Non-profit organizations that provide food, shelter, and other services to people in need, rely on volunteers to deliver their services. Unlike paid labor, non-profit organizations have less control over unpaid volunteers' schedules, efforts, and reliability. However, these organizations can invest in volunteer engagement activities to ensure a steady and adequate supply of volunteer labor. We study a key operational question of how a non-profit organization can manage its volunteer workforce capacity to ensure consistent provision of services. In particular, we formulate a multiclass queueing network model to characterize the optimal engagement activities for the non-profit organization to minimize the costs of enhancing volunteer engagement, while maximizing productive work done by volunteers. Because this problem appears intractable, we formulate an approximating Brownian control problem in the heavy traffic limit and study the dynamic control of that system. Our solution is a nested threshold policy with explicit congestion thresholds that indicate when the non-profit should optimally pursue various types of volunteer engagement activities. A numerical example calibrated using data from a large food bank shows that our dynamic policy for deploying engagement activities can significantly reduce the food bank's total annual cost of its volunteer operations while still maintaining almost the same level of social impact. This improvement in performance does not require any additional resources - it only requires that the food bank strategically deploy its engagement activities based on the number of volunteers signed up to work volunteer shifts.

翻译：为有需要人群提供食物、住所及其他服务的非营利组织依赖志愿者来提供服务。与有偿劳动不同，非营利组织对无薪酬志愿者的日程安排、工作投入和可靠性缺乏控制力。然而，这些组织可以通过投资志愿者参与活动来确保稳定且充足的志愿劳动力供给。本研究探讨了一个关键运营问题：非营利组织如何管理其志愿工作者队伍容量以实现服务的持续供给。我们构建了一个多类别排队网络模型，以刻画非营利组织在最大化志愿者有效产出同时最小化参与激励成本的最优参与活动策略。鉴于该问题的复杂性，我们提出了一个重流量极限下的布朗控制问题近似模型，并研究了该系统的动态控制方法。所得到的嵌套阈值策略具有明确的拥塞阈值，能够指示非营利组织应在何时采取不同类型的志愿者参与活动。基于大型食品银行实际数据校准的数值算例表明，本研究的动态参与活动部署策略可在保持相近社会影响力的前提下，显著降低食品银行志愿者运营的年总成本。这种绩效提升无需额外资源投入，仅要求食品银行根据已登记志愿工作班次的人数，策略性地部署其参与活动。