Nonprofit organizations (NPOs) exist to reduce inequalities in public services created by failures in the public and private sectors. Yet, whether NPOs do so is not always clear. In the education sector, researchers have found that NPOs are an avenue through which existing inequalities are maintained, and perhaps perpetuated: Well-resourced schools tend to have the most NPO partners. Schools serving high proportions of low-income students, which have greater need, have fewer NPO partners. An open question is how this happens. In our study, we adapt a process modeling framework (Little's Law), often used to calculate the inventory in production systems, to represent the school's problem of allocating limited time and resources to build and maintain a high inventory of NPO partners. To contextualize the process flow framework in this new setting, we draw on 36 hour-long, one-on-one interviews with principals and teachers from six public and charter schools representing different levels of socio-economic hardship. Our model, taken together with these rich first-hand accounts, contributes an operational understanding of how under-resourced schools come to maintain fewer NPO partnerships than well-resourced schools. Finally, we use our process model as a tool to analyze policy interventions that could re-balance school-NPO partnerships to better promote equity in school services and educational outcomes.