Optimal hierarchy structures for multi-attribute-criteria decisions

A problem of a hierarchy structure optimization is considered. Hierarchical structures are widely used in the Analytic Hierarchy Process, conjoint analysis, and various other methods of multiple criteria decision making. The problem consists in finding a structure that needs a minimum number of pair comparisons for a given total number of the alternatives. For an optimal hierarchy, the minimum efforts are needed for eliciting data and synthesizing the local preferences across the hierarchy to get the global priorities or utilities. Special estimation techniques are developed and numerical simulations performed. Analytical and numerical results suggest optimal ways of priority evaluations for practical managerial decisions in a complex environment.