Inverse Optimization, Incentive Design and Healthcare Policy

This dissertation presents mathematical models and algorithms that draw from optimization and statistics and are motivated by practical problems in operations management. We discuss theoretical properties of the proposed models as well as their relevance to practice. In particular, we focus on the role these models can play in addressing challenges in healthcare operations and policy./nIn Chapter 2, we address the problem of building models of agent behavior from observational data regarding the agent's decisions. Concretely, we consider the inverse optimization problem, which refers to the estimation of unknown model parameters of a convex optimization problem from observations of its optimal solutions. First, we provide a new formulation for inverse optimization, which takes the form of a bi-level program where the optimality conditions of the lower level program are expressed using strong duality. In contrast to existing methods, we show that the parameter estimates produced by our formulation are statistically consistent under appropriate conditions. Second, we propose two solution algorithms based on our duality-based formulation: an enumeration algorithm that is applicable to settings where the dimensionality of the parameter space is modest, and a semiparametric approach that combines nonparametric statistics with a modified version of our formulation. These numerical algorithms are shown to maintain the statistical consistency of the underlying formulation. Lastly, using both synthetic and real data, we demonstrate that our approach performs competitively when compared with existing heuristics./nIn Chapter 3, we employ an inverse optimization approach to redesign a class of Medicare contracts. We formulate the existing contract between Medicare and a provider as a principal-agent model. We then propose an alternate contract, which we show to dominate the status quo contract under reasonable conditions by producing a strictly higher expected payoff for both Medicare and the provider. We then propose an estimator based on inverse optimization for estimating a model of provider behavior, using a dataset containing the financial performance of a group of Medicare providers that account for 7 million beneficiaries and over $70 billion in Medicare spending. We estimate a performance improvement -- in terms of savings accrued by Medicare -- of 40% under the alternate contract, which suggests significant room for improvement in the status quo./nIn Chapter 4, we propose a data-driven modeling approach to facility location in a setting where the location of demand points is subject to uncertainty. The model is motivated by the problem of placing automated external defibrillators in public locations in anticipation of sudden cardiac arrest. We propose a distributionally robust optimization approach where the demand distribution is continuous in the plane and uncertain. We propose a solution technique based on row-and-column generation that exploits the structure of the uncertainty set and allows us to solve practical-sized instances of the defibrillator deployment problem. Using real cardiac arrest data, we conduct an extensive numerical study and find that hedging against cardiac arrest location uncertainty can produce defibrillator deployments that outperform a intuitive sample average approximation by 9 to 15%. Our findings suggest that accounting for cardiac arrest location uncertainty can lead to improved accessibility of defibrillators during cardiac arrest emergencies and the potential for improved survival outcomes.

Advisor: Shen, Zuo-Jun