Линейные целочисленные модели распределения потоков в задачах проектирования и анализа многопродуктовых коммуникационных сетей

В статье предлагаются модели распределения дискретных многопродуктовых потоков, представленные в виде задач линейного программирования. Проведен краткий обзор методов и алгоритмов, используемых в настоящее время для решения задач подобного класса. Показано, что практическое использование методов декомпозиции Данцига-Вулфа и релаксации ограничений Розена для решения сформулированных задач позволило установить границы их разумного применения для реальных сетей - от 30 до 100 узлов, и они могут быть использованы при проектировании распределения потоков на нижних уровнях иерархической сетевой структуры. Отмечается, что для решения задач распределения потоков в децентрализованных распределенных сетях, содержащих более 200 узлов и 12000 дуг, целесообразно использовать сетевые постановки задач и приближенные методы решения, существенно опирающиеся на специфику структуры данных задач и содержательные эвристические соображения.У статті пропонуються моделі розподілу дискретних багатопродуктових потоків, представлені у виді задач лінійного програмування. Проведено короткий огляд методів і алгоритмів, використовуваних у даний час для рішення задач подібного класу. Показано, що практичне використання методів декомпозиції Данцига-Вулфа і релаксації обмежень Розена для рішення сформульованих задач дозволило установити границі їхнього розумного застосування для реальних мереж - від 30 до 100 вузлів, і вони можуть бути використані при проектуванні розподілу потоків на нижніх рівнях ієрархічної мережної структури. Відзначається, що для рішення задач розподілу потоків у децентралізованих розподілених мережах, що містять більш 200 вузлів і 12000 дуг, доцільно використовувати мережні постановки задач і наближені методи рішення, що істотно спираються на специфіку структури даних задач і змістовні евристичні розуміння.The models of distribution of the discrete multicommodity flows, submitted as problems of linear programming are offered in this article. The brief review of methods and the algorithms now in use for the decision of problems of a similar class is conducted. Practical use of methods of decomposition of Dantzig - Wolfe and a relaxation of restrictions Rosen for the decision of the formulated problems is shown, that, has allowed to establish borders of their reasonable application for real networks - from 30 up to 100 vertices, and they can be used at designing distribution of flows at the bottom levels of hierarchical network structure. It is marked, that for the decision of problems of distribution of flows in the noncentralized distributed networks, containing more of 200 vertices and 12000 arches it is expedient to use network productions of problems and the approached methods of the decision, essentially basing on specificity of structure of the given problems and substantial heuristic reasons

OPTIMIZATION OF RAILWAY TRANSPORTATION HAZMATS AND REGULAR COMMODITIES

Transportation of dangerous goods has been receiving more attention in the realm of academic and scientific research during the last few decades as countries have been increasingly becoming industrialized throughout the world, thereby making Hazmats an integral part of our life style. However, the number of scholarly articles in this field is not as many as those of other areas in SCM. Considering the low-probability-and-high-consequence (LPHC) essence of transportation of Hazmats, on the one hand, and immense volume of shipments accounting for more than hundred tons in North America and Europe, on the other, we can safely state that the number of scholarly articles and dissertations have not been proportional to the significance of the subject of interest. On this ground, we conducted our research to contribute towards further developing the domain of Hazmats transportation, and sustainable supply chain management (SSCM), in general terms. Transportation of Hazmats, from logistical standpoint, may include all modes of transport via air, marine, road and rail, as well as intermodal transportation systems. Although road shipment is predominant in most of the literature, railway transportation of Hazmats has proven to be a potentially significant means of transporting dangerous goods with respect to both economies of scale and risk of transportation; these factors, have not just given rise to more thoroughly investigation of intermodal transportation of Hazmats using road and rail networks, but has encouraged the competition between rail and road companies which may indeed have some inherent advantages compared to the other medium due to their infrastructural and technological backgrounds. Truck shipment has ostensibly proven to be providing more flexibility; trains, per contra, provide more reliability in terms of transport risk for conveying Hazmats in bulks. In this thesis, in consonance with the aforementioned motivation, we provide an introduction into the hazardous commodities shipment through rail network in the first chapter of the thesis. Providing relevant statistics on the volume of Hazmat goods, number of accidents, rate of incidents, and rate of fatalities and injuries due to the incidents involving Hazmats, will shed light onto the significance of the topic under study. As well, we review the most pertinent articles while putting more emphasis on the state-of-the-art papers, in chapter two. Following the discussion in chapter 3 and looking at the problem from carrier company’s perspective, a mixed integer quadratically constraint problem (MIQCP) is developed which seeks for the minimization of transportation cost under a set of constraints including those associating with Hazmats. Due to the complexity of the problem, the risk function has been piecewise linearized using a set of auxiliary variables, thereby resulting in an MIP problem. Further, considering the interests of both carrier companies and regulatory agencies, which are minimization of cost and risk, respectively, a multiobjective MINLP model is developed, which has been reduced to an MILP through piecewise linearization of the risk term in the objective function. For both single-objective and multiobjective formulations, model variants with bifurcated and nonbifurcated flows have been presented. Then, in chapter 4, we carry out experiments considering two main cases where the first case presents smaller instances of the problem and the second case focuses on a larger instance of the problem. Eventually, in chapter five, we conclude the dissertation with a summary of the overall discussion as well as presenting some comments on avenues of future work

