We consider the problem of optimal stochastic scheduling for nonlinear systems with Poisson noise disturbances and a performing index including both operating costs and costs for scheduling changes. In general, the value functions of the dynamic programming, quasivariational inequalities which define the optimality conditions for such problems are not differentiable. However, we can treat them as 'viscosity solutions' as introduced by Crandall and Lions. Existence and uniqueness questions are studied from this point of view.