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.

Hub Location Problem e Site Selection: il caso FAAC Technologies

Questa tesi ha l’obbiettivo di studiare e seguire la creazione un modello matematico che possa risolvere un problema logistico di Hub Facility Location reale, per l’individuazione del posizionamento ottimale di uno o più depositi all’interno di una rete distributiva europea e per l’assegnazione dei rispettivi clienti. Si fa riferimento alla progettazione della rete logistica per rispondere alle necessità del cliente, relativamente ad una domanda multiprodotto. Questo problema è stato studiato a partire da un caso reale aziendale per la valutazione della convenienza nella sostituzione di quattro magazzini locali con uno/due hub logistici che possano servire tutte le aree. Il modello distributivo può anche essere adoperato per valutare l’effetto della variazione, dal punto di vista economico, del servizio di trasporto e di tariffario. La determinazione della posizione ottimale e del numero dei magazzini avviene tramite un modello matematico che considera al proprio interno sia costi fissi relativi alla gestione dei magazzini (quindi costo di stabilimento, personale e giacenza) e sia i costi relativi al trasporto e alla spedizione dei prodotti sulle diverse aree geografiche. In particolare, la formulazione matematica si fonda su un modello Programmazione Lineare Intera, risolto in tempi molto brevi attraverso un software di ottimizzazione, nonostante la grande mole di dati in input del problema. In particolare, si ha lo studio per l’integrazione di tariffari di trasporto diversi e delle economie di scala per dare consistenza ad un modello teorico. Inoltre, per ricercare la migliore soluzione di quelle ottenute sono poi emersi altri fattori oltre a quello economico, ad esempio il tempo di trasporto (transit-time) che è un fattore chiave per ottenere la soddisfazione e la fedeltà del cliente e attitudine dell’area geografica ad accogliere una piattaforma logistica, con un occhio sugli sviluppi futuri.

Design and management of a supply chain: a joint location-inventory problem under uncertainty (Part A)

In this paper, a joint location-inventory model is proposed that simultaneously optimises strategic supply chain design decisions such as facility location and customer allocation to facilities, and tactical-operational inventory management and production scheduling decisions. All this is analysed in a context of demand uncertainty and supply uncertainty. While demand uncertainty stems from potential fluctuations in customer demands over time, supply-side uncertainty is associated with the risk of “disruption” to which facilities may be subject. The latter is caused by external factors such as natural disasters, strikes, changes of ownership and information technology security incidents. The proposed model is formulated as a non-linear mixed integer programming problem to minimise the expected total cost, which includes four basic cost items: the fixed cost of locating facilities at candidate sites, the cost of transport from facilities to customers, the cost of working inventory, and the cost of safety stock. Next, since the optimisation problem is very complex and the number of evaluable instances is very low, a "matheuristic" solution is presented. This approach has a twofold objective: on the one hand, it considers a larger number of facilities and customers within the network in order to reproduce a supply chain configuration that more closely reflects a real-world context; on the other hand, it serves to generate a starting solution and perform a series of iterations to try to improve it. Thanks to this algorithm, it was possible to obtain a solution characterised by a lower total system cost than that observed for the initial solution. The study concludes with some reflections and the description of possible future insights.

Invited review: Models for the optimization of regional wastewater treatment systems

European Journal of Operational Research, nº 73 (1994)

Median problems in networks

The P-median problem is a classical location model par excellence . In this paper we, firstexamine the early origins of the problem, formulated independently by Louis Hakimi andCharles ReVelle, two of the fathers of the burgeoning multidisciplinary field of researchknown today as Facility Location Theory and Modelling. We then examine some of thetraditional heuristic and exact methods developed to solve the problem. In the third sectionwe analyze the impact of the model in the field. We end the paper by proposing new lines ofresearch related to such a classical problem.

