TY - GEN A1 - Grötschel, Martin A1 - Raack, Christian A1 - Werner, Axel T1 - Towards optimizing the deployment of optical access networks N2 - In this paper we study the cost-optimal deployment of optical access networks considering variants of the problem such as fiber to the home (FTTH), fiber to the building (FTTB), fiber to the curb (FTTC), or fiber to the neighborhood (FTTN). We identify the combinatorial structures of the most important sub-problems arising in this area and model these, e.g., as capacitated facility location, concentrator location, or Steiner tree problems. We discuss modeling alternatives as well. We finally construct a “unified” integer programming model that combines all sub-models and provides a global view of all these FTTx problems. We also summarize computational studies of various special cases. T3 - ZIB-Report - 13-11 KW - FTTx, FTTH, FTTB, FTTC, FTTN, telecommunications, access networks, passive optical networks, network design, routing, energy efficiency Y1 - 2013 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-18627 SN - 1438-0064 ER - TY - GEN A1 - Raack, Christian A1 - Raymond, Annie A1 - Werner, Axel A1 - Schlechte, Thomas T1 - Integer Programming and Sports Rankings N2 - Sports rankings are obtained by applying a system of rules to evaluate the performance of the participants in a competition. We consider rankings that result from assigning an ordinal rank to each competitor according to their performance. We develop an integer programming model for rankings that allows us to calculate the number of points needed to guarantee a team the ith position, as well as the minimum number of points that could yield the ith place. The model is very general and can thus be applied to many types of sports. We discuss examples coming from football (soccer), ice hockey, and Formula~1. We answer various questions and debunk a few myths along the way. Are 40 points enough to avoid relegation in the Bundesliga? Do 95 points guarantee the participation of a team in the NHL playoffs? Moreover, in the season restructuration currently under consideration in the NHL, will it be easier or harder to access the playoffs? Is it possible to win the Formula~1 World Championship without winning at least one race or without even climbing once on the podium? Finally, we observe that the optimal solutions of the aforementioned model are associated to extreme situations which are unlikely to happen. Thus, to get closer to realistic scenarios, we enhance the model by adding some constraints inferred from the results of the previous years. T3 - ZIB-Report - 13-19 KW - sport ranking KW - integer programming Y1 - 2013 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-18068 SN - 1438-0064 ER - TY - JOUR A1 - Raack, Christian A1 - Raymond, Annie A1 - Schlechte, Thomas A1 - Werner, Axel T1 - Standings in sports competitions using integer programming JF - Journal of Quantitative Analysis in Sports Y1 - 2013 U6 - https://doi.org/10.1515/jqas-2013-0111 VL - 10 IS - 2 SP - 131 EP - 137 PB - De Gruyter ER - TY - JOUR A1 - Grötschel, Martin A1 - Raack, Christian A1 - Werner, Axel T1 - Towards optimizing the deployment of optical access networks JF - EURO Journal on Computational Optimization Y1 - 2013 U6 - https://doi.org/10.1007/s13675-013-0016-x VL - 2 SP - 17 EP - 53 PB - Springer ER - TY - JOUR A1 - Betker, Andreas A1 - Kosiankowski, Dirk A1 - Lange, Christoph A1 - Pfeuffer, Frank A1 - Raack, Christian A1 - Werner, Axel ED - Helber, Stefan ED - Breitner, Michael ED - Rösch, Daniel ED - Schön, Cornelia ED - Graf von der Schulenburg, Johann-Matthias ED - Sibbertsen, Philipp ED - Steinbach, Marc ED - Weber, Stefan ED - Wolter, Anja T1 - Energy efficiency in extensive IP-over-WDM networks with protection JF - Operations Research Proceedings 2012 Y1 - 2014 U6 - https://doi.org/10.1007/978-3-319-00795-3_14 SP - 93 EP - 99 PB - Springer ER - TY - JOUR A1 - Leitner, Markus A1 - Ljubić, Ivana A1 - Sinnl, Markus A1 - Werner, Axel T1 - On the Two-Architecture Connected Facility Location Problem JF - Electronic Notes in Discrete Mathematics Y1 - 2013 U6 - https://doi.org//10.1016/j.endm.2013.05.113 VL - 41 SP - 359 EP - 366 CY - Costa Adeje ER - TY - JOUR A1 - Werner, Axel T1 - Kombinatorische Optimierung und die 40-Punkte-Regel JF - Mitteilungen der DMV Y1 - 2011 VL - 19 SP - 153 EP - 157 ER - TY - JOUR A1 - Werner, Axel A1 - Wotzlaw, Ronald T1 - On linkages