The "last mile" of a supply chain is the final step of that supply chain before the product reaches the end consumer. In humanitarian and health delivery supply chains, the last mile represents the final leg of the journey for health care or other assistance to reach beneficiaries, and is a critical bottleneck contributing to the acutely inadequate health care access in resource-limited regions. Operations research methodology can be used to evaluate, lessen, and ultimately overcome this bottleneck. In this dissertation, we present four models developed for this context. First, we develop an inventory model to analyze the interaction between a stockpile and a downstream relief operation for large humanitarian organizations such as the United Nations High Commissioner for Refugees. Second, we present an optimization model that explicitly includes treatment adherence when integrating a clinic's capacity decisions with population health outcomes. Our final two models investigate the effectiveness, then the efficiency and equity, of fleet management programs for health worker vehicles (e.g., nonprofit Riders for Health) in places like rural sub-Saharan Africa. Health access challenges are fundamentally supply chain problems, and these models are a first step in using operations research tools to improve health delivery in resource-limited regions. Humanitarian organizations must use their financial resources wisely to carry out their mandates, and models such as these can help organizations make the best use of their limited response resources.