Spatial market expansion through mergers

In this paper we present a model that studies firm mergers in a spatial setting. A new model is formulated that addresses the issue of finding the number of branches that have to be eliminated by a firm after merging with another one, in order to maximize profits. The model is then applied to an example of bank mergers in the city of Barcelona. Finally, a variant of the formulation that introduces competition is presented together with some conclusions.

Simultaneous Embeddings Of Graphs As Median And Antimedian Subgraphs

The distance DG(v) of a vertex v in an undirected graph G is the sum of the distances between v and all other vertices of G. The set of vertices in G with maximum (minimum) distance is the antimedian (median) set of a graph G. It is proved that for arbitrary graphs G and J and a positive integer r 2, there exists a connected graph H such that G is the antimedian and J the median subgraphs of H, respectively, and that dH(G, J) = r. When both G and J are connected, G and J can in addition be made convex subgraphs of H.

LOCALITZA: una herramienta SIG para resolver problemas de localización óptima

LOCALITZA software is a tool that increases GIS applications possibilities to analyze and solve optimal facility location problems. This system, that it is being migrated from Delphi to Python, allows to evaluate how existing facility supply covers the demand. ON the other hand, it includes the resolution of an elevated number of classic location-allocation models and, in some cases, includes new models

Tipos de lógica utilizadas en la toma de decisiones estratégicas de marketing

Para el administrador el proceso de la toma de decisiones es uno de sus mayores retos y responsabilidades, ya que en su desarrollo se debe definir el camino más acertado en un sin número de alternativas, teniendo en cuenta los obstáculos sociales, políticos y económicos del entorno empresarial. Para llegar a la decisión adecuada no hay que perder de vista los objetivos y metas propuestas, además de tener presente el proceso lógico, detectando, analizando y demostrando el porqué de esa elección. Consecuentemente el análisis que propone esta investigación aportara conocimientos sobre los tipos de lógica utilizados en la toma de decisiones estratégicas al administrador para satisfacer las demandas asociadas con el mercadeo para que de esta manera se pueda generar y ampliar eficientemente las competencia idóneas del administrador en la inserción internacional de un mercado laboral cada vez mayor (Valero, 2011). A lo largo de la investigación se pretende desarrollar un estudio teórico para explicar la relación entre la lógica y la toma de decisiones estratégicas de marketing y como estos conceptos se combinan para llegar a un resultado final. Esto se llevara a cabo por medio de un análisis de planes de marketing, iniciando por conceptos básicos como marketing, lógica, decisiones estratégicas, dirección de marketing seguido de los principios lógicos y contradicciones que se pueden llegar a generar entre la fundamentación teórica

Two-level network design with intermediate facilities: An application to electrical distribution systems

We consider the two-level network design problem with intermediate facilities. This problem consists of designing a minimum cost network respecting some requirements, usually described in terms of the network topology or in terms of a desired flow of commodities between source and destination vertices. Each selected link must receive one of two types of edge facilities and the connection of different edge facilities requires a costly and capacitated vertex facility. We propose a hybrid decomposition approach which heuristically obtains tentative solutions for the vertex facilities number and location and use these solutions to limit the computational burden of a branch-and-cut algorithm. We test our method on instances of the power system secondary distribution network design problem. The results show that the method is efficient both in terms of solution quality and computational times. (C) 2010 Elsevier Ltd. All rights reserved.

Confidence in heuristic solutions?

Solutions to combinatorial optimization problems frequently rely on heuristics to minimize an objective function. The optimum is sought iteratively and pre-setting the number of iterations dominates in operations research applications, which implies that the quality of the solution cannot be ascertained. Deterministic bounds offer a mean of ascertaining the quality, but such bounds are available for only a limited number of heuristics and the length of the interval may be difficult to control in an application. A small, almost dormant, branch of the literature suggests using statistical principles to derive statistical bounds for the optimum. We discuss alternative approaches to derive statistical bounds. We also assess their performance by testing them on 40 test p-median problems on facility location, taken from Beasley’s OR-library, for which the optimum is known. We consider three popular heuristics for solving such location problems; simulated annealing, vertex substitution, and Lagrangian relaxation where only the last offers deterministic bounds. Moreover, we illustrate statistical bounds in the location of 71 regional delivery points of the Swedish Post. We find statistical bounds reliable and much more efficient than deterministic bounds provided that the heuristic solutions are sampled close to the optimum. Statistical bounds are also found computationally affordable.