Telecommunications network design and max-min optimization problem, Journal of Telecommunications and Information Technology, 2005, nr 3

Telecommunications networks are facing increasing demand for Internet services. Therefore, the problem of telecommunications network design with the objective to maximize service data flows and provide fair treatment of all services is very up-to-date. In this application, the so-called maxmin fair (MMF) solution concept is widely used to formulate the resource allocation scheme. It assumes that the worst service performance is maximized and the solution is additionally regularized with the lexicographic maximization of the second worst performance, the third one, etc. In this paper we discuss solution algorithms for MMF problems related to telecommunications network design. Due to lexicographic maximization of ordered quantities, theMMF solution concept cannot be tackled by the standard optimization model (mathematical programme). However, one can formulate a sequential lexicographic optimization procedure. The basic procedure is applicable only for convex models, thus it allows to deal with basic design problems but fails if practical discrete restrictions commonly arriving in telecommunications network design are to be taken into account. Then, however, alternative sequential approaches allowing to solve non-convex MMF problems can be used

Journal of Telecommunications and Information Technology, 2006, nr 4

kwartalni

Groupage et protection du trafic dynamique dans les réseaux WDM

Avec les nouvelles technologies des réseaux optiques, une quantité de données de plus en plus grande peut être transportée par une seule longueur d'onde. Cette quantité peut atteindre jusqu’à 40 gigabits par seconde (Gbps). Les flots de données individuels quant à eux demandent beaucoup moins de bande passante. Le groupage de trafic est une technique qui permet l'utilisation efficace de la bande passante offerte par une longueur d'onde. Elle consiste à assembler plusieurs flots de données de bas débit en une seule entité de données qui peut être transporté sur une longueur d'onde. La technique demultiplexage en longueurs d'onde (Wavelength Division Multiplexing WDM) permet de transporter plusieurs longueurs d'onde sur une même fibre. L'utilisation des deux techniques : WDM et groupage de trafic, permet de transporter une quantité de données de l'ordre de terabits par seconde (Tbps) sur une même fibre optique. La protection du trafic dans les réseaux optiques devient alors une opération très vitale pour ces réseaux, puisqu'une seule panne peut perturber des milliers d'utilisateurs et engendre des pertes importantes jusqu'à plusieurs millions de dollars à l'opérateur et aux utilisateurs du réseau. La technique de protection consiste à réserver une capacité supplémentaire pour acheminer le trafic en cas de panne dans le réseau. Cette thèse porte sur l'étude des techniques de groupage et de protection du trafic en utilisant les p-cycles dans les réseaux optiques dans un contexte de trafic dynamique. La majorité des travaux existants considère un trafic statique où l'état du réseau ainsi que le trafic sont donnés au début et ne changent pas. En plus, la majorité de ces travaux utilise des heuristiques ou des méthodes ayant de la difficulté à résoudre des instances de grande taille. Dans le contexte de trafic dynamique, deux difficultés majeures s'ajoutent aux problèmes étudiés, à cause du changement continuel du trafic dans le réseau. La première est due au fait que la solution proposée à la période précédente, même si elle est optimisée, n'est plus nécessairement optimisée ou optimale pour la période courante, une nouvelle optimisation de la solution au problème est alors nécessaire. La deuxième difficulté est due au fait que la résolution du problème pour une période donnée est différente de sa résolution pour la période initiale à cause des connexions en cours dans le réseau qui ne doivent pas être trop dérangées à chaque période de temps. L'étude faite sur la technique de groupage de trafic dans un contexte de trafic dynamique consiste à proposer différents scénarios pour composer avec ce type de trafic, avec comme objectif la maximisation de la bande passante des connexions acceptées à chaque période de temps. Des formulations mathématiques des différents scénarios considérés pour le problème de groupage sont proposées. Les travaux que nous avons réalisés sur le problème de la protection considèrent deux types de p-cycles, ceux protégeant les liens (p-cycles de base) et les FIPP p-cycles (p-cycles protégeant les chemins). Ces travaux ont consisté d’abord en la proposition de différents scénarios pour gérer les p-cycles de protection dans un contexte de trafic dynamique. Ensuite, une étude sur la stabilité des p-cycles dans un contexte de trafic dynamique a été faite. Des formulations de différents scénarios ont été proposées et les méthodes de résolution utilisées permettent d’aborder des problèmes de plus grande taille que ceux présentés dans la littérature. Nous nous appuyons sur la méthode de génération de colonnes pour énumérer implicitement les cycles les plus prometteurs. Dans l'étude des p-cycles protégeant les chemins ou FIPP p-cycles, nous avons proposé des formulations pour le problème maître et le problème auxiliaire. Nous avons utilisé une méthode de décomposition hiérarchique du problème qui nous permet d'obtenir de meilleurs résultats dans un temps raisonnable. Comme pour les p-cycles de base, nous avons étudié la stabilité des FIPP p-cycles dans un contexte de trafic dynamique. Les travaux montrent que dépendamment du critère d'optimisation, les p-cycles de base (protégeant les liens) et les FIPP p-cycles (protégeant les chemins) peuvent être très stables.With new technologies in optical networking, an increasing quantity of data can be carried by a single wavelength. This amount of data can reach up to 40 gigabits per second (Gbps). Meanwhile, the individual data flows require much less bandwidth. The traffic grooming is a technique that allows the efficient use of the bandwidth offered by a wavelength. It consists of assembling several low-speed data streams into a single data entity that can be carried on a wavelength. The wavelength division multiplexing (WDM) technique allows carrying multiple wavelengths on a single fiber. The use of the two techniques,WDMand traffic grooming, allows carrying a quantity of data in the order of terabits per second (Tbps) over a single optical fiber. Thus, the traffic protection in optical networks becomes an operation very vital for these networks, since a single failure can disrupt thousands of users and may result in several millions of dollars of lost revenue to the operator and the network users. The survivability techniques involve reserving additional capacity to carry traffic in case of a failure in the network. This thesis concerns the study of the techniques of grooming and protection of traffic using p-cycles in optical networks in a context of dynamic traffic. Most existing work considers a static traffic where the network status and the traffic are given at the beginning and do not change. In addition, most of these works concerns heuristic algorithms or methods suffering from critical lack of scalability. In the context of dynamic traffic, two major difficulties are added to the studied problems, because of the continuous change in network traffic. The first is due to the fact that the solution proposed in the previous period, even if optimal, does not necessarily remain optimal in the current period. Thus, a re-optimization of the solution to the problem is required. The second difficulty is due to the fact that the solution of the problem for a given period is different from its solution for the initial period because of the ongoing connections in the network that should not be too disturbed at each time period. The study done on the traffic grooming technique in the context of dynamic traffic consists of proposing different scenarios for dealing with this type of traffic, with the objective of maximizing the bandwidth of the new granted connections at each time period. Mathematical formulations of the different considered scenarios for the grooming problem are proposed. The work we have done on the problem of protection considers two types of p-cycles, those protecting links and FIPP p-cycles (p-cycle protecting paths). This work consisted primarily on the proposition of different scenarios for managing protection p-cycles in a context of dynamic traffic. Then, a study on the stability of cycles in the context of dynamic traffic was done. Formulations of different scenarios have been proposed and the proposed solution methods allow the approach of larger problem instances than those reported in the literature. We rely on the method of column generation to implicitly enumerate promising cycles. In the study of path protecting p-cycles or FIPP p-cycles, we proposed mathematical formulations for the master and the pricing problems. We used a hierarchical decomposition of the problem which allows us to obtain better results in a reasonable time. As for the basic p-cycles, we studied the stability of FIPP p-cycles in the context of dynamic traffic. The work shows that depending on the optimization criterion, the basic p-cycles (protecting the links) and FIPP p-cycles (protecting paths) can be very stable

