Randomized clinical trial (RCT) studies are the gold standard for scientific evidence on treatment benefits to patients. RCT outcomes may not be generalizable to clinical practice if the trial population is not representative of the patients for which the treatment is intended. Specifically, enrollment plans may not adequately include groups of patients with protected attributes, such as gender, race, or ethnicity. Inequities in RCTs are a major concern for funding agencies such as the National Institutes of Health (NIH) and for policy makers. We address this challenge by proposing a goal-programming approach, explicitly integrating measurable enrollment goals, to design equitable enrollment plans for RCTs. We evaluate our model in both single and multisite settings using the enrollment criteria and study population from the Systolic Blood Pressure Intervention Trial (SPRINT) study. Our model can successfully generate equitable enrollment plans that satisfy multiple goals such as sample representativeness and minimum total financial cost. Our model can detect deviations from a target plan during the enrollment process and update the plan to reduce deviations in the remaining process. Finally, through appropriate site selection in the planning stage, the model can demonstrate the possibility of enrolling a nationally representative study population if geographic constraints exist in multisite recruitment (e.g., clinical centers in a particular region). Our model can be used to prospectively produce and retrospectively evaluate how equitable enrollment plans are based on subjects' protected attributes, and it allows researchers to provide justifications on validity of scientific analysis and evaluation of subgroup disparities.