The U.S. Foster Care System: A Resource Allocation Perspective

Abigail Rose Lindner
Abigail Lindner
Worcester Polytechnic Institute

Foster care can be defined as situations where children are placed by a competent authority for the purpose of alternative care in the domestic environment of a family other than the children’s own family that has been selected, qualified, approved and supervised for providing such care [11]

In the United States, over 400,000 children reside in foster care at a time. Since its validation as a state-operated child welfare service over a century ago, the U.S. foster care system has evolved considerably as societal norms and political influences have changed and fields like developmental psychology have grown. Goals, however, have stayed the same.

One of the first goals is protection and care for children who, for whatever reasons, are unable to reside with their biological families. A second goal is eventual settlement of those children in permanent placements. For the latter, reunification with the biological family has been the top priority for a number of decades. Where reunification is not possible and kin are unable or unavailable to care for the child, adoption is oftentimes the next recourse. In these cases, the child is said to have a permanency plan of adoption.

The fulfillment of these goals requires sufficient resources, proportionate distribution of those resources to children in foster care and their families, consistent communication between all stakeholders, and, where reunification fails and adoption has been deemed appropriate for the child, efficient matching between children who need families and families who want to adopt them. Legislation in the late twentieth century and early twenty-first century aimed at alleviating roadblocks to achieving these goals has helped to some extent - providing funding, pioneering programs, collecting national data to inform policy - but challenges remain. Many of the challenges come down to limited resources: social services, foster families, staff, time, etc.

In recent decades, operations research has come into play to meet these challenges. Such research includes assessment of housing subsidies on foster care placement and family stability [8], prediction of average lengths of stay based on analysis of dozens of cultural and socioeconomic factors [10], and evaluation of risk factors to guide casework decisions [2]. Long accustomed to dealing with problems in business and transportation, operations research is primed with the tools to address two of the main problems in the foster care system - allocating finite resources and matching children who have permanency plans of adoption with the right families.

The foster care system in the United States is a complex and important institution. In the interest of assessing both problems with as much detail as they deserve, we will be dividing this discussion into two parts. In this issue (Fall/Winter 2022), we will cover the operations research involved in foster care resource allocation. In the next issue (Spring/Summer 2023), we will describe parent-child matching.

Resource Allocation

Each state has a responsibility to provide resources and services to children in their foster care systems, to the families who foster, and to the biological families to support the health and well-being of the child and, when possible, the reunification of the child to their original family. Between and within states, the number and type of resources and services varies. In addition to caregivers and social services staff, the finite resources needing to be allocated may include mental health services, substance use treatment, healthcare, special education classes, vocational training, and in-home parenting services [7].

A common hindrance in foster care is the paucity and expense of services. However, eliminating services is not an option, as they are crucial to stabilizing the children and families involved and shortening the amount of the time that children stay in out-of-home placements. With over 400,000 children in the system on any given day, though, efficiently and accurately identifying which children and/or families need which services is difficult.

Sounds like a problem for operations research, right?

To consider the problem of resource allocation in the U.S. foster care system, we will focus on two undergraduate projects written by students from my current academic institution. The first takes a national view and the second focuses on a single state.

The Children’s Bureau within the U.S. Department of Health & Human Services has in place several systems to collect data on children involved in the child welfare system. Two of these are the National Child Abuse and Neglect Data System (NCANDS) and the Adoption and Foster Care Analysis and Reporting System (AFCARS).

  • NCANDS collects data on all child maltreatment reports that received investigations or assessment responses in the 50 States, the District of Columbia, and Puerto Rico. State and regional agencies voluntarily submit NCANDS child file data, which includes “demographics of children and their perpetrators, types of maltreatment, investigation or assessment dispositions, risk factors, and services provided as a result of the investigation or assessment” [1].
  • AFCARS is a federally-mandated system. It collects “case-level information on all children in foster care and those who have been adopted with title IV-E agency involvement” [4]. Title IV-E is an amendment to the Social Security Act, a piece of twentieth century legislation that provided social welfare to Americans.

In U.S.-based studies on the child welfare system that use either or both of these datasets, it is important to bear in mind that they are notoriously coarse. For instance, regarding NCANDS, one study notes that the data does not indicate “whether a service is given multiple times to a family or a child. The only indication is whether a service has ever been received” [6].

A Nationwide Project

In the first study, Diefendorf et al. (2019) [6] used key child identifiers to combine NCANDS and AFCARS datasets from 2010 to 2015, resulting in a national sample of about 147,000 children who had been discharged from foster care and a survey of 60 data points. The goal was to create a model that predicted the number of days that a child would reside in foster care based on child and family demographic characteristics, child and family risk factors, and child- and family-level services received.

With approximately 1,700 features to use in the predictive model, the researchers executed a two-phase approach, first eliminating the majority of insignificant factors using a Least Absolute Shrinkage and Selection Operator (LASSO) regression technique and then assessing the remaining factors via a linear regression model. Records from 2010-2014 were used for the LASSO and linear tests and records from 2015 were used for the predictive and optimization models.

In the end, the model included fifty-three predictors, each with a 0.005 significance level. An adjusted R-squared of 0.706 suggested that the model fit the data well, though it had a large margin of error - about 20%. The researchers estimated total time in care for each child using the predictive model, and from there developed an optimization model to minimize the total days spent in care based on service allocation.

