A Polyhedral Study of Mixed 0-1 Set

We consider a variant of the well-known single node fixed charge network flow set with constant capacities. This set arises from the relaxation of more general mixed integer sets such as lot-sizing problems with multiple suppliers. We provide a complete polyhedral characterization of the convex hull of the given set

Investigation of Game-Theoretic Mechanisms for the Valuation of Energy Resources

Electricity systems are facing the pressure to change in response to the effects of new technology, particularly the proliferation of renewable technologies (such as solar PV systems and wind generation) leading to the retirement of traditional generation technologies that provide stabilising inertia. These changes create an imperative to consider potential future market structures to facilitate the participation of distributed energy resources (DERs; such as EVs and batteries) in grid operation. However, this gives rise to general questions surrounding the ethics of market structures and how they could be fairly applied in future electricity systems. Particularly the most basic question "how should electricity be valued and traded" is fundamentally a moral question without any easy answer. We give a survey of philosophical attitudes around such a question, before presenting a series of ways that these intuitions have been cast into mathematics, including: the Vickrey-Clarke-Groves mechanism, Locational Marginal Pricing, the Shapley Value, and Nash bargaining solution concepts. We compared these different methods, and attempted a new synthesis that brought together the best features of each of them; called the 'Generalised Neyman and Kohlberg Value' or the GNK-value for short. The GNK value was developed as a novel bargaining solution concept for many player non-cooperative transferable utility generalised games, and thus it was intrinsically flexible in its application to various aspects of powersystems. We demonstrated the features of the GNK-value against the other mathematical solutions in the context of trading the immediate consumption/generation of power on small sized networks under linear-DC approximation, before extending the computation to larger networks. The GNK value proved to be difficult to compute for large networks but was shown to be approximable for larger networks with a series of sampling techniques and a proxy method. The GNK value was ethically compared to other mechanisms with the unfortunate discovery that it allowed for participants to be left worse-off for participating, violating the ethical notion of 'euvoluntary exchange' and 'individual rationality'; but was offered as an interesting innovation in the space of transferable utility generalised games notwithstanding. For sampling the GNK value, there was a range of new and different techniques developed for stratified random sampling which iteratively minimise newly derived concentration inequalities on the error of the sampling. These techniques were developed to assist in the computation of the GNK value to larger networks, and they were evaluated in the context of sampling synthetic data, and in computation of the Shapley Value of cooperative game theory. These new sampling techniques were demonstrated to be comparable to the more orthodox Neyman sampling method despite not having access to stratum variances

Fuelling the zero-emissions road freight of the future: routing of mobile fuellers

The future of zero-emissions road freight is closely tied to the sufficient availability of new and clean fuel options such as electricity and Hydrogen. In goods distribution using Electric Commercial Vehicles (ECVs) and Hydrogen Fuel Cell Vehicles (HFCVs) a major challenge in the transition period would pertain to their limited autonomy and scarce and unevenly distributed refuelling stations. One viable solution to facilitate and speed up the adoption of ECVs/HFCVs by logistics, however, is to get the fuel to the point where it is needed (instead of diverting the route of delivery vehicles to refuelling stations) using "Mobile Fuellers (MFs)". These are mobile battery swapping/recharging vans or mobile Hydrogen fuellers that can travel to a running ECV/HFCV to provide the fuel they require to complete their delivery routes at a rendezvous time and space. In this presentation, new vehicle routing models will be presented for a third party company that provides MF services. In the proposed problem variant, the MF provider company receives routing plans of multiple customer companies and has to design routes for a fleet of capacitated MFs that have to synchronise their routes with the running vehicles to deliver the required amount of fuel on-the-fly. This presentation will discuss and compare several mathematical models based on different business models and collaborative logistics scenarios

Internationales Kolloquium über Anwendungen der Informatik und Mathematik in Architektur und Bauwesen : 20. bis 22.7. 2015, Bauhaus-Universität Weimar

