Optimal Models for Adding Relation to an Organization Structure with Different Numbers of Subordinates at Each Level

Abstract

This study aims at revealing optimal additional relations to a pyramid organization such that the communication of information between every member in the organization becomes the most efficient. This paper proposes models of adding a relation between two members in the same level of the organization structure in which each member of $m$-th level below the top has different number of subordinates, $m+2$ in Model-1 and $2m+2$ in Model-2. The total shortening distance which is the sum of shortening lengths of shortest paths between every pair of all nodes is formulated and is illustrated with numerical examples to obtain an optimal level of two members between which a relation is added for each of Model-1 and Model-2.