Concentrator location in telecommunications

We survey the main results in the author's PhD Thesis presented in December 2002 at the Université Libre de Bruxelles and supervised by Prof. Martine Labbé. The dissertation is written in English and is available at smg.ulb.ac.be. Several versions of concentrator location problems in telecommunication networks are studied. The thesis presents a list of polyhedral results for these problems and a branch and cut algorithm for the most general problem introduced. © Springer-Verlag 2004

Polyhedral analysis for concentrator location problems

The concentrator location problem is to choose a subset of a given terminal set to install concentrators and to assign each remaining terminal node to a concentrator to minimize the cost of installation and assignment. The concentrators may have capacity constraints. We study the polyhedral properties of concentrator location problems with different capacity structures. We develop a branch and cut algorithm and present computational results. © 2006 Springer Science + Business Media, Inc

Operations Research in action

Wie der Titel bereits andeutet bezieht sich diese Dissertation auf ein Operations Research Projekt, dass der Ä Osterreichische Telekommunikationsanbieter Telekom Austria in den Jahren 2006 bis 2009 durchfÄuhrte. Die wachsende Zahl von Internet Nutzern, neue Anwendungen im Internet und die zunehmende Konkurrenz von mobilem Internet zwingen Festnetzbetreiber wie Telekom Austria ihre Produkte fÄur den Internet Zugang mit hÄoheren Bandbreiten zu versehen. ZwangslÄau¯g mÄussen die Zugangsnetze verbessert werden, was nur mit hohen Investitionskosten erreichbar ist. Aus diesem Grund kommt der kostenoptimalen Planung solcher Netzwerke eine zentrale Rolle zu. Ein wesentliches Projektziel war es, den Planungsprozess mit Methoden der diskreten Optimie- rung aus dem Bereich Network Design zu unterstÄutzen. Die Ergebnisse, die in dieser Disserta- tion beschrieben werden, beschÄaftigen sich mit Algorithmen aus dem Gebiet Facility Location (Bestimmung von Versorgungsstandorten). Vor der PrÄasentation der dazugehÄorigen Theorie und ihrer Anwendung auf die gestellten Problem werden zweitere grÄundlich analysiert. ZunÄachst wird der Telekommunikationsmarkt bis 2009 mit speziellem Fokus auf den Zeitraum zwischen 2006 und 2009 beschrieben. Die Telekommunikationsindustrie hatte bereits einige Strategien zur Verbesserung der Netzwerkinfrastruktur entwickelt. Ihre Relevanz fÄur die ge- stellten Probleme wird herausgearbeitet Dem folgt eine Au°istung der Problemspezi¯kationen, wie sie in der Evaluierungsphase des Projekts mit den beteiligten Anwendern erstellt wurde. Mit Hilfe eines dynamischen Programmes wird die gestellte Fragestellung unter BerÄucksichtigung aller Spezi¯kationen gelÄost. Eine Au°istung von Bedingungen, wann dieser Algorithmus die optimale LÄosung liefert, und die dazugehÄorigen Beweise beschlie¼en Kapitel 1. In der Folge stellte sich allerdings heraus, dass die Praktiker mit dieser ersten LÄosung nicht zufrieden waren. Die Liste der Spezi¯kationen war nicht vollstÄandig. Sie musste verÄandert und erweitert werden. Mangelnde E±zienz machte die LÄosungen fÄur die Praxis unbrauchbar. Die LÄosungen enthielten Versorgungsstandorte, die minder ausgelastet waren (underutilized), d.h. diesen Standorten waren zu wenige Kunden zugeordnet worden. Solche Lokationen mussten aus den LÄosungen entfernt werden. Dann aber waren die Verbleibenden so zu repositionieren, dass die Versorgung mit einer vorgegebenen MindestÄubertragungsrate fÄur die grÄo¼tmÄogliche Menge an Kunden sichergestellt werden konnte. Diese Strategie wurde mit Hilfe des Konzepts der k-Mediane umgesetzt: Unter der Nebenbedingung, dass die Anzahl der Standorte durch eine Konstante k beschrÄankt ist, wird die optimale Zuordnung von Kunden zu Versorgungs- standorten, d.h. ihre Versorgung, gesucht. Anschlie¼end lÄost man dann k-Median Probleme fÄur verschiedene Werte von k und bestimmt die Mindestauslastungen und Versorgungsraten, die diese LÄosungen erzielen. Dieses Vorgehen versetzt den Anwender in die Lage unter verschie- denen LÄosungen zwischen e±zienter Auslastung der Versorgungsstandorten und der HÄohe der Versorgungsraten balancieren zu kÄonnen. In Kapitel 2 werden zunÄachst die Ereignisse und Diskussionen beschrieben, die eine ÄAnderung der LÄosungsstrategie notwendig machten, und die geÄanderten bzw. neuen Spezi¯kationen wer- den prÄasentiert. Dem folgt die Vorstellung der Theorie der k-Mediane inklusive der Beschrei- bung eines Algorithmus aus der Literatur. Am Ende des zweiten Kapitels wird eine Variante dieses Algorithmus entwickelt, der fÄur die spezi¯schen Anforderungen noch besser geeignet ist: Der Algorithmus aus der Literatur fÄugt Lokationen schrittweise in die LÄosung ein, d.h. pro Iteration erhÄoht sich die Anzahl der Versorgungsstandorte um einen, bis die maximale Anzahl von Lokationen erreicht