The Weber Problem

Drezner, Zvi; Klamroth, Kathrin; Schöbel, Anita; Wesolowsky, George O.

doi:10.1007/978-3-642-56082-8_1

Cited by 90 publications

(69 citation statements)

References 133 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The classical location theory is dedicated to the problem of locating a new facility such that all relevant distances, e.g. to customers, are minimized [7,8,11,13,19,35,42]. Nevertheless, since some facilities also cause negative effects like noise, stench or even danger, such facilities need to be established as far away as possible from nature reserves and residential areas.…”

Section: Application and Numerical Resultsmentioning

confidence: 99%

Solving DC programs with a polyhedral component utilizing a multiple objective linear programming solver

Löhne¹,

Wagner²

2017

J Glob Optim

View full text Add to dashboard Cite

A class of non-convex optimization problems with DC objective function is studied, where DC stands for being representable as the difference f = g − h of two convex functions g and h. In particular, we deal with the special case where one of the two convex functions g or h is polyhedral. In case g is polyhedral, we show that a solution of the DC program can be obtained from a solution of an associated polyhedral projection problem. In case h is polyhedral, we prove that a solution of the DC program can be obtained by solving a polyhedral projection problem and finitely many convex programs. Since polyhedral projection is equivalent to multiple objective linear programming (MOLP), a MOLP solver (in the second case together with a convex programming solver) can be used to solve instances of DC programs with polyhedral component. Numerical examples are provided, among them an application to locational analysis.

show abstract

Section: Application and Numerical Resultsmentioning

confidence: 99%

Solving DC programs with a polyhedral component utilizing a multiple objective linear programming solver

Löhne¹,

Wagner²

2017

J Glob Optim

View full text Add to dashboard Cite

show abstract

“…If appropriate probabilistic assumptions about underlying error distributions are made, least squares produces what is known as the maximum-likelihood estimate parameters. Even if the probabilistic assumptions are not satisfied, research in this areas has shown that least squares produces useful results [1,2,5,6,7,8,9,10,11,14,15,19,21,22,23,24,25,26] A very common source of least squares is curve fitting. Let x be the independent variable and let y  x denote an unknown function of x that we want to approximate.…”

Section: Optimal Designmentioning

confidence: 99%

“…There are numerous publications where facility location problems have been discussed [4,5,8,9,10,13,14,15,17,19,20,21,22,23].The problem has given rise to extraordinary number of generalizations, extensions and modifications. It would literally require volumes to do them justice; space only permits only a brief and somewhat arbitrarily selected summary.…”

Section: Location Theorymentioning

confidence: 99%

“…This problem is sometimes called Weber problem and it arises in many fields such as signal processing, networking, communications and called many names such as the Fermat -Torricelli problem, the Steiner problem, the Steiner-Weber problem, the median center problem, the minisum problem, and the spartial problem [10]. We are to find the "minisum" point  x f , y f   X which minimizes the sum of weighted Euclidean distances from itself to n fixed points with coordinates  xi , yi   P , i  1, ..., n .The weights which are associated with the fixed points are denoted by wi .One simple scenario for the problem is that of locating a distribution centre and that the weights wi are the cost per unit distance of shipping the requirements to customers located at the fixed points  xi , yi  ;  x f , y f  is then the distribution centre that minimizes the transportation costs.…”

Section: Location Theorymentioning

confidence: 99%

See 1 more Smart Citation

A Note on Convex Programming in Practical Problems

Osinuga

Agunbiade

2013

BSMaSS

View full text Add to dashboard Cite

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].

show abstract

“…Also, many other types of distances have been used in the facility location problems [3][4][5]. In general, a lot of extensions and modifications of the Weber location problem are known.…”

Section: Introductionmentioning

confidence: 99%

Application of Heuristic and Metaheuristic Algorithms in Solving Constrained Weber Problem with Feasible Region Bounded by Arcs

Stojanović

Brajević

Stanimirović

et al. 2017

Mathematical Problems in Engineering

View full text Add to dashboard Cite

The continuous planar facility location problem with the connected region of feasible solutions bounded by arcs is a particular case of the constrained Weber problem. This problem is a continuous optimization problem which has a nonconvex feasible set of constraints. This paper suggests appropriate modifications of four metaheuristic algorithms which are defined with the aim of solving this type of nonconvex optimization problems. Also, a comparison of these algorithms to each other as well as to the heuristic algorithm is presented. The artificial bee colony algorithm, firefly algorithm, and their recently proposed improved versions for constrained optimization are appropriately modified and applied to the case study. The heuristic algorithm based on modified Weiszfeld procedure is also implemented for the purpose of comparison with the metaheuristic approaches. Obtained numerical results show that metaheuristic algorithms can be successfully applied to solve the instances of this problem of up to 500 constraints. Among these four algorithms, the improved version of artificial bee algorithm is the most efficient with respect to the quality of the solution, robustness, and the computational efficiency.

show abstract

The Weber Problem

Cited by 90 publications

References 133 publications

Solving DC programs with a polyhedral component utilizing a multiple objective linear programming solver

Solving DC programs with a polyhedral component utilizing a multiple objective linear programming solver

A Note on Convex Programming in Practical Problems

Application of Heuristic and Metaheuristic Algorithms in Solving Constrained Weber Problem with Feasible Region Bounded by Arcs

Contact Info

Product

Resources

About