This paper considers the problem of generating conflict-free movement schedules for a set of vehicles that are operating simultaneously in a common airspace. In both civilian air traffic management and military air campaign planning contexts, it is crucial that the movements of different vehicles be coordinated so as to avoid collisions and near misses. Our approach starts from a view of airspace management as a 4D resource allocation problem, where the space in which vehicles must maneuver is itself managed as a capacitated resource. We introduce a linear octree representation of airspace capacity to index vector-based vehicle routes and efficiently detect regions of potential conflict. Generalizing the notion of contention-based search heuristics, we next define a scheduling algorithm that proceeds by first solving a relaxed version of the problem to construct a spatial capacity profile (represented as an octree), and then using spatio-temporal regions where demand exceeds capacity to make conflict-avoiding vehicle routing and scheduling decisions. We illustrate the utility of this basic representation and search algorithm in two ways. First, to demonstrate the overall viability of the approach, we present experimental results using data representing a realistically sized air campaign planning domain. Second, we define a more abstract notion of ‘encounter set’, which tolerates some amount of conflict on the assumption that on-board deconfliction processes can take appropriate avoidance maneuvers at execution time, and show that generation of this more abstract form of predictive guidance can be obtained without loss in computational efficiency.