Models and algorithms for the capacitated location-routing problem

Le problème de localisation-routage avec capacités (PLRC) apparaît comme un problème clé dans la conception de réseaux de distribution de marchandises. Il généralisele problème de localisation avec capacités (PLC) ainsi que le problème de tournées de véhicules à multiples dépôts (PTVMD), le premier en ajoutant des décisions liées au routage et le deuxième en ajoutant des décisions liées à la localisation des dépôts. Dans cette thèse on dévelope des outils pour résoudre le PLRC à l’aide de la programmation mathématique. Dans le chapitre 3, on introduit trois nouveaux modèles pour le PLRC basés sur des flots de véhicules et des flots de commodités, et on montre comment ceux-ci dominent, en termes de la qualité de la borne inférieure, la formulation originale à deux indices [19]. Des nouvelles inégalités valides ont été dévelopées et ajoutées aux modèles, de même que des inégalités connues. De nouveaux algorithmes de séparation ont aussi été dévelopés qui dans la plupart de cas généralisent ceux trouvés dans la litterature. Les résultats numériques montrent que ces modèles de flot sont en fait utiles pour résoudre des instances de petite à moyenne taille. Dans le chapitre 4, on présente une nouvelle méthode de génération de colonnes basée sur une formulation de partition d’ensemble. Le sous-problème consiste en un problème de plus court chemin avec capacités (PCCC). En particulier, on utilise une relaxation de ce problème dans laquelle il est possible de produire des routes avec des cycles de longueur trois ou plus. Ceci est complété par des nouvelles coupes qui permettent de réduire encore davantage le saut d’intégralité en même temps que de défavoriser l’apparition de cycles dans les routes. Ces résultats suggèrent que cette méthode fournit la meilleure méthode exacte pour le PLRC. Dans le chapitre 5, on introduit une nouvelle méthode heuristique pour le PLRC. Premièrement, on démarre une méthode randomisée de type GRASP pour trouver un premier ensemble de solutions de bonne qualité. Les solutions de cet ensemble sont alors combinées de façon à les améliorer. Finalement, on démarre une méthode de type détruir et réparer basée sur la résolution d’un nouveau modèle de localisation et réaffectation qui généralise le problème de réaffectaction [48].

A hybrid method for the probabilistic maximal covering location-allocation problem

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Heuristic algorithms for the Capacitated Location-Routing Problem and the Multi-Depot Vehicle Routing Problem

The Capacitated Location-Routing Problem (CLRP) is a NP-hard problem since it generalizes two well known NP-hard problems: the Capacitated Facility Location Problem (CFLP) and the Capacitated Vehicle Routing Problem (CVRP). The Multi-Depot Vehicle Routing Problem (MDVRP) is known to be a NP-hard since it is a generalization of the well known Vehicle Routing Problem (VRP), arising with one depot. This thesis addresses heuristics algorithms based on the well-know granular search idea introduced by Toth and Vigo (2003) to solve the CLRP and the MDVRP. Extensive computational experiments on benchmark instances for both problems have been performed to determine the effectiveness of the proposed algorithms. This work is organized as follows: Chapter 1 describes a detailed overview and a methodological review of the literature for the the Capacitated Location-Routing Problem (CLRP) and the Multi-Depot Vehicle Routing Problem (MDVRP). Chapter 2 describes a two-phase hybrid heuristic algorithm to solve the CLRP. Chapter 3 shows a computational comparison of heuristic algorithms for the CLRP. Chapter 4 presents a hybrid granular tabu search approach for solving the MDVRP.

Enabling long journeys in electric vehicles:design and demonstration of an infrastructure location model

This research develops a methodology and model formulation which suggests locations for rapid chargers to help assist infrastructure development and enable greater battery electric vehicle (BEV) usage. The model considers the likely travel patterns of BEVs and their subsequent charging demands across a large road network, where no prior candidate site information is required. Using a GIS-based methodology, polygons are constructed which represent the charging demand zones for particular routes across a real-world road network. The use of polygons allows the maximum number of charging combinations to be considered whilst limiting the input intensity needed for the model. Further polygons are added to represent deviation possibilities, meaning that placement of charge points away from the shortest path is possible, given a penalty function. A validation of the model is carried out by assessing the expected demand at current rapid charging locations and comparing to recorded empirical usage data. Results suggest that the developed model provides a good approximation to real world observations, and that for the provision of charging, location matters. The model is also implemented where no prior candidate site information is required. As such, locations are chosen based on the weighted overlay between several different routes where BEV journeys may be expected. In doing so many locations, or types of locations, could be compared against one another and then analysed in relation to siting practicalities, such as cost, land permission and infrastructure availability. Results show that efficient facility location, given numerous siting possibilities across a large road network can be achieved. Slight improvements to the standard greedy adding technique are made by adding combination weightings which aim to reward important long distance routes that require more than one charge to complete.

