Electric buses are increasingly becoming an important topic in urban transportation systems. Many cities are beginning to incorporate them for their environmental and health benefits. Despite these advantages, electric bus systems face many technical challenges when compared to traditional gasoline powered buses. Various strategies have been proposed in the literature to leverage the flexibility of individually owned electric vehicles and fleets. A crucial component of the problem lies in the local electric grid load created by the demand from charging the vehicles. The collective demand from charging an entire fleet of vehicles results in a significant demand spike, insofar that charging the vehicles becomes a price-making activity, rather than a price-taking one. This shift poses further challenges in the vehicle scheduling in that we must optimize by reducing costs, but the choices also affect and determine the costs. In this study, we introduce methods to tackle this chicken-and-egg problem by iteratively solving the electric bus vehicle scheduling problem, and learning the costs of the routes
that affect and are affected by the grid load.

Simulating energy generation from intermittent sources like solar and biomass is vital for efficient energy planning. Accurate estimation and analysis of these sources are crucial for system design and decision-making. However, conventional approaches fail to capture the intricate dynamics of these time series, necessitating more advanced modeling techniques. In this study, we highlight the limitations of traditional methodologies and propose an exogenous variable-dependent Hidden Markov Model (HMM) that incorporates time-variant transition matrices. This novel approach enables more realistic simulations, as demonstrated in the context of biomass generation. Moreover, we present an integrated application of a Time Variant Hidden Markov Model in a SDDP framework in a real world scenario of a hydrothermal power system model, where the model involves an independent system operator (ISO) responsible for monthly planning the economic dispatch for power plants and water stored in reservoirs while meeting energy demand. The main contributions of this research include the formulation of the adapted HMM, best practices and implementation details and real-world application in renewable energy simulations.

Most decision-making under uncertainty problems found in industry and studied by the scientific community can be framed as a two-stage stochastic program. In the past decades, the standard framework to address this class of mathematical programming problems follows a sequential two-step process, usually referred to as estimate-then-optimize, in which a predictive distribution of the uncertain parameters is firstly estimated, based on some machine/statistical learning (M/SL) method, and, then, a decision is prescribed by solving the two-stage stochastic program using the estimated distribution. In this context, most M/SL methods typically focus only on minimizing the prediction error of the uncertain parameters, not accounting for its impact on the downstream decision problem. However, practitioners argue that their main interest is to obtain near-optimal solutions from the available data with minimum decision error rather than a least-error prediction. Therefore, in this talk, we discuss the new framework referred to as task-based learning in which the M/SL training function also accounts for the downstream decision problem. As the M/SL method, we focus on decision trees, and study decision-making problems framed as a two-stage linear program. We present an exact Mixed-Integer Linear Program (MILP) formulation for the task-based learning method and construct two efficient recursive-partitioning Heuristic Strategies for the MILP. We conclude the talk by analyzing a set of numerical experiments illustrating the capability and effectiveness of the task-based prescriptive tree learning framework, benchmarking against the standard estimate-then-optimize framework, and discussing the computational capability of the constructed heuristic strategies vis-à-vis the MILP formulation.

We have developed a novel analytics framework that computes contextually robust data-driven decisions with recourse. In contrast to existing contextual prescriptive approaches, our framework completely disregards the predictive step. Considering contextual information reduces uncertainty, leading to significant economic benefits, such as lower operating costs than those estimated by traditional robust optimization models. A simple parameterization allows robustness control, enabling optimal decisions ranging from contextual to unconditional robustness. We provide a single-level reformulation with the same complexity as the unconditional problem. Finally, we demonstrate the framework's performance in a economic dispatch problem with uncertain demand and renewable generation.