Air cargo hub operations couple break-down, internal routing and storage, outbound unit load device (ULD) packing, and build-up execution under shared capacities and tight departure deadlines. When these stages are planned separately, locally reasonable decisions can still create downstream infeasibilities and missed outbound connections. This paper develops and evaluates an integrated, decomposed rolling-horizon optimisation framework for outbound cargo handling at a major European air cargo hub, using operational data from a real terminal environment. The framework decomposes the problem into four sequential planning stages that follow the physical cargo flow: break-down scheduling, routing between direct-to-buffer and storage-mediated paths, capacity-based outbound packing, and build-up scheduling with dispatch to the ramp. Downstream infeasibilities are coordinated through a repair loop with procedural rebooking when no feasible assignment remains within the planning horizon. Outbound service performance is measured by the original-flight rate for export and transfer piece-groups with a modelled outbound flight. In the evaluated instances, the model improves the mean original-flight rate from 85.5\% to 92.0\%. This improvement is achieved while break-down remains highly utilised, indicating that coordination and prioritisation matter under realistic capacity pressure. The paper concludes by discussing limitations of deterministic modelling and capacity-based packing, and by outlining directions for stochastic extensions, richer loadability checks, and broader empirical validation. ... Read more