To optimize the operation of automated vehicles and ride-hailing, we introduce a tradable permit system with a dynamic scheduling auction on a recursively structured network and apply the Vickley-Clarke-Groves (VCG) mechanism as a method to determine the allocation pattern of permits. Our proposed system is characterized by its flexibility in responding to changes in demand and road conditions, making it more user-friendly than conventional methods. However, the scheduling problem determining the permit allocation pattern is classified as NP-hard. Moreover, due to the dynamics, the load for recalculation is high. For such problems, we propose a complete enumeration method based on zero suppressed binary decision diagrams (ZDD), in which the alternatives are structured, and show its high performance against recalculation by comparing it with a linear relaxation method.