On Embedding Advanced Predictive Models into Optimization Models

There has been a significant proliferation of research in and application of machine learning and discrete optimization. These two analytical domains have frequently been used in a single business decision-making context but for different purposes. Machine learning techniques are typically used to predict what is likely to happen in the future, while optimization methods are typically used to search through feasible solutions strategically. In this dissertation, we consider the integration of these two domains where the features of predictive models are variables in a decision problem, and the output of the predictive model is a part of the objective function. We study two applications that fall under this paradigm and introduce an optimization solver called JANOS to solve such problems. The first application is a retail network expansion problem. Given an existing retail network, how can one decide which possible expansion locations to select in order to maximize expected revenue? Using data from an add-on product retailer, we train radial-kernel support vector regression models and embed them within classical expansion optimization models. We identify expansion decisions that are superior to those determined from conventional approaches. In a second application, we study automated team formation. Using real-world data from student-team simulations in general management classes, we train both linear regression models and neural networks to predict team performance. We embed these predictive models within a partitioning optimization model to form teams that are superior in predicted performance to those identified through heuristics. Through these studies, a common theme arises: can we embed advanced predictive models within an optimization model, and design efficient algorithms for solving the resulting problem? In an attempt towards achieving this goal, we create an optimization solver called JANOS that allows users to embed machine learning models within an optimization model, leveraging the power of optimization solvers to automate decision making. This framework is easily extensible to many decision-making scenarios, enabling researchers and practitioners to broaden the scope of integrating machine learning models with decision problems