Composite variable formulations for express shipment service network design

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2000.Includes bibliographical references (p. 181-187).In this thesis, we consider large-scale network design problems, specifically the problem of designing the air network of an express shipment (i.e., overnight) delivery operation. We focus on simultaneously determining the route structure, the assignment of fleet types to routes, and the flow of packages on aircraft. Traditional formulations for network design involve modeling both flow decisions and design decisions explicitly. The bounds provided by their linear programming relaxations are often weak. Common solution strategies strengthen the bounds by adding cuts, but the shear size of the express shipment problem results in models that are intractable. To overcome this shortcoming, we introduce a new modeling approach that 1) removes the flow variables as explicit decisions and embeds them within the design variables and 2) combines the design variables into composite variables, which represent the selection of multiple aircraft routes that cover the demands for some subset of commodities. The resulting composite variable formulation provides tighter bounds and enables very good solutions to be found quickly. We apply this type of formulation to the express shipment operations of the United Parcel Service (UPS). Compared with existing plans, the model produces a solution that reduces the number of required aircraft by almost 11 percent and total annual cost by almost 25 percent. This translates to potential annual savings in the hundreds of millions of dollars. We establish the composite variable formulation to be at least as strong as the traditional network design formulation, even when the latter is strengthened by Chvital-Gomory rounding, and we demonstrate cases when strength is strictly improved. We also place the composite variable formulation in a more general setting by presenting it as a Dantzig-Wolfe decomposition of the traditional (intractable) network design formulation and by comparing composite variables to Chvital-Gomory cuts in the dual of a related formulation. Finally, we present a composite variable formulation for the Pure Fixed Charge Transportation Problem to highlight the potential application of this approach to general network design and fixed-charge problems.by Andrew P. Armacost.Ph.D