In this dissertation, we study mixed-integer programming (MIP) approaches to solve resource allocation problems with applications in healthcare asset management and epidemics. In particular, we study (i) valid inequalities for solving large-scale one-dimensional zero-one (0–1) knapsack problems (KPs), (ii) healthcare asset-replacement problems that involve several styles and types of magnetic resonance imaging (MRI) machines, and (iii) epidemics involving the Ebola virus disease (EVD) under resource constraints. Using recursive solutions of the dynamic programming (DP), we present valid inequalities that can be added to the original 0–1 KP as cutting planes (CP) to tighten and improve the model formulation for facilitating solution methods. Extensive computational experiments show that our inequalities yield competitive results. Operating assets generally suffer from deterioration, which results in high operation and maintenance (O&M) cost and decreased salvage value, while technologies allow newer machines to operate more efficiently at a lower cost. Therefore, we study the multiple style and type parallel asset-replacement problem (MST-PRES), which determines an optimal policy for keeping or replacing a group of assets that operate in parallel under a limited budget. Results show that the proposed MIP model provides valuable insights and strategies for decision-makers and government entities on the capital asset management. Epidemic diseases, which are occurring more frequently, are a major health and economic problem for mankind. This section begins with a review of epidemiological disease models that have been used to study transmission dynamics of Ebola and their estimated key parameters from existing data set in order to explain important patterns by which it spreads to make significant public healthcare decisions. Following the review of Ebola, we develop a mixed-integer optimization of epidemic model to address the efficient allocation of epidemic resources and to assess the impact of traveling within Guinea, Liberia, and Sierra Leone for control of the 2014 Ebola outbreak. We conclude by presenting effective combinations of future intervention strategies and policy recommendation for controlling the EVD epidemics.