The 20th International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering will be held at the Bauhaus University Weimar from 20th till 22nd July 2015. Architects, computer scientists, mathematicians, and engineers from all over the world will meet in Weimar for an interdisciplinary exchange of experiences, to report on their results in research, development and practice and to discuss. The conference covers a broad range of research areas: numerical analysis, function theoretic methods, partial differential equations, continuum mechanics, engineering applications, coupled problems, computer sciences, and related topics. Several plenary lectures in aforementioned areas will take place during the conference. We invite architects, engineers, designers, computer scientists, mathematicians, planners, project managers, and software developers from business, science and research to participate in the conference

Internationales Kolloquium über Anwendungen der Informatik und Mathematik in Architektur und Bauwesen : 20. bis 22.7. 2015, Bauhaus-Universität Weimar

The 20th International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering will be held at the Bauhaus University Weimar from 20th till 22nd July 2015. Architects, computer scientists, mathematicians, and engineers from all over the world will meet in Weimar for an interdisciplinary exchange of experiences, to report on their results in research, development and practice and to discuss. The conference covers a broad range of research areas: numerical analysis, function theoretic methods, partial differential equations, continuum mechanics, engineering applications, coupled problems, computer sciences, and related topics. Several plenary lectures in aforementioned areas will take place during the conference. We invite architects, engineers, designers, computer scientists, mathematicians, planners, project managers, and software developers from business, science and research to participate in the conference

Managing computational complexity through using partitioning, approximation and coordination

Problem: Complex systems are composed of many interdependent subsystems with a level of complexity that exceeds the ability of a single designer. One way to address this problem is to partition the complex design problem into smaller, more manageable design tasks that can be handled by multiple design teams. Partitioning-based design methods are decision support tools that provide mathematical foundations, and computational methods to create such design processes. Managing the interdependency among these subsystems is crucial and a successful design process should meet the requirements of the whole system which needs coordinating the solutions for all the partitions after all. Approach: Partitioning and coordination should be performed to break down the system into subproblems, solve them and put these solutions together to come up with the ultimate system design. These two tasks of partitioning-coordinating are computationally demanding. Most of the proposed approaches are either computationally very expensive or applicable to only a narrow class of problems. These approaches also use exact methods and eliminate the uncertainty. To manage the computational complexity and uncertainty, we approximate each subproblem after partitioning the whole system. In engineering design, one way to approximate the reality is using surrogate models (SM) to replace the functions which are computationally expensive to solve. This task also is added to the proposed computational framework. Also, to automate the whole process, creating a knowledge-based reusable template for each of these three steps is required. Therefore, in this dissertation, we first partition/decompose the complex system, then, we approximate the subproblem of each partition. Afterwards, we apply coordination methods to guide the solutions of the partitions toward the ultimate integrated system design. Validation: The partitioning-approximation-coordination design approach is validated using the validation square approach that consists of theoretical and empirical validation. Empirical validation of the design architecture is carried out using two industry-driven problems namely the a hot rod rolling problem’, ‘a dam network design problem’, ‘a crime prediction problem’ and ‘a green supply chain design problem’. Specific sub-problems are formulated within these problem domains to address various research questions identified in this dissertation. Contributions: The contributions from the dissertation are categorized into new knowledge in five research domains: • Creating an approach to building an ensemble of surrogate models when the data is limited – when the data is limited, replacing computationally expensive simulations with accurate, low-dimensional, and rapid surrogates is very important but non-trivial. Therefore, a cross-validation-based ensemble modeling approach is proposed. • Using temporal and spatial analysis to manage the uncertainties - when the data is time-based (for example, in meteorological data analysis) and when we are dealing with geographical data (for example, in geographical information systems data analysis), instead of feature-based data analysis time series analysis and spatial statistics are required, respectively. Therefore, when the simulations are for time and space-based data, surrogate models need to be time and space-based. In surrogate modeling, there is a gap in time and space-based models which we address in this dissertation. We created, applied and evaluated the effectiveness of these models for a dam network planning and a crime prediction problem. • Removing assumptions regarding the demand distributions in green supply chain networks – in the existent literature for supply chain network design, there are always assumptions about the distribution of the demand. We remove this assumption in the partition-approximate-compose of the green supply chain design problem. • Creating new knowledge by proposing a coordination approach for a partitioned and approximated network design. A green supply chain under online (pull economy) and in-person (push economy) shopping channels is designed to demonstrate the utility of the proposed approach

Book of abstracts of the 24th Euro Working Group on Transportation Meeting

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