Allocation of Funds in Bilevel Subsidy Welfare Programs.

The article focuses on optimizing fund allocation in subsidy welfare programs characterized by a bilevel hierarchical structure, where a funding agency distributes limited resources to multiple service organizations that invest in local activities to generate societal impact. It proposes an equity-ensuring, forward-looking bilevel optimization model that accounts for the funding agency's equity considerations, complex contextual factors influencing societal impact, and information asymmetry regarding potential future additional funds earmarked for specific areas. The analysis reveals that the funding agency should allocate more funds to areas with a balanced mix of subsidy-accepting and nonaccepting providers, or fewer nonaccepting providers, and where investments yield higher returns, while also adjusting allocations based on the likelihood of additional future funds in other areas. Comparative evaluations show that although simple formula-based methods may sometimes yield higher total societal impact with moderate inequity, the proposed equity-ensuring method consistently eliminates inequity without severely sacrificing impact, and contrasts with efficiency-focused methods that maximize impact but can exacerbate inequity, especially amid large disparities in beneficiary populations. A case study of Massachusetts' child care subsidy program illustrates that the equity-ensuring method can reduce inequity and increase overall societal impact by approximately 3% compared to current formula-based allocations.