We consider multi-agent systems with stochastic non-linear dynamics in continuous space-time. We focus on systems of agents that aim to visit a number of given target locations at given points in time at minimal control cost. The on- line optimization of which agent has to visit which target requires the solution of the Hamilton-Jacobi-Bellman (HJB) equation, which is a non-linear partial differential equation (PDE). Under some conditions, the log-transform can be applied to turn the HJB equation into a linear PDE.We then show that the optimal solution in the multi-agent scheduling problem can be expressed in closed form as a sum of single schedule solutions.