Homeless persons have elevated risk of tuberculosis (TB) and are under-served by conventional health services. Approaches to active case-finding (ACF) and treatment tailored to their needs are required. A transmission-dynamic model was developed to assess the effectiveness and efficiency of screening with mobile Chest X-ray, GeneXpert, or both. Effectiveness of ACF depends upon the prevalence of infection in the population (which determines screening 'yield'), patient willingness to wait for GeneXpert results, and treatment adherence. ACF is efficient when TB prevalence exceeds 78/100,000 and 46% of drug sensitive TB cases and 33% of multi-drug resistant TB cases complete treatment. This threshold increases to 92/100,000 if additional post-ACF enhanced case management (ECM) increases treatment completion to 85%. Generally, the most efficient option is one-step screening of all patients with GeneXpert, but if too many patients (>27% without ECM, >19% with ECM) are unwilling to wait the 90 minutes required then two-step screening using chest X-ray (which is rapid) followed by GeneXpert for confirmation of TB is the most efficient option. Targeted ACF and support services benefit health through early successful treatment and averting TB transmission and disease. The optimal strategy is setting-specific, requiring careful consideration of patients' needs regarding testing and treatment.