Project Management and the Three-Body Problem

Projects are composed of three fundamental elements. Cost, Schedule, and?Technical outcomes. The?Technical Outcomes?go far beyond the PMI-style?scope?terms. In this paradigm, the technical outcomes are at the end of a chain.

Here are examples of that chain -?Capabilities,?Measures of Effectiveness,?Measures of Performance,?Key Performance Parameters?(there are 5 in our domain), and?Technical Performance Measures.

At the TPM level, things like quality are traceable to the KPPs.

These three elements are?coupled?in dynamic ways. Their connections are?springy in that changes in one impact the other two, but rarely is this impact linear and rigid.

The?Iron Triangle?notion is a Three-Body problem in which all three elements impact each other and simultaneously respond to that impact.

All projects have these three elements coupled in this way. Changes in one impact the other two. Changes in two impact each other, and the third. We need to know the dynamics of cost, schedule, and technical performance to have a credible understanding of these variables.?

The Three-Body Problem

According to Newton's law of inverse squares, the three-body problem determines the possible motions of three-point masses m1, m2, and m3, which attract each other. It started with Newton's perturbative studies on the inequalities of lunar motion. In the 1740s, there was a search for solutions (or at least approximate solutions) of a system of ordinary differential equations by the works of?Euler,?Clairaut,?and?d'Alembert?(with an explanation by Clairaut of the motion of the lunar apogee).

Developed further by?Lagrange,?Laplace, and their followers, the mathematical theory entered a new era at the end of the 19th?century with the works of?Poincaré?and since the 1950s with the development of computers. While the?two-body problem?is integrable and its solutions completely understood, solutions of the?three-body problem?(Java 7 in 64-bit Browser needed) may be of arbitrary complexity and are very far from being completely understood.

The forces between the bodies can be?self-attractive or a central force - the restrictive three-body problem. Or a combination of the two. This is the basis of complex systems, where multiple forces are applied to?objects, changing the forces. As an aside, the double pendulum and the three-body problem are used as examples of complex systems. Without acknowledging that the underlying mathematics is?deterministic?since the Java example above draws the lines from an algorithm.

This is a common mistake by those unable to?do the math?or who want to suggest the problems of the day are beyond solution.

Three Body Problems and Three Elements of Project Management

The three-body problem uses gravity as the force between the masses. There is a simpler example of three masses connected with three springs. This model is found in chemistry and biology at the molecular level. Gravity is not in effect, of course, but electromagnetic force.

Consider a simplified model for the vibrations of an ozone molecule consisting of three equal oxygen atoms. Three equal point masses represent the atoms in?equilibrium positions at the vertices of an equilateral triangle. They are connected by equal springs of constant?k?that lie along the arcs of the circle circumscribing the triangle. Mass points and springs are constrained to move on the circle so that, e.g., the potential energy of a spring is determined by the arc length covered.

This class of problems is called?soft body dynamics. The visible outcome is rendering flexible graphical objects in movies and games - like?three-dimensional garments.

Now to Projects

If we assume for the moment that cost, schedule, and technical performance are dynamic variables, with?forces?between them described by their functional equations. In our functional equations, the force between them is not constant, but are relationships like this:

• Cost?is a function of?schedule?- Time is money.
• The Schedule?is a cost function?- We can buy time and shorten the schedule, but at what cost?
• Cost?is a function of?Technical Performance?- Want to get fast? How much will that cost?
• Cost?is a non-linear function of?Schedule?- This is not a 1:1 exchange for the schedule question.
• Technical Performance?as a non-linear Function of?Cost?- What can we afford to do?
• Technical Performance?as a non-linear function of?schedule?- When can we have fast?

The interactions between the three core elements (cost, schedule, technical performance) are two-way, so the spring analogy needs to be corrected since the spring force doesn't know which end it is pushing or pulling.

The Point

It's NOT an?Iron Triangle; it's a non-linear springy triangle.

The connections are non-linear, and most importantly, they are probabilistically driven by the project's underlying statistical and probabilistic processes. Let's start with the picture below.

All project processes are?probabilistic. They have behaviors that are not fixed. The notion that you can?slice?work into the same-sized?chunks?and execute these chunks with the same effort would violate the basic?aleatory?uncertainties of all work processes. An understanding of the statistical processes, driven by either?aleatory?or?epistemic?uncertainties, is followed by asking probabilistic questions.?

What's the probability that we'll complete on or before a date,?or?what's the probability we'll compete at or below a cost?

With a probability and statistics foundation, we can now create a credible plan driven by the underlying stochastic. All work is connected in dependent ways. The work effort, duration, and outcomes are also statistically driven. This picture is typical of such a project.

In the Project Context

• Statistics - I know the completion durations of the last 20 times I did this task. Or I have a model I can use to inform me about the completion durations, cost, and technical performance.
• Probability - with these statistics and an activity network (schedule), cost estimating relationship (CER) model, or CAD dynamics model, what's the probability I will be disappointed with the outcome of my work efforts?

For some good background, see the GAO Cost Estimating Handbook and the NASA Cost Estimating Handbook. And while there, look at the Schedule Management Handbook, Earned Value Management Handbook, Project Planning & Control Handbook and how to put all three (cost, schedule, and performance management) together in EVM and Schedule Management.

In The End

• We need to know all three properties.
• We need to know the underlying statistical behaviors. If not, go find out or pick a?reference class.
• We need to speak about confidence intervals, not deterministic values (single-point values).
• We need to know something about the cost. You need to know the value or ROI. It's that simple. It's basic financial management.?

So we can:

• Learn to estimate.
• Understand that those with the money need to know how much money and when to release that money.
• Those waiting for the?value?need to know when they will receive it.
• Those consuming other people's money to produce that value need to know how time, money, and value production take place outside their narrow world, of?it's all about me.?