Ex-Post Funding : How Should a Resource-Constrained Non-Profit Organization Allocate Its Funds?

We study a resource allocation problem for a resource-constrained non-profit organization (NPO) that implements social development projects for public good. In addition to raising funds from donors who contribute prior to project implementation ("traditional donors"), the NPO uses a novel approach, which we term as the "ex-post funding" approach to also raise funds from donors who care about the results delivered by the NPO ('ex-post donors'). In this approach, the NPO uses its initial funds to implement early phases of the project, creates "results-certificates" from the completed phases, and invites ex-post donors to purchase these certificates. The donations raised from selling the results-certificates are used to recover the NPO's own funds used in the project implementation. Operationalizing this approach is complicated when the project must incur a large fixed cost before any benefits are delivered by the project, and the total benefit delivered is time sensitive. We show that for a given amount of initial funds available, there exists a threshold amount of funds that the NPO should raise from traditional donors before implementing the project phases so as to maximize the total expected benefit delivered. Through numerical studies, we analyze how the threshold of funds raised from traditional donors and the total benefit delivered vary with donor characteristics such as donor willingness to give and the proportion of donors who contribute prior to project implementation. Our numerical studies suggest that even with relatively small amount of initial funds, the NPO can deliver substantially higher benefit by using the ex-post funding approach when compared to using a traditional approach that requires the NPO to raise all the funds required upfront