Computationally tractable planning problems reported in the literature have almost exclusively been defined by syntactical restrictions. To better exploit the inherent structure in problems, it is probably necessary to study also structural restrictions on the underlying state-transition graph. Such restrictions are typically hard to test since this graph is of exponential size. We propose an intermediate approach, using a state variable model for planning and defining restrictions on the state-transition graph for each state variable in isolation. We identify such restrictions which are tractable to test and we present a planning algorithm which is correct and runs in polynomial time under these restrictions.Moreover, we present an exhaustive map over the complexity results for planning under all combinations of four previously studied syntactical restrictions and our five new structural restrictions. This complexity map considers both the bounded and unbounded plan generation problem. Finally, we extend a provably correct, polynomial-time planner to plan for a miniature assembly line, which assembles toy cars. Although somewhat limited, this process has many similarities with real industrial processes.