in polytope graphs JF - Adv. Geom. Y1 - 2011 U6 - https://doi.org/10.1515/ADVGEOM.2011.015 VL - 11 IS - 3 SP - 411 EP - 427 ER - TY - GEN A1 - Uslu, Svenja A1 - Werner, Axel T1 - A Two-Phase Method for the Biobjective k-Architecture Connected Facility Location Problem and Hypervolume Computation N2 - We apply customized versions of the ε-constraint Method and the Two-Phase Method to a problem originating in access network planning. We introduce various notions of quality measures for approximated/partial sets of nondominated points, utilizing the concept of hypervolume for biobjective problems. We report on computations to assess the performance of the two methods in terms of these measures. T3 - ZIB-Report - 15-08 KW - Biobjective Optimization KW - Connected Facility Location KW - Hypervolume Y1 - 2015 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-53753 SN - 1438-0064 ER - TY - JOUR A1 - Paffenholz, Andreas A1 - Werner, Axel T1 - Constructions for 4-polytopes and the cone of flag vectors. JF - Contemporary Mathematics Y1 - 2006 VL - 423 SP - 283 EP - 303 PB - Algebraic and geometric combinatorics. Euroconference in mathematics, algebraic and geometric combinatorics, Anogia, Crete, Greece, August 20–26, 2005. Providence, RI: American Mathematical Society (AMS) ER - TY - GEN A1 - Werner, Axel T1 - Smallest non-trivial 2s2s-polytope Y1 - 2005 UR - http://www.eg-models.de/2005.12.001 PB - EG Model, online ER - TY - GEN A1 - Betker, Andreas A1 - Kosiankowski, Dirk A1 - Lange, Christoph A1 - Pfeuffer, Frank A1 - Raack, Christian A1 - Werner, Axel T1 - Energy efficiency in extensive multilayer core and regional networks with protection N2 - Energy-efficient operation of large telecommunication networks is an important issue today and in the near future. Given that the energy consumption rises with the ever increasing demand for capacity and network speed, there is a growing interest in strategies for a sustainable network management. It is a well-known fact that traffic demands vary significantly over time, most notably in day/night- and in weekly cycles. This provides the main potential for energy-saving strategies. We study the question of how much power is necessary to operate a network with state-of-the-art hardware during peak or low-traffic times. The study respects realistic side constraints, such as protection requirements and routing schemes, and takes the special structure of an extensive nation-wide optical network, including backbone and regional sections, into account. We formulate mixed integer programming models for the corresponding optimization problems using predictions for traffic matrices, as well as state-of-the-art hardware and power models. We address questions as the following: How much energy is spent in the core and in metro regions of the network and how big are the savings in low-demand scenarios if we always assume the system power-minimum in these situations? What is the influence of different hardware on the overall energy consumption? How much do different routing schemes or protection scenarios restrict potential energy savings? T3 - ZIB-Report - 12-45 KW - telecommunications KW - network design KW - routing KW - energy efficiency Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-17154 SN - 1438-0064 ER - TY - JOUR A1 - Leitner, Markus A1 - Ljubic, Ivana A1 - Sinnl, Markus A1 - Werner, Axel T1 - ILP heuristics and a new exact method for bi-objective 0/1 ILPs: Application to FTTx-network design JF - Computers & Operations Research Y1 - 2016 U6 - https://doi.org/10.1016/j.cor.2016.02.006 ER - TY - GEN A1 - Draegert, Andreas A1 - Eisenblätter, Andreas A1 - Gamrath, Inken A1 - Werner, Axel T1 - Optimal Battery Controlling for Smart Grid Nodes N2 - Energy storages can be of great value when added to power grids. They introduce the possibility to store and release energy whenever this is favorable. This is particularly relevant, for example, if power supply is volatile (as is the case with renewable energy) and the network is small (so that there are few other nodes that might balance fluctuations in consumption or production). We present models and methods from mathematical optimization for computing an optimized storage schedule for this purpose. We look at alternative optimization objectives, such as smallest possible peak load, low energy costs, or the close approximation of a prescribed load curve. The optimization