Partial Cooperation in Location Choice: Salop’s Model with Three Firms

We consider how three firms compete in a Salop location model and how cooperation in location choice by two of these firms affects the outcomes. We con- sider the classical case of linear transportation costs as a two-stage game in which the firms select first a location on a unit circle along which consumers are dispersed evenly, followed by the competitive selection of a price. Standard analysis restricts itself to purely competitive selection of location; instead, we focus on the situation in which two firms collectively decide about location, but price their products competitively after the location choice has been effectuated. We show that such partial coordination of location is beneficial to all firms, since it reduces the number of equilibria significantly and, thereby, the resulting coordination problem. Subsequently, we show that the case of quadratic transportation costs changes the main conclusions only marginally.

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.

Malnutrition and pressure ulcer risk in adults in Australian health care facilities

Aims To determine the effect of nutritional status on the presence and severity of pressure ulcers in statewide? public healthcare facilities, in Queensland, Australia. Research Methods A multicentre, cross sectional audit of nutritional status of a convenience sample of subjects was carried out as part of a large audit of pressure ulcers in a sample of state based public healthcare facilities in 2002 and 2003. Dietitians in 20 hospitals and six residential aged care facilities conducted single day nutritional status audits of 2208 acute and 839 aged care subjects using the Subjective Global Assessment. The effect of nutritional status on the presence, highest stage and number of pressure ulcers was determined by logistic regression in a model controlling for age, gender, medical specialty and facility location. The potential clustering effect of facility was accounted for in the model using an analysis of correlated data approach. Results Subjects with malnutrition had an adjusted odds risk of 2.6 (95% CI 1.8-3.5, p<0.001) of having a pressure ulcer in acute facilities and 2.0 (95% CI 1.5-2.7, p<0.001) for residential aged care facilities. There was also increased odds risk of having a pressure ulcer, having a higher stage pressure ulcer and a higher number of pressure ulcers with increased severity of malnutrition. Conclusion Malnutrition was associated with at least twice the odds risk of having a pressure ulcer of in public healthcare facilities in Queensland. Action must be taken to identify, prevent and treat malnutrition, especially in patients at risk of pressure ulcer.

Efficient algorithms for domination and Hamilton circuit problems on permutation graphs

The domination and Hamilton circuit problems are of interest both in algorithm design and complexity theory. The domination problem has applications in facility location and the Hamilton circuit problem has applications in routing problems in communications and operations research.The problem of deciding if G has a dominating set of cardinality at most k, and the problem of determining if G has a Hamilton circuit are NP-Complete. Polynomial time algorithms are, however, available for a large number of restricted classes. A motivation for the study of these algorithms is that they not only give insight into the characterization of these classes but also require a variety of algorithmic techniques and data structures. So the search for efficient algorithms, for these problems in many classes still continues.A class of perfect graphs which is practically important and mathematically interesting is the class of permutation graphs. The domination problem is polynomial time solvable on permutation graphs. Algorithms that are already available are of time complexity O(n2) or more, and space complexity O(n2) on these graphs. The Hamilton circuit problem is open for this class.We present a simple O(n) time and O(n) space algorithm for the domination problem on permutation graphs. Unlike the existing algorithms, we use the concept of geometric representation of permutation graphs. Further, exploiting this geometric notion, we develop an O(n2) time and O(n) space algorithm for the Hamilton circuit problem.

Characterizing distribution rules for cost sharing games

In noncooperative cost sharing games, individually strategic agents choose resources based on how the welfare (cost or revenue) generated at each resource (which depends on the set of agents that choose the resource) is distributed. The focus is on finding distribution rules that lead to stable allocations, which is formalized by the concept of Nash equilibrium, e.g., Shapley value (budget-balanced) and marginal contribution (not budget-balanced) rules.

