## Saturday, December 8, 2012

### Project non-linearities

Pavel Barseghyan has a recent posting on project nonlinearities entitled "Missing nonlinearities in quantitative project management"

Defining a non-linearity:
Before we get into his main points, you might ask: what is a nonlinearity and why should I care?
A good answer is provided in Donella Meadows' fine book on systems: "Think in systems: a primer" . Donnella actually quotes from James Gleick's "Chaos, making a new science":
A nonlinear relationship is one in which the cause does not produce a proportional effect. The relationship between cause and effect can only be drawn with curves or wiggles, not with a straight line.

Curves or wiggles! Really? Consider this wit -- Brooks' Law -- from Dr. Frederick P. Brooks, Jr.:
Adding manpower to a late .... project makes it later

Brooks is the author of "The Mythical Manmonth", the theme of which is that time and persons are not interchangeable. Why? You guessed it: non-linearities!

Project example
And non-linearities are also what's behind Brooks' Law. He posits that the communication overhead that goes with additional staff -- to say nothing of the inefficiency to divert energy and time toward integrating new team members -- is the gift that keeps on giving. This communication overhead is a constant drag on productivity, affecting throughput and thus schedule.

There's actually a formula that explains this non-linearity to some extent. That is: the number of communication paths between project team members expands almost as the square of the number, N, of team members:
The number of bidirectional communication paths between N persons is equal to:
N * (N -1), or N*N - N
Now, anytime we see a variable, like N, modifying itself, as in the factor N*N, we have a nonlinearity.

To see how this formula works, consider you and I communicating with each. N = 2, and formula forecasts that there are 4 - 2 = 2 paths: I talk to you, and you talk to me.

Now, add one more person and the number of paths increases by 4! Good grief. We jump from 2 paths for two people to 6 paths for three people: 3*3 - 3 = 6.  Talk about your nonlinearity!

Test it for yourself: 1 and 2: I talk to you and you talk to me; 3 and 4: I talk to the third person and she talks to me; 5 and 6: you and third person talk back and forth.

Of course, this example is only one of a myriad of non-linearities faced by project managers, so that makes Pavel's posting all the more important.

Pavel makes these three main points:
1. Nonlinear relationships between project parameters ... arise as a consequence of the balance between complexity of work, objectives of work, and productivity of work performers.
2. Nonlinearities .... arise as a consequence of the limited capabilities of work performers, and limitations that are connected with technological feasibility of work
3. Nonlinear relationships ... characterize communication and contacts between people, and, as a consequence, team productivity
We've already discussed an example of point #3; the big issue in point #2 is the non-linearity experienced when we reach our limits of capability and feasibility. At the limit, no matter how much more we put into it, we just don't get a proportional response.

Point #1 goes to the issue of complexity, and outgrowth of complicated. The latter does not necessarily beget the former. Complexity is the emergence of behavior and characteristics not observable or discernable just by examining the parts. Complicated is the presence of a lot of parts.

To see this by example, consider your project team in a large open-plan work space. If there's plenty of room to move about, that situation may be complicated by all the people and tools spread about, but not complex.

Now, compress the work space so that people bump into one another moving about, tools interfere with each other, and one conversation interferes with another.

This situation is complex: the behaviors and performance is different and emergent from that observable when the situation was only complicated.