needs to respect general operational and economic constraints as well as limitations in the use of storage, which are imposed by the chosen storage technology. We therefore introduce alternative approaches for modeling the non-linear properties of energy storages and study their impact on the efficiency of the optimization process. Finally, we present a computational study with batteries as storage devices. We use this to highlight the trade-off between solution quality and computational tractability. A version of the model for the purpose of leveling peaks and instabilities has been implemented into a control system for an office-building smart grid scenario. T3 - ZIB-Report - 15-06 KW - energy optimization, non-linear optimization, smart grid Y1 - 2015 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-53550 SN - 1438-0064 ER - TY - GEN A1 - Coniglio, Stefano A1 - Grimm, Boris A1 - Koster, Arie M.C.A. A1 - Tieves, Martin A1 - Werner, Axel T1 - Optimal offline virtual network embedding with rent-at-bulk aspects N2 - Network virtualization techniques allow for the coexistence of many virtual networks (VNs) jointly sharing the resources of an underlying substrate network. The Virtual Network Embedding problem (VNE) arises when looking for the most profitable set of VNs to embed onto the substrate. In this paper, we address the offline version of the problem. We propose a Mixed-Integer Linear Programming formulation to solve it to optimality which accounts for acceptance and rejection of virtual network requests, allowing for both splittable and unsplittable (single path) routing schemes. Our formulation also considers a Rent-at-Bulk (RaB) model for the rental of substrate capacities where economies of scale apply. To better emphasize the importance of RaB, we also compare our method to a baseline one which only takes RaB into account a posteriori, once a solution to VNE, oblivious to RaB, has been found. Computational experiments show the viability of our approach, stressing the relevance of addressing RaB directly with an exact formulation. Y1 - 2015 ER - TY - GEN A1 - Orlowski, Sebastian A1 - Werner, Axel A1 - Wessäly, Roland T1 - Estimating trenching costs in FTTx network planning N2 - In this paper we assess to which extent trenching costs of an FTTx network are unavoidable, even if technical side constraints are neglected. For that purpose we present an extended Steiner tree model. Using a variety of realistic problem instances we demonstrate that the total trenching cost can only be reduced by about 5 percent in realistic scenarios. This work has been funded by BMBF (German Federal Ministry of Education and Research) within the program "KMU-innovativ". T3 - ZIB-Report - 11-49 KW - Optical access networks KW - Optimization KW - Steiner trees Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-14884 SN - 1438-0064 ER - TY - GEN A1 - Leitner, Markus A1 - Ljubic, Ivana A1 - Sinnl, Markus A1 - Werner, Axel T1 - On the Two-Architecture Connected Facility Location Problem N2 - We introduce a new variant of the connected facility location problem that allows for modeling mixed deployment strategies (FTTC/FTTB/FTTH) in the design of local access telecommunication networks. Several mixed integer programming models and valid inequalities are presented. Computational studies on realistic instances from three towns in Germany are provided. T3 - ZIB-Report - 13-29 KW - Connected Facility Location, Branch-and-Cut, FTTx Deployment Y1 - 2013 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-18610 SN - 1438-0064 ER - TY - CHAP A1 - Bentz, Winfried A1 - Eckel, Klaus A1 - Louchet, Hadrien A1 - Orlowski, Sebastian A1 - Patzak, Erwin A1 - Seibel, Julia A1 - Werner, Axel A1 - Wessäly, Roland T1 - Schätze heben bei der Planung von FTTx-Netzen T2 - Breitbandversorgung in Deutschland Y1 - 2011 VL - 227 PB - VDE-Verlag ER - TY - CHAP A1 - Orlowski, Sebastian A1 - Werner, Axel A1 - Wessäly, Roland ED - Klatte, Diethart ED - Lüthi, Hans-Jakob ED - Schmedders, Karl T1 - Estimating trenching costs in FTTx network planning T2 - Operations Research Proceedings 2011 Y1 - 2012 SP - 89 EP - 94 PB - Springer Verlag ER - TY - JOUR A1 - Sanyal, Raman A1 - Werner, Axel A1 - Ziegler, Günter T1 - On Kalai’s conjectures concerning centrally symmetric polytopes. JF - Discrete Comput. Geom. Y1 - 2009 U6 - https://doi.org/10.1007/s00454-008-9104-8 VL - 41 IS - 2 SP - 183 EP - 198 ER -