Proposta de localização de uma unidade de tratamento de óleo e gordura residual de fritura na cidade do Natal/RN para produção de biodiesel

This work addresses biodiesel by transesterification from the use of waste frying oil as a possible technological alternative for both reducing greenhouse gas emissions and by presenting themselves as an environmental call to designate a rational use of oil when no longer played in the environment to become renewable energy. It has proposed location of a residual oil and fat treatment plant to produce biodiesel, using models of Location and Routing for the improvement of routes. To achieve the goal, questionnaires were administered in establishments that use oil or vegetable fat in their productive activities in order to quantify the residue, to analyze actions and environmental perception of people who work directly with the residue on the destination you are being given to oil and fat used. It has indicated using of two single setup location, the method of Center of Gravity and the model of Ardalan, a geographical point that minimizes the costs of transporting waste to the treatment plant. Actions have been proposed for the improvement of collection routes this residue using the Routing Method of Scanning, as an illustration. The results demonstrated the lack of knowledge of the people who deal directly with large amounts of waste, on the environmental impacts caused by their incorrect disposal. The models used were uniform since point out to neighborhoods in similar regions. The neighborhoods of Lagoa Nova / Morro Branco (Ardalan) and Nova Descoberta (Center of Gravity) as ideal for the installation of treatment plant. However, it is suggested to be tested other models that take into account new variables than those used (supply of waste and the distance between points). The routing through the method of scanning has shown that it is possible, in a simple way to optimize routes in order to reduce distances and therefore the logistics costs in the collection of such waste. Introducing a route as a test to gather the twenty largest oil suppliers used in sample frying, using as a main factor time 8 hour of working shift every day

Melhoria da segurança pública: uma proposta para alocação de unidades policiais utilizando o modelo das p-medianas e do caixeiro viajante

The decrease in crime is one of the core issues that cause concern in society today. This study aims to propose improvements to public safety from the choice of points to the location of police units, ie the points which support the car and the police. For this, three models were developed in order to assist decision making regarding the best placement of these bases. The Model of Police Units Routing has the intention to analyze the current configuration of a given region and develop optimal routes for round preventative. The Model of Allocation and Routing for New Police Units (MARNUP) used the model of facility location called p-median weighted and traveling salesman problem (TSP) combined aiming an ideal setting for regions that do not yet have support points or to assess how far the distribution is present in relation to that found in solution. The Model Redefinition and Routing Unit Police (MRRUP) seek to change the current positioning taking into account the budgetary constraints of the decision maker. To verify the applicability of these models we used data from 602 points to instances of police command that is responsible for the capital city of Natal. The city currently has 31 police units for 36 of these 19 districts and police have some assistance. This reality can lead to higher costs and higher response times for answering emergency calls. The results of the models showed that in an ideal situation it is possible to define a distance of 500 km/round, whereas in this 900 km are covered by approximately round. However, a change from three-point lead reduced to 700 km / round which represents a decrease of 22% in the route. This reduction should help improve response time to emergency care, improving the level of service provided by the increase of solved cases, reducing police shifts and routing preventive patrols

Algoritmos para o problema de localização de uma facilidade com distâncias limitadas e restrições de atendimento

The objective in the facility location problem with limited distances is to minimize the sum of distance functions from the facility to the customers, but with a limit on each distance, after which the corresponding function becomes constant. The problem has applications in situations where the service provided by the facility is insensitive after a given threshold distance (eg. fire station location). In this work, we propose a global optimization algorithm for the case in which there are lower and upper limits on the numbers of customers that can be served

Calculating the Best Dual Bound for Problems with Multiple Lagrangian Relaxations

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)