An algorithmic framework for the exact solution of tree-star problems

Many problems arising in the area of telecommunication ask for solutions with a tree-star topology. This paper proposes a general procedure for finding optimal solutions to a family of these problems. The family includes problems in the literature named as connected facility location, rent-or-buy and generalized Steiner tree-star. We propose a solution framework based on a branch-and-cut algorithm which also relies on sophisticated reduction and heuristic techniques. An important ingredient of this framework is a dual ascent procedure for asymmetric connected facility location. This paper shows how this procedure can be exploited in combination with various mixed integer programming formulations. Using the new framework, many benchmark instances in the literature for which only heuristic results were available so far, can be solved to provable optimality within seconds. To better assess the computational performance of the new approach, we additionally consider larger instances and provide optimal solutions for most of them too

Mixed integer programming approaches to problems combining network design and facility location

Viele heutzutage über das Internet angebotene Dienstleistungen benötigen wesentlich höhere Bandbreiten als von bestehenden lokalen Zugangsnetzen bereitgestellt werden. Telekommunikationsanbieter sind daher seit einigen Jahren bestrebt, ihre zum Großteil auf Kupferkabeln basierenden Zugangsnetze entsprechend zu modernisieren. Die gewünschte Erweiterung der bereitgestellten Bandbreiten wird oftmals erzielt, indem ein Teil des Kupfernetzes durch Glasfaser ersetzt wird. Dafür sind Versorgungsstandorte notwendig, an welchen die optischen und elektrischen Signale jeweils in einander umgewandelt werden. In der Praxis gibt es mehrere Strategien für die Installation von optischen Zugangsnetzen. Fiber-to-the-Home bezeichnet Netze, in denen jeder Haushalt direkt per Glasfaser angebunden wird. Wird je Wohngebäude eine optische Verbindung bereitgestellt, nennt man dies Fiber-to-the-Building. Endet die Glasfaserverbindung an einem Versorgungsstandort, welcher die Haushalte eines ganzen Wohnviertels durch Kupferkabel versorgt, bezeichnet man dies als Fiber-to-the-Curb. Inhalt dieser Dissertation sind mathematische Optimierungsmodelle für die kosteneffiziente Planung von auf Glasfaser basierenden lokalen Zugangsnetzen. Diese Modelle decken mehrere Aspekte der Planung ab, darunter die Fiber-to-the-Curb-Strategie mit zusätzlichen Restriktionen betreffend Ausfallssicherheit, gemischte Fiber-to-the-Home und Fiber-to-the-Curb-Netze sowie die Kapazitätenplanung von Fiber-to-the-Curb-Netzen. Ergebnis dieser Dissertation sind die theoretische Analyse der beschriebenen Modelle sowie effiziente Lösungsalgorithmen. Es kommen Methoden der kombinatorischen Optimierung zum Einsatz, darunter Umformulierungen auf erweiterten Graphen, zulässige Ungleichungen und Branch-and-Cut-Verfahren.In recent years, telecommunication service providers started to adapt their local access networks to the steadily growing demand for bandwidth of internet-based services. Most existing local access networks are based on copper cable and offer a limited bandwidth to customers. A common approach to increase this bandwidth is to replace parts of the network by fiber-optic cable. This requires the installation of facilities, where the optical signal is transformed into an electrical one and vice versa. Several strategies are commonly used to deploy fiber-optic networks. Connecting each customer via a fiber-optic link is referred to as Fiber-to-the-Home. If there is a fiber-optic connection for every building this is commonly referred to as Fiber-to-the-Building. If a fiber-optic connection leads to each facility that serves an entire neighborhood, this is referred to as Fiber-to-the-Curb. In this thesis we propose mathematical optimization models for the cost-efficient design of local access networks based on fiber-optic cable. These models cover several aspects, including the Fiber-to-the-Curb strategy under additional reliability constraints, mixed Fiber-to-the-Home and Fiber-to-the-Curb strategies and capacity planning of links and facilities for Fiber-to-the-Curb networks. We provide a theoretical analysis of the proposed models and develop efficient solution algorithms. We use state-of-the-art methods from combinatorial optimization including polyhedral comparisons, reformulations on extended graphs, valid inequalities and branch-and-cut procedures

