A novel strong duality-based reformulation for trilevel infrastructure models in energy systems development

Olli Herrala, Steven A. Gabriel, Fabricio Oliveira and Tommi Ekholm

Journal of the Operational Research Society, 2025, vol. 76, issue 3, 438-453

Abstract: We explore the class of trilevel equilibrium problems with a focus on energy-environmental applications and present a novel single-level reformulation for such problems, based on strong duality. To the best of our knowledge, only one alternative single-level reformulation for trilevel problems exists. This reformulation uses a representation of the bottom-level solution set, whereas we propose a reformulation based on strong duality. Our novel reformulation is compared to this existing formulation, discussing both model sizes and computational performance. In particular, we apply this trilevel framework to a power market model, exploring the possibilities of an international policymaker in reducing emissions of the system. Using the proposed approach, we are able to obtain globally optimal solutions for a five-node case study representing the Nordic countries and assess the impact of a carbon tax on the electricity production portfolio.

Date: 2025
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DOI: 10.1080/01605682.2024.2365807

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