Delay and size in hierarchical organizations

As material and information flow through an organization, work is being performed; its very act incurs time and hence delay. It may be intuitive that, the larger an organization is, the longer the delay will be. This turns out to be not entirely true. In this paper, size and delay are found to be inversely related to each other, under certain conditions, enabling a speed-up with additional agents. Analytical relations and bounds are then developed, followed by simulations under generalized conditions. Without exception, analyses and simulations both exhibit globally optimal configurations in size and in delay.