Putnam, Norden, Rayleigh Curves

1. Introduction

In the 1960s and 1970s, people actively sought ways to mathematically predict the time and cost of a project as a function of the requirements and other parameters of the problem. The most advanced fruit of these efforts was Barry Boehm's COnstructive COst Model. While the formulae derived in those efforts are not (today) widely used, there is still value in understanding the relationships they capture.

This paper is a brief introduction to (and commentary on) Putnam, Norden, Rayleigh (PNR) curves and what they tell us about project staffing.

2. Staffing and the Rayleigh Curve

It is very natural for a project manager to want to:

• figure out how many people will be needed to complete a project.
• assign them to it.
• divide the number of estimated staff months by the head-count to get an expected completion time.

1. Peter Norden (of IBM, in 1963) observed that a project is not a single monolithic activity, to be accomplished by a single team. Rather, it is a sequence of distinct but overlapping phases, each of which has is own natural team size and composition.
2. Frederick Brooks (in the Mythical Man Month) pointed out that time and man-power are not interchangeable because team size and composition affect productivity.

Every project actually has a natural staffing curve, and these curves seem to have a consistent and predictable shape.

We can attempt to force a flat staffing profile on such a project, but it will result in considerable waste:

• In the early stages, there will be people standing around with nothing to do, because the requirements and architecture development process is more gated by time than by labor.
• In the mid stages, work may be delayed by not having enough people available to perform all of the defined tasks.
• In the late stages, over-staffing will not bring the project to completion any sooner, because the collection of feedback and shaking out of final problems is (again) more gated by time than available labor.

If we want to accomplish a project efficiently, we much understand the distinct phases, along with their respective skill and activity requirements. The notion that we can prepare an estimate in staff months and predict completion time by choosing a staffing level and dividing that into the total project size is a canard.

3. Time/Effort and the PNR Curve

Lawrence Putnam (of RADC) applied Norden and Rayleigh's work to the effort to quantitatively predict the work associated with software projects. After studying numerous projects, he concluded that the effort required to deliver a project varied inversely as the fourth power of the time allotted to its completion.

The clear message here is that every project has an optimal staffing level, and (correspondingly) an optimal time in which it will be completed. Going significantly above or below the optimal staffing level will reduce work efficiency ... and there may be a point beyond which adding people actually delays the project.

This curve breaks down into four zones:

1. An impossible zone
   The project cannot be accomplished in less time than this, no matter how many people are applied to the problem. This situation is classically summarized as: "Nine women cannot have a baby in one month".
2. An "Haste makes waste" zone
   Adding people does accelerate delivery, but not in proportion to the added effort. Each additional person added to the project lowers our productivity (they have to be trained, more time goes into communication and coordination, more misunderstandings). This is a very inefficient way to operate.
3. A linear range
   This is the range of efficient staffing, and within this range it is possible to trade man-power for time, or vice versa.
4. An under-staffed/over-staffed zone
   This curve does not yield completion time as a function of staffing, but merely shows the relationship between staffing level and completion times. What we can clearly see on the right of the curve is that productivity is dropping. Why might this be?
   • If the project is critically under-staffed, productivity will suffer because there aren't enough people to deal with the problems.
   • if the project is greatly over-staffed communications overhead will reduce efficiency and misunderstandings will create problems and result in wasted work.