Discrete facility location with nonlinear facility costs

Körkel, Manfred

doi:10.1051/ro/1991250100311

Cited by 5 publications

(3 citation statements)

References 17 publications

(28 reference statements)

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“…These data sets are of much bigger size than those reported so far in the literature on the problem [18,17]. In fact, our sets are so big that the distance matrix cannot be properly handled.…”

Section: Computational Resultsmentioning

confidence: 97%

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A computational study of a nonlinear minsum facility location problem

Carrizosa

Ushakov

Vasilyev

2012

Computers & Operations Research

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A discrete location problem with nonlinear objective is addressed. A set of p plants is to be open to serve a given set of clients. Together with the locations, the number p of facilities is also a decision variable. The objective is to minimize the total cost, represented as the transportation cost between clients and plants, plus an increasing nonlinear function of p.Two Lagrangean relaxations are considered to derive lower bounds. Dual information is also used to design a core heuristic.Computational results are given, showing that nearly optimal solutions are obtained in short running times.

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Section: Computational Resultsmentioning

confidence: 97%

“…A heuristic algorithm is designed which, by bisection in p, reduces the problem to a series of uncapacitated facility location or p-median problems. Limited computational experience is given, as it is also given in [18], where the convexity assumption on f is relaxed. The reader is referred to, e.g.…”

Section: Introductionmentioning

confidence: 99%

A computational study of a nonlinear minsum facility location problem

Carrizosa

Ushakov

Vasilyev

2012

Computers & Operations Research

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“…In the discrete-space facility location problem, the facility location needs to be selected from a pre-specified set of potential locations, typically the nodes of a network. Several studies [1,11,19,23,41,45,49] have been developed to address this issue. Unfortunately, because the facility can be only located at one of the specific points, the optimal discrete facility locations are worse compared to the optimal continuous solution for a given metric.…”

Section: Literature Reviewmentioning

confidence: 99%

A note on the warehouse location problem with data contamination

Gao

Cui²

2021

RAIRO-Oper. Res.

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To determine the optimal warehouse location, it is usually assumed that the collected data are uncontaminated. However, this assumption can be easily violated due to the uncertain environment and human error in disaster response, which results in the biased estimation of the optimal warehouse location. In this study, we investigate this possibility by examining these estimation effects on the warehouse location determination. Considering different distances, we propose the corresponding estimation methods for remedying the difficulties associated with data contamination to determine the warehouse location. Although data can be contaminated in the event of a disaster, the findings of the study is much broader and applicable to any situation where the outliers exist. Through the simulations and illustrative examples, we show that solving the problem with center of gravity lead to biased solutions even if only one outlier exists in the data. Compared with the center of gravity, the proposed methods are quite efficient and outperform the existing methods when the data contamination is involved.

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A posteriori error estimates for nonlinear problems:Lr, (0,T;W1,ρ (Ω))-error estimates for finite element discretizations of parabolic equations

Verfürth

1998

Numer. Methods Partial Differential Eq.

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Using the abstract framework of [R. Verfürth, Math. Comput. 62, 445-475 (1996)], we analyze a residual a posteriori error estimator for space-time finite element discretizations of parabolic PDEs. The estimator gives global upper and local lower bounds on the error of the numerical solution. The finite element discretizations in particular cover the so-called θ-scheme, which includes the implicit and explicit Euler methods and the Crank-Nicolson scheme. As particular examples we consider scalar quasilinear parabolic PDEs of 2nd order and the time-dependent incompressible Navier-Stokes equations.

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Discrete facility location with nonlinear facility costs

Cited by 5 publications

References 17 publications

A computational study of a nonlinear minsum facility location problem

A computational study of a nonlinear minsum facility location problem

A note on the warehouse location problem with data contamination

A posteriori error estimates for nonlinear problems:Lr, (0,T;W1,ρ (Ω))-error estimates for finite element discretizations of parabolic equations

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