We present a GPU-accelerated method for compiling multi-valued decision diagrams (MDDs) for dynamic programming models. MDD construction expands states in layers defined by their distance from the root, a structure that enables independent parallel expansion of all states in a layer. We exploit this by partitioning each layer into limited-size fragments and executing the full expansion of each fragment on the GPU, including successor generation, dominance filtering, duplicate elimination, and pruning of suboptimal states. By systematically traversing fragments in a depth-first manner, we obtain a parallel Complete Anytime Decision Diagram Search that preserves exactness and anytime behavior. Applied to the Traveling Salesman Problem with Time Windows, our implementation yields speedups of up to two orders of magnitude, and outperforms other state-based methods as well as a state-of-the-art dedicated optimization method for this application.