Supporting ranking queries in database systems has been a popular research topic recently. However, there is a lack of study on supporting ranking queries in data warehouses where ranking is on multidimensional aggregates instead of on measures of base facts. To address this problem, we propose a query execution model to answer different types of ranking aggregate queries based on a unified, partial cube structure, ARCube. The query execution model follows a candidate generation and verification framework, where the most promising candidate cells are generated using a set of high-level guiding cells. We also identify a bounding principle for effective pruning: once a guiding cell is pruned, all of its children candidate cells can be pruned. We further address the problem of efficient online candidate aggregation and verification by developing a chunk-based execution model to verify a bulk of candidates within a bounded memory buffer. Our extensive performance study shows that the new framework not only leads to an order of magnitude performance improvements over the state-of-the-art method, but also is much more flexible in terms of the types of ranking aggregate queries supported.