Matrix organization

This paper attempts to explain organizational structure of a multi-function, multi-project firm. There exists spillover among agents in the same dimension. Agents in the lowest level decide their fraction of devotion according to the incentive provided by managers from two dimensions. Organizational structure corresponds to the allocation of responsibility to managers. A mathematical model reflecting these characters is established. Our results consist of the relationship between organizational structure and spillover. A matrix organization is most effective when spillover within functional and project dimensions is complementary. When they are in conflict, either a functional or a divisional organization is optimal depending on the parameters of spillover. In special situations, performance of the firm is irrelevant to the organizational structure. We also investigate the effect of asymmetry on the optimal organization.