119 research outputs found
On multimodality of obnoxious faclity location models
Obnoxious single facility location models are models that have the aim to find the best location
for an undesired facility. Undesired is usually expressed in relation to the so-called demand
points that represent locations hindered by the facility. Because obnoxious facility location
models as a rule are multimodal, the standard techniques of convex analysis used for locating
desirable facilities in the plane may be trapped in local optima instead of the desired global
optimum. It is assumed that having more optima coincides with being harder to solve. In this
thesis the multimodality of obnoxious single facility location models is investigated in order to know which models are challenging problems in facility location problems and which are
suitable for site selection. Selected for this are the obnoxious facility models that appear to be most important in literature. These are the maximin model, that maximizes the minimum
distance from demand point to the obnoxious facility, the maxisum model, that maximizes the
sum of distance from the demand points to the facility and the minisum model, that minimizes
the sum of damage of the facility to the demand points. All models are measured with the
Euclidean distances and some models also with the rectilinear distance metric. Furthermore a
suitable algorithm is selected for testing multimodality. Of the tested algorithms in this thesis, Multistart is most appropriate. A small numerical experiment shows that Maximin models have on average the most optima, of which the model locating an obnoxious linesegment has the
most. Maximin models have few optima and are thus not very hard to solve. From the Minisum
models, the models that have the most optima are models that take wind into account. In general can be said that the generic models have less optima than the weighted versions. Models that are measured with the rectilinear norm do have more solutions than the same models measured with the Euclidean norm. This can be explained for the maximin models in the numerical example because the shape of the norm coincides with a bound of the feasible area, so not all solutions are different optima. The difference found in number of optima of the Maxisum and Minisum can not be explained by this phenomenon
Locating a semi-obnoxious facility in the special case of Manhattan distances
The aim of thiswork is to locate a semi-obnoxious facility, i.e. tominimize the distances
to a given set of customers in order to save transportation costs on the one hand and to
avoid undesirable interactions with other facilities within the region by maximizing
the distances to the corresponding facilities on the other hand. Hence, the goal is to
satisfy economic and environmental issues simultaneously. Due to the contradicting
character of these goals, we obtain a non-convex objective function. We assume that
distances can be measured by rectilinear distances and exploit the structure of this
norm to obtain a very efficient dual pair of algorithms
Three location tapas calling for CG sauce
Based on some recent modelling considerations in location theory we call for study of three CG constructs of Voronoi type that seem not to have been studied much before
Semi-obnoxious location models: a global optimization approach
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.Dirección General de Investigación CientÃfica y Técnic
Problemas de localização-distribuição de serviços semiobnóxios: aproximações e apoio à decisão
Doutoramento em Gestão IndustrialA presente tese resulta de um trabalho de investigação cujo objectivo se
centrou no problema de localização-distribuição (PLD) que pretende abordar,
de forma integrada, duas actividades logÃsticas intimamente relacionadas: a
localização de equipamentos e a distribuição de produtos.
O PLD, nomeadamente a sua modelação matemática, tem sido estudado na
literatura, dando origem a diversas aproximações que resultam de diferentes
cenários reais. Importa portanto agrupar as diferentes variantes por forma a
facilitar e potenciar a sua investigação. Após fazer uma revisão e propor uma
taxonomia dos modelos de localização-distribuição, este trabalho foca-se na
resolução de alguns modelos considerados como mais representativos. É feita
assim a análise de dois dos PLDs mais básicos (os problema capacitados com
procura nos nós e nos arcos), sendo apresentadas, para ambos, propostas de
resolução. Posteriormente, é abordada a localização-distribuição de serviços
semiobnóxios. Este tipo de serviços, ainda que seja necessário e
indispensável para o público em geral, dada a sua natureza, exerce um efeito
desagradável sobre as comunidades contÃguas. Assim, aos critérios
tipicamente utilizados na tomada de decisão sobre a localização destes
serviços (habitualmente a minimização de custo) é necessário adicionar
preocupações que reflectem a manutenção da qualidade de vida das regiões
que sofrem o impacto do resultado da referida decisão.
A abordagem da localização-distribuição de serviços semiobnóxios requer
portanto uma análise multi-objectivo. Esta análise pode ser feita com recurso a
dois métodos distintos: não interactivos e interactivos. Ambos são abordados
nesta tese, com novas propostas, sendo o método interactivo proposto
aplicável a outros problemas de programação inteira mista multi-objectivo.
Por último, é desenvolvida uma ferramenta de apoio à decisão para os
problemas abordados nesta tese, sendo apresentada a metodologia adoptada
e as suas principais funcionalidades. A ferramenta desenvolvida tem grandes
preocupações com a interface de utilizador, visto ser direccionada para
decisores que tipicamente não têm conhecimentos sobre os modelos
matemáticos subjacentes a este tipo de problemas.This thesis main objective is to address the location-routing problem (LRP)
which intends to tackle, using an integrated approach, two highly related
logistics activities: the location of facilities and the distribution of materials.
The LRP, namely its mathematical formulation, has been studied in the
literature, and several approaches have emerged, corresponding to different
real-world scenarios. Therefore, it is important to identify and group the
different LRP variants, in order to segment current research and foster future
studies. After presenting a review and a taxonomy of location-routing models,
the following research focuses on solving some of its variants. Thus, a study of
two of the most basic LRPs (capacitated problems with demand either on the
nodes or on the arcs) is performed, and new approaches are presented.
Afterwards, the location-routing of semi-obnoxious facilities is addressed.
These are facilities that, although providing useful and indispensible services,
given their nature, bring about an undesirable effect to adjacent communities.
Consequently, to the usual objectives when considering their location (cost
minimization), new ones must be added that are able to reflect concerns
regarding the quality of life of the communities impacted by the outcome of
these decisions.
The location-routing of semi-obnoxious facilities therefore requires to be
analysed using multi-objective approaches, which can be of two types: noninteractive
or interactive. Both are discussed and new methods proposed in this
thesis; the proposed interactive method is suitable to other multi-objective
mixed integer programming problems.
Finally, a newly developed decision-support tool to address the LRP is
presented (being the adopted methodology discussed, and its main
functionalities shown). This tool has great concerns regarding the user
interface, as it is directed at decision makers who typically don’t have specific
knowledge of the underlying models of this type of problems
Covering point sets with two disjoint disks or squares
Open archive-ElsevierWe study the following problem: Given a set of red points and a set of blue points on the plane, find two unit disks CR and CB
with disjoint interiors such that the number of red points covered by CR plus the number of blue points covered by CB is maximized.
We give an algorithm to solve this problem in O(n8/3 log2 n) time, where n denotes the total number of points. We also show that
the analogous problem of finding two axis-aligned unit squares SR and SB instead of unit disks can be solved in O(nlog n) time,
which is optimal. If we do not restrict ourselves to axis-aligned squares, but require that both squares have a common orientation,
we give a solution using O(n3 log n) time
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