I had a conversation of sorts with a self proclaimed leader in project management theory. The approach to this "theory," is to define a set of differential equations that model the STATIC behavior of the parameters the project. Effort, Duration, Productivity. Things like that. Simple parameters by the way. Guess that's why its a theory.

The starting point - and the very quick ending point - is the discussion the project duration. This is a critical concept that bears restating as many times as it takes to get through. (Picture clipped from I Love Charts, via twopointsevenone).

*The duration of a project is defined by the Critical Path of the assemblage of work comprising the activity network. This work can be Work Packages or Tasks.*

*The duration of the project is NOT, I repeat NOT defined as an end-to-end path through these activities.*

The duration of the project is defined in the following notional way. It is defined as the path through the network of work activities, where the probabilistic duration of the schedule is created by the stochastic processes of each work activity. The STATIC critical path (that thing PMI talks about) is just notional.

There is use for the notional Critical Path. In our domain (space and defense) is serves as the Program Master Schedule. The PMS is used for high level briefings to Generals and senior procurement folks. But it is juts that "notional."

In reality - and all theories need to come in contact with reality if they are to be useful - this collection of activities are characterized by a probability distribution (show as the curve in the box) for each work element (a task or a Work Package). The reason these are probabilistic, is simple. The duration of any work effort,be it human or machine, is a random variable, with a Mean and a Standard Deviation. That's a simple minded definition. The actual description is the duration is defined by a Stochastic process. (A Stochastic process is a random processes that is non-deterministic. A system's subsequent state is determined both by the process's predictable actions and by a random element.)

When this probabilistic activity network is assessed in a static manner using the "Most Likely" duration. This is called the DETERMINISTIC schedule. The PROBABILISTIC schedule is composed of three points that make up the Probability Distribution Function (PDF). This is defined by the Most Likely and the variance from that Most Likely - the lower and upper bounds.

These three numbers - and there is a whole side bar topic on the estimating processes - are used on a Monte Carlo Simulator to create a set of numbers representing the Probability Distribution for the values that can be used to model the duration(s) for the work activities.

There is nothing STATIC about this approach. All schedules are DYNAMIC. All schedules are stochastic.

A stochastic process is one whose behavior is non-deterministic, in that a system's subsequent state is determined both by the process's predictable actions and by a random element. Of course the random element is the duration of the work activity - for what every reason - and there are enough reasons to go around.

**In the End**

Forget the static view of projects. It is simply not true. It was never true. Forget defining the project duration as a end-to-end - the Period of Performance - when that period is defined in the absence of probabilistic activity network.

Forget speaking about work activities and the resulting project duration in the absence of the probabilistic understanding of the duration of the individual activities the resulting total duration.