Analytical processing on multi-dimensional data is performed over data warehouse. This, in general, is presented in the form of cuboids. The central theme of the data warehouse is represented in the form of fact table. A fact table is built from the related dimension tables. The cuboid that corresponds to the fact table is called base cuboid. All possible combination of the cuboids could be generated from base cuboid using successive roll-up operations and this corresponds to a lattice structure. Some of the dimensions may have a concept hierarchy in terms of multiple granularities of data. This means a dimension is represented in more than one abstract form. Typically, neither all the cuboids nor all the concept hierarchy are required for a specific business processing. These cuboids are resided in different layers of memory hierarchy like cache memory, primary memory, secondary memory, etc. This research work dynamically finds the most cost effective path from the lattice structure of cuboids based on concept hierarchy to minimize the query access time. The knowledge of location of cuboids at different memory elements is used for the purpose. © 2014 Elsevier B.V.