GBSSS: The generalized big square small square method for planar single-facility location

Plastria, Frank

doi:10.1016/0377-2217(92)90244-4

Cited by 111 publications

(62 citation statements)

References 17 publications

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“…Since z(·) is a Lipschitz function on S \ H, [20], and our proposed lower bound is at least as sharp as the one given in [17], see Proposition 4, we obtain a similar convergence result than in the case of BSSS with crude bound, see [17].…”

Section: Convergencesupporting

confidence: 65%

“…The BSSS method is a Branch-and-Bound procedure, proposed by Hansen et al, [7,8], and modified by Plastria, [17], whose success is due to its simplicity and versatility to solve planar problems.…”

Section: The Bsss With Sharper Boundsmentioning

confidence: 99%

“…We do not go into further details on the scheme of the algorithm, which is well documented e.g. in [7,8,10,17] and focus our attention on our contribution to the basic BSSS, namely, how to obtain sharper lower bounds for min x∈R z(x) for a given rectangle R.…”

Section: The Bsss With Sharper Boundsmentioning

confidence: 99%

“…In this subsection we propose a lower bound for z * (R), using Lagrangean relaxation techniques, [15], and compare the sharpness of this bound with respect to the bound proposed in [7,8,17]. By using the monotonicity of the functions f a , g a , one obtains the following crude bound.…”

Section: Boundingmentioning

confidence: 99%

“…The bound z 0 (R) is easily computed after computing the highest distance (following · a − ) from each a ∈ A to the rectangle R, and the projection (following · a + ) of such points onto R. Since the function · −a a − is convex, it attains its maximum on R at some vertex of R. Hence finding max x∈R x − a a − reduces to evaluating the four vertices of R. On the other hand, although calculating min x∈R x − a a + amounts in general to solve a convex programme, [12], a straightforward procedure has been suggested for the case in which · a + is an l p norm, see [8,17] for details.…”

Section: Remarkmentioning

confidence: 99%

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Semi-obnoxious location models: A global optimization approach

Morales

Carrizosa

Conde

1997

European Journal of Operational Research

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In the last decades there has been an increasing interest in environmental topics. This interest has been reflected in modeling the location of obnoxious facilities, as shown by the important number of papers published in this field. However, a very common drawback of the existing literature is that, as soon as environmental aspects are taken into account, economical considerations (e.g. transportation costs) are ignored, leading to models with dubious practical interest. In this paper we take into account both the environmental impact and the transportation costs caused by the location of an obnoxious facility, and propose as solution method of the well-known BSSS, with a new bounding scheme which exploits the structure of the problem.

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Section: Convergencesupporting

confidence: 65%

Section: The Bsss With Sharper Boundsmentioning

confidence: 99%

Section: The Bsss With Sharper Boundsmentioning

confidence: 99%

Section: Boundingmentioning

confidence: 99%

Section: Remarkmentioning

confidence: 99%

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Semi-obnoxious location models: A global optimization approach

Morales

Carrizosa

Conde

1997

European Journal of Operational Research

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General Further Discarding Tests in Geometric Branch‐and‐Bound Methods for Non‐Convex Multicriteria Optimization Problems

Scholz

2011

Multi Criteria Decision Anal

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Using a geometric branch-and-bound technique, my goal in this paper is to compute a sharp outer approximation of all Pareto-optimal solutions in multicriteria optimization problems. To this end, I propose some general further discarding tests that are based on the Fritz John necessary conditions for Pareto optimality.The branch-and-bound solution method as well as the general further discarding tests leads to a very useful tool especially for multicriteria facility location problems. Therefore, my suggested approach is demonstrated on some multicriteria facility location problems with excellent numerical results.

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The gradual covering problem

Drezner

Wesolowsky

Drezner

2004

Naval Research Logistics

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Abstract:In this paper we investigate the gradual covering problem. Within a certain distance from the facility the demand point is fully covered, and beyond another specified distance the demand point is not covered. Between these two given distances the coverage is linear in the distance from the facility. This formulation can be converted to the Weber problem by imposing a special structure on its cost function. The cost is zero (negligible) up to a certain minimum distance, and it is a constant beyond a certain maximum distance. Between these two extreme distances the cost is linear in the distance. The problem is analyzed and a branch and bound procedure is proposed for its solution. Computational results are presented.

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GBSSS: The generalized big square small square method for planar single-facility location

Cited by 111 publications

References 17 publications

Semi-obnoxious location models: A global optimization approach

Semi-obnoxious location models: A global optimization approach

General Further Discarding Tests in Geometric Branch‐and‐Bound Methods for Non‐Convex Multicriteria Optimization Problems

The gradual covering problem

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