However, there was some interesting things that came out of the paper.
Starting with a very simple two person "mom and pop shop"
organizational model, the model is extended into a flat organizational
structure, and finally, a hierarchical structure. Some of the
interesting formalities that fall out of the math:
1) In a hierarchical organizational structure, the optimum
number of people in each sub-tree of the hierarchy is 6, which
agrees closely with military doctrine.
2) If you calculate the magnitude of resources required to
complete a project by summing the the sub-components in the
pert chart, you will make an optimistic error of a factor of 2
in the resources or time required to complete the project,
which agrees with Brooks and Ulam's observations. (In NP
problems, in some sense, the sum of the parts is larger than
the whole.)
3) Flatter organization structures are superior, except when
the complexity of what the organization is attempting to do
passes a certain point, then hierarchical structures are more
efficient, which seems to be supported by military doctrine.
4) In flat structures, the economic optimum, and the minimum
time to solve a problem are coincident solutions-in
hierarchical structures, they are not-but are close (eg., in
hierarchical organizational structures, you may do a project
with minimum cost, or minimum time, but not both-but in flat
structures you can.)
4) There exists an economic optimum, for an organization
solving a problem of a given complexity, and this economic
function has a law of diminishing returns on the number of
people that are assigned to solve the problem. The point at
which adding more resources actually delays the solution of
the problem might be a mathematical definition of bureaucracy.
5) When I dug out the paper, (to look at the bureaucratic
content,) I was somewhat astonished that the best methodology
of increasing organizational performance was through learning
of skill sets-which, oddly enough, completely dominated
technical, structural, and organizational methodology, at
least in large organizations. (It is the only variable which
has a linear effect on the complexity of the problem-all of
the others have decreasing returns.)
I was fascinated by that-even though the organizational models are
probably too simple to be of any practical or quantitative value, it
would seem that their may some qualitative significance. The LaTeX
sources from the beginning of the paper are attached. There is a lot
of optimization calculus (LaTeX supports math symbols very well,)
which I can not ever remember proofing. But if you want (eg., you
have insomnia,) you can print it, if not file it in /dev/null.
For what its worth ...
John
From: john@johncon.com (John Conover)
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Host's Note: John included the full text of his paper in the message, but
I've taken the liberty of deleting it. If you'd like the full text in, I
suggest you mail John directly.
-- Rick Karash, rkarash@world.std.com, host for learning-org
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