Data model is a basic aspect in the research field of data warehouses. It has been argued that traditional data models, such as the ER model and the relational model, are in principle not powerful enough for modeling the data structure and semantics of data warehouse and supporting OLAP (on-line analysis processing). As a result, several multidimensional models based on multidimensional view of data have emerged. However, these multidimensional data models still fall short of ability to model complex data in some real-world application domains and to support complete OLAP operations. In this paper, the authors propose a new multidimensional data model based on the concepts of partial order and mapping. This model addresses supporting for complex data structure and semantics of data warehouses, especially complex hierarchies in dimensions. Along with the model, they also present an associated algebra that includes a complete set of OLAP operations and supports complex aggregation, roll-up and drill-down along hierarchies in dimensions. A new concept of aggregation function constraint is also presented in this paper, and the mechanism for expressing and checking the aggregation function constraint is included in the model.