Decision-making under uncertainty has been studied for a long time by the operations management research community. In the past, uncertainty models were often derived based on domain knowledge. However, the availability of vast amounts of data in the recent years has shifted interests towards data-driven approaches for uncertainty quantification. More specifically, statistical models are employed within this framework for characterizing the uncertain components of a stochastic optimization problem based on historical data.
In this dissertation, we focus on applications of data-driven decision-making under uncertainty in the healthcare and energy management sectors. The first part of our work provides a mathematical framework for efficient call assignment under Direct Load Control (DLC) contracts (i.e. an incentive-based demand-response program that is widely used by utility firms for balancing the supply and demand of electricity during peak times). Specifically, we employ a model for forecasting energy consumption and develop a large-scale integer stochastic dynamic optimization problem. We then propose a novel hierarchical approximation scheme for efficient execution of the contracts. We evaluate the quality of our proposed approach using real-world data obtained from California Independent System Operator (CAISO), which is the umbrella organization of utility firms in California. A large utility firm in California has implemented our model and informed us that they have experienced a 4\% additional r duction in their cost.
Following a similar predict-then-optimize methodological framework, the second part of this dissertation studies data-driven healthcare intervention planning. Specifically, we develop a continuous-time latent-space Markovian model for describing disease progression based on discrete-time irregularly-spaced observations. Our model is capable of incorporating the effect of interventions on progression of disease. We discuss the computational challenges of parameter estimation for this model and present a novel efficient estimation approach based on the Expectation-Maximization (EM) algorithm. A population-level optimization model for intervention planning in the behavioral healthcare sector is then developed using the fitted disease progression model. Afterward, we present an extension of the model, which is more appropriate for medical healthcare domains such as cancer maintenance therapy, and formulate an EM algorithm for estimating the model parameters. Finally, we develop an individual-level intervention planning problem based on the patient's historical data using the estimated model.
