  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 youths 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 homeless
youth 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 knapsack 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, particularly those at-risk of being trafficked.
