TY - RPRT A1 - Amer, Zeina A1 - Avdzhieva, Ana A1 - Bongarti, Marcelo A1 - Dvurechensky, Pavel A1 - Farrell, Patricio A1 - Gotzes, Uwe A1 - Hante, Falk M. A1 - Karsai, Attila A1 - Kater, Stefan A1 - Liero, Matthias A1 - Spreckelsen, Klaus A1 - Taraz, Johannes A1 - Peschka, Dirk A1 - Plato, Luisa T1 - Modeling Hydrogen Embrittlement for Pricing Degradation in Gas Pipelines N2 - This paper addresses the critical challenge of hydrogen embrittlement in the context of Germany’s transition to a sustainable, hydrogen-inclusive energy system. As hydrogen infrastructure expands, estimating and pricing embrittlement become paramount due to safety, operational, and economic concerns. We present a twofold contribution: (1) We discuss hydrogen embrittlement modeling using both continuum models and simplified approximations. (2) Based on these models, we propose optimization-based pricing schemes for market makers, considering simplified cyclic loading and more complex digital twin models. Our approaches leverage widely-used subcritical crack growth models in steel pipelines, with parameters derived from experiments. The study highlights the challenges and potential solutions for incorporating hydrogen embrittlement into gas transportation planning and pricing, ultimately aiming to enhance the safety and economic viability of Germany’s future energy infrastructure. Y1 - 2025 ER - TY - RPRT A1 - Oggioni, Giorgia A1 - Schwartz, Alexandra A1 - Zöttl, Gregor A1 - Wiertz, Ann-Kathrin T1 - Dynamic Pricing and Strategic Retailers in the Energy Sector: A Multi-Leader-Follower Approach N2 - We consider strategic retail pricing in markets, where retail companies buy commodities at fluctuating wholesale prices and resell them to final consumers by applying dynamic retail tariffs. This is of especially large relevance in the context of energy markets where substantial wholesale price fluctuations are observed. Policy makers currently foster the introduction of such dynamic tariff schemes. From a modelling point of view, we propose a multi-leader-follower problem to investigate the implications of strategic retail pricing and we compare the impacts of implementing dynamic tariffs on retailers and final consumers. Our analysis tackles different aspects: first, we formulate the model and provide theoretical results. Second, we develop algorithms, which solve the multi-leader-follower problem and allow us to characterize the resulting market equilibria. Third, we calibrate and solve our framework based on data of the German retail electricity market for the years 2020 and 2021. This allows us to quantitatively assess the impact of introducing real time prices on retailers’ profits and customers’ benefits. As our results show, dynamic real-time pricing on the one hand typically increases market efficiency, which confirms previous results obtained without the explicit consideration of strategic behavior. On the other hand, however, as a novel aspect, dynamic real-time pricing turns out to significantly reduce equilibrium profits in case of strategic firms. This effect is especially large in environments with strongly fluctuating wholesale prices. Y1 - 2022 ER - TY - RPRT A1 - Walther, Tom A1 - Hiller, Benjamin T1 - Modelling compressor stations in gas networks N2 - Gas networks are an important application area for optimization. When considering long-range transmission, compressor stations play a crucial role in these applications. The purpose of this report is to collect and systematize the models used for compressor stations in the literature. The emphasis is on recent work on simple yet accurate polyhedral models that may replace more simplified traditional models without increasing model complexity. The report also describes an extension of the compressor station data available in GasLib (http://gaslib.zib.de/) with the parameters of these models. KW - gas compressor modeling KW - compressor station KW - polyhedral model KW - MINLP model KW - nonlinear model Y1 - 2017 ER - TY - RPRT A1 - Arulselvan, Ashwin A1 - Cseh, Ágnes A1 - Groß, Martin A1 - Manlove, David F. A1 - Matuschke, Jannik T1 - Matchings with lower quotas: Algorithms and complexity N2 - We study a natural generalization of the maximum weight many-to-one matching problem. We are given an undirected bipartite graph G = (A∪P,E) with weights on the edges in E, and with lower and upper quotas on the vertices in P. We seek a maximum weight many-to-one matching satisfying two sets of constraints: vertices in A are incident to at most one matching edge, while vertices in P are either unmatched or they are incident to a number of matching edges between their lower and upper quota. This problem, which we call maximum weight many-to-one matching with lower and upper quotas (wmlq), has applications to the assignment of students to projects within university courses, where there are constraints on the minimum and maximum numbers of students that must be assigned to each project. In this paper, we provide a comprehensive analysis of the complexity of wmlq from the viewpoints of classical polynomial time algorithms, fixed-parameter tractability, as well as approximability. We draw the line between NP-hard and polynomially tractable instances in terms of degree and quota constraints and provide efficient algorithms to solve the tractable ones. We further show that the problem can be solved in polynomial time for instances with bounded treewidth; however, the corresponding runtime is exponential in the treewidth with the maximum upper quota u_max as basis, and we prove that this dependence is necessary unless FPT = W[1]. The approximability of wmlq is also discussed: we present an approximation algorithm for the general case with performance guarantee umax + 1, which is asymptotically best possible unless P = NP. Finally, we elaborate on how most of our positive results carry over to matchings in arbitrary graphs with lower quotas. Y1 - 2016 U6 - https://doi.org/10.1007/978-3-662-48971-0_16 ER -