Mixed-integer formulations for large-scale energy-environmental optimization

To support decision making in complex systems, different mathematical programming approaches have been developed for both modelling the decision process and finding the best decisions or policies. This dissertation focuses on decision making in the context of climate change mitigation, considering two different perspectives on the topic. The first is a global perspective of research and development of negative emission technologies and their effect on the optimal emission levels in the next 50 years. The second is a more localized perspective of regulating a competitive power market, aiming to efficiently reduce the emissions of electricity production. The structures contained within these problems render them incompatible with existing solution methods. First, many of the uncertainties in climate change mitigation, such as the cost of reducing emissions in the future, depend on the earlier decisions such as the level of research investment. While different types of decision-dependent uncertainty have been researched before, combining these types in a way that would allow for accurate modeling of the decision process has not been possible. Second, a bilevel hierarchical structure of a power market with a transmission system operator and electricity producers has received significant attention in the literature, but these methods are not directly applicable to problems with a third hierarchical level representing, in our case, the international regulator. This dissertation enables more realistic modeling of decision-dependent uncertainty and hierarchical decision making by reformulating the problems using mixed-integer programming (MIP). Using mixed-integer optimization as the main solution framework allows us to utilize the vast developments in solving mixed-integer models. Additionally, implementing explicit risk measures in MIP models has received significant attention in the literature, and these developments can be applied to the proposed models with minor adjustments. However, the computational efficiency of solving mixed-integer models depends not only on the solution method, but also the formulation used. The articles in this dissertation discuss and compare three different MIP formulations for limited memory influence diagrams, and two single-level reformulations for trilevel equilibrium models. Despite their simplified nature, the case studies in this dissertation provide policy insights on cost-benefit optimal emission trajectories and the effect of a carbon tax on the Nordic electricity market. Such models can help justify decisions when developing policies in complex and controversial contexts such as climate change mitigation. While the focus of the dissertation is on energy and environment, the methodological developments in this dissertation are equally applicable to a variety of problems in fields such as healthcare, systems monitoring and traffic planning.