Dynamic optimization is often needed in engineering processes. The system under study is given by a set of differential equations subject to constraints represented by algebraic or differential equations. Generalized polynomial chaos dynamic optimization has the advantage of expanding spectrally both Gaussian and non-Gaussian processes using deterministic coefficients. This paves the way of transforming the stochastic differential equation to a system of differential equations with deterministic coefficients. Then, numerical discretization of the system is conducted using orthogonal collocation finite elements.