Dual-level scenario trees Scenario generation and applications in energy planning Michal Kaut 1 , Kjetil T. Midthun 1 , Adrian S. Werner 1 , Asgeir Tomasgard 1,2 , Lars Hellemo 1 , and Marte Fodstad 1 1 SINTEF Technology and Society, Department for Applied Economics and Operations Research, Trondheim, Norway 2 Norwegian University of Science and Technology (NTNU), Department of Industrial Economics and Technology Management, Trondheim, Norway July 2012 Infrastructure-planning models are challenging because of their combination of different time scales: while planning and building the infrastructure involves strate- gic decisions with time horizons of many years, one needs an operational time scale to get a proper picture of the infrastructure’s performance and profitability. In addi- tion, both the strategic and operational levels are typically subject to significant un- certainty, which has to be taken into account. This combination of uncertainties on two different time scales creates problems for the traditional multistage stochastic- programming formulation of the problem due to the exponential growth in model size. In this paper, we present an alternative formulation of the problem that combines the two time scales, using what we call a dual-level approach. We demonstrate the approach on two applications from energy planning. Keywords: stochastic programming, multistage, energy planning 1 Introduction Infrastructure-planning models typically focus on long-term investment strategies, with time horizons of years or even decades. For many such models it is important to acknowledge how operational aspects will affect (and will be affected by) these strategic decisions: in order to find truly robust, flexible, and profitable solutions, it is necessary to assess how the infrastructure can be used, at what cost, and how it can respond to varying conditions. Hence, the goal is often to design infrastructure in a way that maximizes the discounted expected profit (or minimizes the discounted expected costs) of constructing, maintaining, and using the infrastructure, while 1