  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.
