Operational planning at transshipment nodes is a wide and challenging field of research that covers a vast number of distinct relevant applications, spanning from seaport container terminals to rail terminals to cross-docks. In this work, we study the feasibility version of a fundamental synchronization problem that assigns incoming vehicles to docking resources subject to handover relations. We carry out a comprehensive analysis of computational complexity of various problem variants and establish structural connections to famous decision problems in graph theory. We further propose an exact solution algorithm for finding feasible dock assignments, if vehicles can visit the node only once and evaluate its performance in a comprehensive computational study.