ist. Im Falle von Zugangsnetzen ist die zu erwartende Anzahl von Standorten aber eher gro¼. Daher ist es vorteilhafter die gewÄunschte Anzahl von oben, durch Reduktion der Anzahl von Versorgungsstandorten in der LÄosung zu erreichen. Kapitel 3 liefert eine extensive empirische Analyse von 106 verschiedenen Zugangsnetzen. Kon- kreter Zweck dieser Demonstration ist es einen Eindruck zu vermittelt, wie man die entwickel- ten und adaptierten Methoden bei der Vorbereitung des Planungsprozesses einsetzen kann. So ist es einerseits mÄoglich strategischen Fragestellungen vorab zu analysieren (z.B. E®ekt der Erzwingung des HV Kreises, Balance zwischen Auslastung der Versorgungsstandorte und der Versorgungsrate), und andererseits VorschlÄage fÄur passende Planungsprozesse fÄur die An- wender zu entwickeln (z.B. durch Laufzeitanalysen). ZusÄatzlich werden die beiden Methoden zur LÄosung des k-Median Problems, die in dieser Abreit vorgestellt werden, noch bzgl. ihres Laufzeitverhaltens verglichen.As indicated by the title this thesis is based on an Operations Research project which was conducted at the Austrian telecommunications provider Telekom Austria between 2006 and 2009. An increasing number of internet users, new internet applications and the growing competition of mobile internet access force ¯xed line providers like Telekom Austria to o®er higher rates for data transmission via their access networks. As a consequence access nets have to be improved which leads to investments of signi¯cant size. Therefore, minimizing such investments by a cost optimal planning of networks becomes a key issue. The main goal of the project was to support the planning process by utilizing discrete opti- mization methods from the ¯eld of network design. The key results which are presented in this thesis are algorithms for facility location. However, before dealing with the theory and the solutions | in practice as well as in this thesis | a thorough analysis of the stated problem is undertaken. To begin with the telecommunication market before 2006 and especially between 2006 and 2009 is reviewed to provide some background information. The industry had already developed di®erent strategies to improve ¯xed line infrastructure. Their relevance for the stated problem is presented. Furthermore, the most important problem speci¯cations as they were gathered in cooperation with the practitioners are listed and discussed in detail. A ¯rst solution was based on a dynamic program for solving the facility location problem which was derived from the speci¯cations. The statement of conditions for the optimality of this algorithm and their proofs conclude Chapter 1. It turned out that this ¯rst solution did not provide the desired result. It rather fostered the discussion process between operations researches and practitioners. New speci¯cations were added to the existing list. The planners dismissed these ¯rst solutions because they were not e±cient enough. These solutions contained facilities which were underutilized, i.e. too few customers were assigned to such facilities. To overcome this problem facilities of low utilization had to be removed from the solutions. The remaining facilities were rearranged in a way to maximize the coverage with a certain minimum transmission rate. This strategy was realized by adapting the concept of the k-median problem: The number of facilities is bounded whereas simultaneously the number of optimally supplied customers is maximized. Then for di®erent bounds the minimum facility utilization is reported. That way the practitioner is enabled to ¯nd the optimal balance between e±cient facility utilization and coverage of customer demands. After sketching the events and discussions which made further development necessary and listing the additional speci¯cations, the theory of the k-median problem is presented and a basic algorithm from the literature is cited. For the speci¯c requirements of the given problem a variant of the algorithm is developed and described at the end of Chapter 2: The algorithm from the literature inserts facilities one by one into the solution that way approaching the bound in an ascending manner. However, since the expected number of facilities is usually large it is more advantageous to approach the bound from above in a descending manner. Finally, an extensive empirical study of 106 di®erent local access areas is presented. The main purpose of this demonstration is to give a concrete impression of how the adapted and developed methods can be utilized in preparation of the planning process by studying strategic questions (e.g. CO circle enforcement, balancing between facility utilization and coverage) and by providing information (runtime) which is useful to set up an appropriate working environment for the future users. Additionally, the two variants of the k-median algorithm | the ascending and the descending method | can be compared

