Recent estimates indicate that there are over 1 million runaway and homeless youth and young adults (RHY) in the United States (US). Exposure to trauma, violence, and substance abuse, coupled with a lack of community support services, puts homeless youth at high risk of being exploited and trafficked. Although access to safe housing and supportive services such as physical and mental healthcare is an effective response to youth’s vulnerability towards being trafficked, the number of youth experiencing homelessness exceeds the capacity of available housing resources in most US communities. We undertake a RHY-informed, systematic, and data-driven approach to project the collective capacity required by service providers to adequately meet the needs of RHY in New York City, including those most at risk of being trafficked. Our approach involves an integer linear programming model that extends the multiple multidimensional knap-sack problem and is informed by partnerships with key stakeholders. The mathematical model allows for time-dependent allocation and capacity expansion, while incorporating stochastic youth arrivals and length of stays, services provided in a periodic fashion, and service delivery time windows. Our RHY and service provider-centered approach is an important step toward meeting the actual, rather than presumed, survival needs of vulnerable youth.