The actual days spent in care for the entire sample was 6,411,901. Using the optimization model, they found that, in the worst-case scenario, a total of 6,327,684 days total might be spent in care, amounting to a savings of 84,217 days altogether or an average of 5.2 days per child. In the most likely scenario, a total of 5,913,547 days might be spent in care, amounting to a savings of 498,347 days altogether or an average of 31 days per child. In addition to the psychological benefit for children of spending less time in out-of-home placements, optimized service allocation would have financial benefits, with over 98 million dollars saved in the worst-case scenario and over 585 million dollars saved in the most likely scenario, based on an average of $70 per child per day in foster care.

Just the Texans Now

Building off Diefendorf et al. (2019) [6], Barrameda et al. (2020) [3] attempted to narrow implementation by focusing analysis on children under 2 from urban areas of Texas who were placed in foster care because of parental substance abuse and had reached permanent discharge. These specifications reduced their population size to 3,173 cases.

The researchers used linear regression to estimate the impacts of a variety of services, then used integer linear programming to optimize service allocation and develop an algebraic model. NCANDS and AFCARS were, again, the main sources of data. In addition, they incorporated environmental risk factors, including county-level crimes rates, unemployment rates, and other statistics found through the U.S. Census Bureau and the Bureau of Labor Statistics. Their predictive model eventually accounted for 157 factors.

The actual total time spent in care was 1,278,050 days; the model underestimated by about 0.3%, predicting 1,274,406 days. The researchers found that an optimized reallocation of services, with the constraint that all services available were allocated, could reduce total time in care by 44,794 days, or about 15.3 days per child. If the constraint to use all services were relaxed, the time savings came out to about 23.2 days per child.

Despite the potential for operations research to benefit the foster care system by optimizing service use and minimizing days spent in care, as demonstrated in these two undergraduate projects, to date little peer-reviewed research exists on this topic.1 Nevertheless, we do have examples from other social service projects that demonstrate the application of operations research for similar problems, such as in humanitarian logistics [5,12,13].

Resource allocation within the foster care system is an important problem open to the input of skilled operations research practitioners who are eager to understand the field, explore the data, and develop models that child welfare professionals can easily implement into their day-to-day operations, learning from the work done in different contexts.

Conclusion & Upcoming Discussion

With almost half a million children to serve on any given day, child welfare professionals and caregivers in the U.S. foster care system have a lot to balance. Nationwide, it is a regular challenge to distribute resources and services within quantity constraints while also meeting the behavioral, emotional, mental, and physical needs of children, their biological families, and their foster families.

As reunification remains the primary goal of the child welfare system for many (or most) state administrators, the Office of the Assistant Secretary for Planning and Evaluation [9] optimized service allocation could be important in facilitating the return of children to their families by shortening the amount of time spent in care, as suggested in the student projects Diefendorf et al. (2019)[6] and Barrameda et al. (2020) [3].

Unlike resource allocation, parent-child matching has received a decent amount of attention from operations research professionals. When a social worker decides that a child would be best served by adoption rather than reunification, kinship placement, guardianship, or long-term foster care, an often-long process of matching the child to the right prospective adoptive family begins. The role of OR in parent-child matching algorithms will be the subject of the next article, which will appear in the Spring/Summer 2023 edition of OR/MS Tomorrow.


1One NSF-funded research project, conducted by investigators at SUNY at Buffalo and incomplete as of writing, is focused on developing a service recommendation algorithm for the foster care system. See further details on the NSF award page.


Administration for Children and Families. (2021, November 23). National Child Abuse and Neglect System (NCANDS) Child File: Findings from the National Child Abuse and Neglect Data System (NCANDS) - Data tables (updated with FY 2015). Accessed August 14, 2022.

[2] Bald, A., Doyle, J.J., Gross, M. & Jacob, B.A. (2022). Economics of foster care. Journal of Economic Perspectives, 36(2), 223-246.

[3] Barrameda, C., Calnan, M., Clemente, J. & Conroy, J. (2020). Using operations research & analytics to increase the effectiveness of service allocation to families with infants in out of home care due to substance abuse in the Texas child welfare system. Unpublished manuscript. Worcester Polytechnic Institute.

[4] Children’s Bureau. (n.d.). About AFCARS. Accessed August 14, 2022.

[5] Das, R. & Hanaoka, S. (2014). An agent-based model for resource allocation during relief distribution. Journal of Humanitarian Logistics and Supply Chain Management, 4(2), 265-285.

[6] Diefendorf, B., Doherty, R., Tropeano, R. & Yagoobi, K. (2019). Improving U.S. foster care service allocation. Unpublished manuscript. Worcester Polytechnic Institute.

[7] Font, S.A. & Gershoff, E.T. (2020). Foster care: how we can, and should, do more for maltreated children. Social Policy Report, 33(3), 1-40. https://doi.orgi/10.1002/sop2.10.

[8] Fowler, P.J., Brown, D.S., Schoeny, M. & Chung, S. (2018). Homelessness in the child welfare system: A randomized controlled trial to assess the impact of housing subsidies on foster care placements and costs. Child Abuse & Neglect, 83, 52-61.

[9] Office of the Assistant Secretary for Planning and Evaluation. (2001, November 30). Assessing the context of permanency and reunification in the foster care system.

[10] Russell, J. & Macgill, S. (2015). Demographics, policy, and foster care rates: a predictive analytics approach. Children & Youth Services Review, 58, 118-126. UNICEF. (n.d.). Definitions. Accessed August 13, 2022.

[11] Yu, L., Zhang, C., Yang, H. & Miao, L. (2018). Novel methods for resource allocation in humanitarian logistics considering human suffering. Computers & Industrial Engineering, 119, 1-20.

[12] Yu, L., Zhang, C., Jiang, J., Yang, H. & Shang, H. (2021). Reinforcement learning approach for resource allocation in humanitarian logistics. Expert Systems with Applications, 173.