Hub Network Design and Discrete Location: Economies of Scale, Reliability and Service Level Considerations

In this thesis, we study three related decision problems in location theory. The first part of the dissertation presents solution algorithms for the cycle hub location problem (CHLP), which seeks to locate p-hub facilities that are connected by means of a cycle, and to assign non-hub nodes to hubs so as to minimize the total cost of routing flows through the network. This problem is useful in modeling applications in transportation and telecommunications systems, where large setup costs on the links and reliability requirements make cycle topologies a prominent network architecture. We present a branch and-cut algorithm that uses a flow-based formulation and two families of mixed-dicut inequalities as a lower bounding procedure at nodes of the enumeration tree. We also introduce a greedy randomized adaptive search algorithm that is used to obtain initial upper bounds for the exact algorithm and to obtain feasible solutions for large-scale instances of the CHLP. Numerical results on a set of benchmark instances with up to 100 nodes confirm the efficiency of the proposed solution algorithms. In the second part of this dissertation, we study the modular hub location problem, which explicitly models the flow-dependent transportation costs using modular arc costs. It neither assumes a full interconnection between hub nodes nor a particular topological structure, instead it considers link activation decisions as part of the design. We propose a branch-and-bound algorithm that uses a Lagrangean relaxation to obtain lower and upper bounds at the nodes of the enumeration tree. Numerical results are reported for benchmark instances with up to 75 nodes. In the last part of this dissertation we study the dynamic facility location problem with service level constraints (DFLPSL). The DFLPSL seeks to locate a set of facilities with sufficient capacities over a planning horizon to serve customers at minimum cost while a service level requirement is met. This problem captures two important sources of stochasticity in facility location by considering known probability distribution functions associated with processing and routing times. We present a nonlinear mixed integer programming formulation and provide feasible solutions using two heuristic approaches. We present the results of computational experiments to analyze the impact and potential benefits of explicitly considering service level constraints when designing distribution systems

Hub Network Design Problems with Profits

In this thesis we study a new class of hub location problems denoted as \textit{hub network design problems with profits} which share the same feature: a profit oriented objective. We start from a basic model in which only routing and location decisions are involved. We then investigate more realistic models by incorporating new elements such as different types of network design decisions, service commitments constraints, multiple demand levels, multiple capacity levels and pricing decisions. We present mixed-integer programming formulations for each variant and extension and provide insightful computational analyses regarding to their complexity, network topologies and their added value compared to related hub location problems in the literature. Furthermore, we present an exact algorithmic framework to solve two variants of this class of problems. We continue this study by introducing joint hub location and pricing problems in which pricing decisions are incorporated into the decision-making process. We formulate this problem as a mixed-integer bilevel problem and provide feasible solutions using two math-heuristics. The dissertation ends with some conclusions and comments on avenues of future research

LOCATION AND ROUTING PROBLEMS: A UNIFIED APPROACH

This thesis is about location and routing problems. We propose a unified algorithmic approach, based on the branch-and-cut-and-price paradigm, for the exact solution of general location and routing problems involving both costs and profits. In particular three different types of N P -hard problems are taken into account: the first is an extension, arising in the context of waste collection management, of the well studied Vehicle Routing Problem. The second is based on the Multi-Depot Vehicle Routing Problem with profits and has applications in the exploration of planetary surfaces. The last problem is about the distribution of drugs in emergency situations. For every problem a detailed description and a mathematical formulation are given. The largest part of the thesis is dedicated to the careful explanation of how our method can be efficiently implemented in every of the problems taken into account. In particular we propose new algorithmic ideas and several modifications and extensions to many procedures already presented in the literature. However, all components of our algorithms are fully presented and analyzed pointing out every methodological and practical issue. Extensive computational experiments and comparisons are carried out to evaluate the performance of our approach and the tractability of the problems addressed

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