The incremental connected facility location problem

We consider the incremental connected facility location problem (incremental ConFL), in which we are given a set of potential facilities, a set of interconnection nodes, a set of customers with demands, and a planning horizon. For each time period, we have to select a set of facilities to open, a set of customers to be served, the assignment of these customers to the open facilities, and a network that connects the open facilities. Once a customer is served, it must remain served in subsequent periods. Furthermore, in each time period the total demand of all customers served must be at least equal to a given minimum coverage requirement for that period. The objective is to minimize the total cost for building the network given by the investment and maintenance costs for the facilities and the network summed up over all time periods. We propose a mixed integer programming approach in which, in each time period, a single period ConFL with coverage restrictions has to be solved. For this latter problem, which is of particular interest in itself, new families of valid inequalities are proposed: these are set union knapsack cover (SUKC) inequalities, which are further enhanced by lifting and/or combined with cut-set inequalities, which are primarily used to ensure connectivity requirements. Details of an efficient branch-and-cut implementation are presented and computational results on a benchmark set of large instances are given, including examples of telecommunication networks in German

Dual-Based Local Search for Deterministic, Stochastic and Robust Variants of the Connected Facility Location Problem

In this dissertation, we propose the study of a family of network design problems that arise in a wide range of practical settings ranging from telecommunications to data management. We investigate the use of heuristic search procedures coupled with lower bounding mechanisms to obtain high quality solutions for deterministic, stochastic and robust variants of these problems. We extend the use of well-known methods such as the sample average approximation for stochastic optimization and the Bertsimas and Sim approach for robust optimization with heuristics and lower bounding mechanisms. This is particular important for NP-complete problems where even deterministic and small instances are difficult to solve to optimality. Our extensions provide a novel way of applying these techniques while using heuristics; which from a practical perspective increases their usefulness

Fiber to the home

In den letzten Jahren gab es zunehmenden Bedarf für breitbandige Telekommunikations Netzwerke. Eine von Telekommunikationsunternehmen angewandte Strategie um die Bandbreite entlang der last-mile des Netzwerks zu erhöhen ist, Glasfaserkabel direkt bis zum Endkunden zu verlegen. Diese Strategie wird fiber to the home (FTTH) genannt. In der vorliegenden Arbeit wird das local access network design problem (LAN) und die Variante mit prize-collecting (PC-LAN) verwendet, um das Problem der FTTH Planung zu modellieren. Das LAN Problem zielt darauf ab eine kostenminimale Lösung zu finden und gestattet es sowohl verschiedene Kabeltechnologien und existierende Infrastruktur, als auch die Zusatzkosten zu modellieren, die anfallen wenn neue Verbindungen hergestellt werden. Darüber hinaus, erlaubt das PC-LAN Problem den Aspekt zu modellieren, dass nicht unbedingt alle Kunden mit FTTH versorgt werden müssen. Stattdessen wird eine Teilmenge der Kunden versorgt mit dem Ziel den Profit zu maximieren. Um LAN und PC-LAN Problem Instanzen zu lösen, werden folgende Methoden des Operations Research angewandt: Preprocessing, ganzzahlige Programmierung, Stärkung der mathematischen Modelle durch Disaggregation der Variablen, Benders' Dekomposition und adaptive Multi-Start-Heuristiken. In einem Projekt von Universität Wien und Telekom Austria wurden große FTTH Datensätze untersucht und die hier vorgestellten Methoden entworfen. Diese Lösungsansätze wurden als Computerprogramme implementiert und ihre Tauglichkeit zur Behandlung von FTTH Planungsfragen konnte gezeigt werden.Within recent years the request for broadband telecommunication networks has been constantly increasing. A strategy employed by telecommunication companies to increase the bandwidth on the last mile of the network is to lay optical fiber directly to the end customer. This strategy is denoted as fiber to the home (FTTH). In this thesis the local access network design problem (LAN) and its prize-collecting variant (PC-LAN) are used to formalize the planning of FTTH networks. The LAN problem asks for a cost minimal solution and allows to model different cable technologies, existing infrastructure and the overhead cost incurred by building new connections. In addition, the PC-LAN problem covers the aspect, that not all customers must necessarily be connected with FTTH, but instead we search for a subset of customers in order to maximize profits. To solve LAN and PC-LAN instances, the following operations research methods are employed: Preprocessing, mixed integer programming, model strengthening by variable disaggregation, Benders' decomposition and adaptive multi-start heuristics. In a project between University of Vienna and Telekom Austria, large real world data sets for FTTH planning were investigated and the methods presented in this thesis have been designed. These solution methods have been implemented as computer programs and empirically verified to be reasonable approaches to FTTH network design problems

Operational research:methods and applications

Throughout its history, Operational Research has evolved to include a variety of methods, models and algorithms that have been applied to a diverse and wide range of contexts. This encyclopedic article consists of two main sections: methods and applications. The first aims to summarise the up-to-date knowledge and provide an overview of the state-of-the-art methods and key developments in the various subdomains of the field. The second offers a wide-ranging list of areas where Operational Research has been applied. The article is meant to be read in a nonlinear fashion. It should be used as a point of reference or first-port-of-call for a diverse pool of readers: academics, researchers, students, and practitioners. The entries within the methods and applications sections are presented in alphabetical order