous problems.

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Facility location in the presence of forbidden regions, I: Formulation and the case of Euclidean distance with one forbidden circle

Cited by 111 publications

References 12 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

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

Introduction to Facility Location

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