Various logistical hurdles make it difficult to train surgical residents. They are often asked to prioritize very different activities by very different agencies—some of whom are the hospital, their mentors, other residents and fellows, educators, and patients. Duty hour restrictions imposed throughout the prior decade have also compressed residents' schedules. As a result, they often spend the majority of their time in locations and activities where learning goals will not be met. They finish residency with very different portfolios of surgical experience and they are seldom in the right place at the right time to achieve continuity of care. This thesis quantifies the degree to which these problems exist on a vascular surgery rotation at a large, urban, academic medical center. It also identifies the causes of these problems—some are that resident rotation lengths are not long enough to allow residents to achieve longitudinal continuity of care with their patients, that residents spend insufficient time in the outpatient clinic, that the delegation of responsibilities and learning opportunities precludes continuity of care, and that existing processes and IT support systems do not enable improve these outcomes. Finally, this thesis recommends policy and process changes to help residents overcome these obstacles. It also includes a description of a simple software application and its heuristic logic that can be used to assign residents to patients so that these outcomes will improve. Finally, it includes optimization models and their computational results. These models can potentially improve on the heuristic logic for greater results. The quantitative analysis and results contributed by this thesis has been lacking in the surgical education literature. The thesis also contributes to the operations research and management science literature identification of an important health care problem which has been overlooked.