Essays on Constrained Optimization Models with Applications in Healthcare and Revenue Management

This dissertation advances the theory and application of constrained optimization for decision-making problems in healthcare, pricing, and revenue management. Constrained optimization offers a powerful framework for incorporating operational, physical, and policy constraints into models that must also account for uncertainty and dynamic change. The work combines methodological innovation with empirical validation, contributing new optimization frameworks and practical insights. Chapter 2 develops a constrained optimization model for estimating average treatment effects from observational data when confounders are only partially observed. The model relaxes strong assumptions such as unconfoundedness and equal confounder distribution, establishes identifiability, derives closed-form optimal solutions, and provides finite-sample concentration bounds. Experiments with an example of the obesity paradox and a real-world application using the PharmGKB Warfarin data set confirm its accuracy and precision. Chapter 3 applies these methods to COVID-19 vaccination and mortality data from England. The analysis reveals Simpson's paradox across age groups and quantifies biases from uneven confounder distributions. By integrating cumulative vaccination records and mortality statistics, the proposed estimation approach corrects for these biases and enables interpretable, generalizable conclusions about vaccine effectiveness. Chapter 4 studies a deterministic dynamic pricing problem for products with network effects in a fixed, heterogeneous customer base. A spatial demand model links location to both intrinsic valuation and network sensitivity, which is represented in a dynamic program. Numerical experiments show that fixed-price policies can perform poorly under strong network effects or long horizons. Analytical bounds, comparative statics, and heuristics with performance guarantees are developed, and a stochastic extension is presented. Together, these contributions illustrate how constrained optimization can integrate theoretical rigor with practical relevance, offering methods and insights for problems involving uncertainty, heterogeneity, and interdependence.