Your previous question

From: John Conover <>
Subject: Your previous question
Date: Tue, 21 Feb 95 14:40 PST

Sorry for the rambling reply earlier. I got about 50 requests for
clarifications on that paper this AM, and my mind is dragging.

Here is rationalization of what happens in an organization. It will
use a lot of "scientific induction," (the technical name for "hand

There has, from time to time, been a lot of empirical observations
that organizations operate in a non-linear fashion. By this I mean, as
you increase the resources in an organization, (eg., add more folks,)
you do not get a linear increase in productivity. Fred Brooks, (the
guy that ran the IBM 360 project, which has the distinction of being
the largest corporate over run in the history of commerce,) noticed
this and made the observation that "birth takes 9 months, no matter
how many women you put on the project." None other than Stanislaw Ulam
made a similar observation, in the academic environment, that the
number management issues increases on the square of the number people
on your staff. (Stanislaw Ulam is the "founding father" of Computer
Science-he was the mathematician that was responsible for using Von
Neumann's computers to solve advanced problems in physics at Los
Alamos National Laboratories in the early 1940's.) If you consult the
abundant literature on management of software development projects,
you will find the same observations. If you look at software
development, it is largely an exercise in coordination issues
(software developers spend only about 15% of their time actually
writing code.) In general, it can be observed that the more
coordination that is required, the more non-linear the characteristics
of the productivity function for the group (as a function of the
number of people in the group.)

If you think about it, it is obvious. If you didn't have manufacturing
you would not have to advise management of product liability issues,
and if you didn't have design engineering, you would not have to
advise management on intellectual property issues. The point is, that
when you add an organization (manufacturing, or design) to another
organization, (legal,) the complexity of operating both organizations
is more than the just the sum of operating the organizations

Now, we have some empirical evidence, and have, by scientific
induction, hypothesized an intuitive reason why we observe the
empirical evidence. It turns out that the types of problems that
exhibit the phenomena of "the sum of the parts being larger than the
whole," is well known, and is one of the "corner stones" of the modern
theory of computability, where these types of problems are simply
called NP problems, (for Non-Polynomial; problems that can execute,
worst case, in polynomial time, do not exhibit the "sum of the parts
is greater than the whole," property-this is generally considered to
be the qualitative difference between the two.)  The implication here
is that the way that organizations operate is by some kind of process,
and the process is non-linear on the complexity of the organization,
whatever that may be. Fortunately, we don't have to define the process
to analyze it, at least in a qualitative fashion, and can draw some
generalized conclusions on the macroscopic behavior of organizations.

If you construct an organizational model along these lines you could
look the "productivity" of the organization in two ways. The first way
is to make a graph of the resources required to complete a project,
vs. the time required to complete the project with those
resources. The second way of looking at "productivity" is to construct
a graph of the time required to complete the project, vs the resources
that have to be committed to complete the project in that amount of
time. The first will represent the time required to complete the
project, the latter will represent the resources required to complete
the project. The first represents your time alternatives, the second
represents you project cost, (ie., resource) alternatives.

In the first case, it would seem, at least intuitively, that adding
more resources will hurry the project along. But this simply is not
true, if the organizational process is NP. However, it will have a
minima, and that minima is the quickest that the project may be
finished, (everything else being constant, except the amount of
resources that we commit to the project.) Adding more resources, past
this minima, will actually increase the project's time to completion.

In the second case, if you commit too few resources, it will require
an abnormally long time to complete the project, and if you commit
too many resources, you will increase the cost of doing the project,
(albeit a shorter time.) So, this graph also has a minima, and that is
the minimum cost of doing the project.

Unfortunately, in hierarchical organizations, the minimum cost scenario, and
the minimum time scenario to complete the project do not coincide.

And that is the answer to your question. If you think about it, it has
to be true. If it was not, then the best way to organize humanity
would be to serialize all the projects in the world, and then put all
4 billion of us on the first project, then the next, and so on. Such a
scheme simply won't work because of the economic law of diminishing
returns. All that is stated above is that the same thing applies to
organizations doing projects-for, essentially, the same reasons. The
fact that organizations exhibit a law of diminishing returns (both on
project cost, and on commitment of resources) is new to some folks.



John Conover,,

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