The problem of computational design for menu systems has been addressed in some specific cases such as the linear menu (list). The classical approach has been to model this problem as an assignment task, where commands are assigned to menu positions while optimizing for users’ selection performance and grouping of associated items. However, we show that this approach fails with larger, hierarchically organized menus because it does not take into account the ways in which users navigate hierarchical structures. This paper addresses the computational menu design problem by presenting a novel integer programming formulation that yields usable, well-ordered command hierarchies from a single model. First, it introduces a novel objective function based on information foraging theory, which minimizes navigation time in a hierarchical structure. Second, it models the hierarchical menu design problem as a combination of the exact set covering problem and the assignment problem, organizing commands into ordered groups of ordered groups. The approach is efficient for large, representative instances of the problem. In a controlled usability evaluation, the performance of computationally designed menus was ∼25% faster to use than existing commercial designs. We discuss applications of this approach for personalization and adaptation.