Recent work that seeks to characterize the space of all such rules shows that the only budget-balanced distribution rules that guarantee equilibrium existence in all welfare sharing games are generalized weighted Shapley values (GWSVs), by exhibiting a specific 'worst-case' welfare function which requires that GWSV rules be used. Our work provides an exact characterization of the space of distribution rules (not necessarily budget-balanced) for any specific local welfare functions remains, for a general class of scalable and separable games with well-known applications, e.g., facility location, routing, network formation, and coverage games.

We show that all games conditioned on any fixed local welfare functions possess an equilibrium if and only if the distribution rules are equivalent to GWSV rules on some 'ground' welfare functions. Therefore, it is neither the existence of some worst-case welfare function, nor the restriction of budget-balance, which limits the design to GWSVs. Also, in order to guarantee equilibrium existence, it is necessary to work within the class of potential games, since GWSVs result in (weighted) potential games.

We also provide an alternative characterization—all games conditioned on any fixed local welfare functions possess an equilibrium if and only if the distribution rules are equivalent to generalized weighted marginal contribution (GWMC) rules on some 'ground' welfare functions. This result is due to a deeper fundamental connection between Shapley values and marginal contributions that our proofs expose—they are equivalent given a transformation connecting their ground welfare functions. (This connection leads to novel closed-form expressions for the GWSV potential function.) Since GWMCs are more tractable than GWSVs, a designer can tradeoff budget-balance with computational tractability in deciding which rule to implement.

Otimização do problema de localização de instalações aplicado ao comércio e distribuição de combustíveis

Um dos problemas mais relevantes em organizações de grande porte é a escolha de locais para instalação de plantas industriais, centros de distribuição ou mesmo pontos comerciais. Esse problema logístico é uma decisão estratégica que pode causar um impacto significativo no custo total do produto comercializado. Existem na literatura diversos trabalhos que abordam esse problema. Assim, o objetivo desse trabalho é analisar o problema da localização de instalações proposto por diferentes autores e definir um modelo que seja o mais adequado possível ao mercado de distribuição de combustíveis no Brasil. Para isso, foi realizada uma análise do fluxo de refino e distribuição praticado neste segmento e da formação do respectivo custo de transporte. Foram consideradas restrições como capacidade de estoque, gama de produtos ofertados e níveis da hierarquia de distribuição. A partir dessa análise, foi definido um modelo matemático aplicado à redução dos custos de frete considerando-se a carga tributária. O modelo matemático foi implementado, em linguagem C, e permite simular o problema. Foram aplicadas técnicas de computação paralela visando reduzir o tempo de execução do algoritmo. Os resultados obtidos com o modelo Single Uncapacited Facility Location Problem (SUFLP) simulado nas duas versões do programa, sequencial e paralela, demonstram ganhos de até 5% em economia de custos e redução do tempo de execução em mais de 50%.

Distributed Placement of Service Facilities in Large-Scale Networks

The effectiveness of service provisioning in largescale networks is highly dependent on the number and location of service facilities deployed at various hosts. The classical, centralized approach to determining the latter would amount to formulating and solving the uncapacitated k-median (UKM) problem (if the requested number of facilities is fixed), or the uncapacitated facility location (UFL) problem (if the number of facilities is also to be optimized). Clearly, such centralized approaches require knowledge of global topological and demand information, and thus do not scale and are not practical for large networks. The key question posed and answered in this paper is the following: "How can we determine in a distributed and scalable manner the number and location of service facilities?" We propose an innovative approach in which topology and demand information is limited to neighborhoods, or balls of small radius around selected facilities, whereas demand information is captured implicitly for the remaining (remote) clients outside these neighborhoods, by mapping them to clients on the edge of the neighborhood; the ball radius regulates the trade-off between scalability and performance. We develop a scalable, distributed approach that answers our key question through an iterative reoptimization of the location and the number of facilities within such balls. We show that even for small values of the radius (1 or 2), our distributed approach achieves performance under various synthetic and real Internet topologies that is comparable to that of optimal, centralized approaches requiring full topology and demand information.

« Resolution Search » et problèmes d’optimisation discrète

Thèse réalisée en cotutelle avec l'Université d'Avignon.

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