We introduce a two-level hierarchical planning and scheduling approach for multi-item, single-machine production systems facing stochastic demand. The hierarchical approach extends the existing heuristics to handle situations where demand levels are high compared to the available production capacity. At the top level of the hierarchy the approach deploys a heuristic procedure for coordinating capacity in the medium term. The heuristic produces target production cycle times and target service levels for each of the products. It iteratively allocates capacity to individual products for maximizing the expected profit while meeting the individual product service level targets set by the management. The bottom level of the hierarchy focuses on the short term and aims to realize the target service level while keeping the production cycles stable. At this level, a fixed-sequence order up-to operational scheduling policy which permits a limited amount of flexibility for reacting to short-term demand variations is implemented. Demand which cannot be met from inventory gets lost. We also present and discuss the results of extensive simulation tests under a wide range of environments that serve to demonstrate the superiority of the approach, especially when the demand level is high.