Putnam Resource Allocation Model in Software Engineering

In software engineering, effective project management is crucial for delivering projects on time and within budget. The Putnam Resource Allocation Model also known as the Putnam Model is one of the models that are helpful in forecasting and resource distribution. Created by Lawrence H. Putnam at the end of the 1970s, this model is used to define the rough order of magnitude that has to be set as resources and schedule for a software development project. It is founded on the dynamics of software project on the similar name, and it is especially useful for large and intricate software projects.

What is the Putnam Model?

The Putnam Model is a formal tool used to quantify the cost, time, and effort required for software project development. It operates on the principle that there is a trade-off between the time available and the resources (effort) needed to complete a project. The model uses the Rayleigh curve to illustrate how effort should be distributed over the project timeline.

The Rayleigh curve represents the distribution of effort over time, showing that effort typically increases to a peak and then decreases as the project progresses. The core concept of the Putnam Model is that the rate at which resources, including manpower, are applied to the project impacts both the project’s costs and its delivery time.

Putnam Resource Allocation Model explained with graph

It can be explained with regards to the Putnam Model for effort distribution over time in a software project using the Rayleigh curve. The graph below shows a typical Rayleigh curve:

Here, the X-axis takes time and the Y-axis takes effort in man hours for instance, months. Effort thus ranges upwards as the project advances and then may drop down as the project approaches its final stages, according to the curve. The shape of the curve implies the total work content necessary to complete the undertaking.

Putnam’s Work Along with Equations

The basis for Putnam’s research is Rayleigh curve and Software Life Cycle Model (SLIM) which he initiated. The SLIM model uses the following key equation, known as the Putnam-Norden-Rayleigh (PNR) equation, to estimate effort:The SLIM model uses the following key equation, known as the Putnam-Norden-Rayleigh (PNR) equation, to estimate effort:

S=Ck^1/3t^4/3

Where:

• S is the software size (in LOC, function points, etc.).
• C is the technology factor, reflecting the capabilities of the development environment and team.
• k is the effort coefficient, a constant depending on the project environment.
• t is the time to complete the project (in months or years).

The model assumes that the total effort is spread out over time following the Rayleigh curve, which is mathematically expressed as:

E(t)= dt/dS=kt^1/3/ck^1/3exp(-t^4/3/3k^1/3)

​Where:

• E(t) is the effort distribution over time.

The PNR equation highlights the trade-off between time and resources. This grants that to shorten the project time that (t) denotes, there is a high likelihood that the effort (k) and resource increase exponentially, thus causing more costs.

Effect of Schedule Change on Cost

Thus, to emphasize the effect of schedule variation on cost according to the given example, let us include an effort coefficient k and a technology factor C. Let’s assume the initial project plan estimates a duration t₁ of 12 months. However, due to market demands, the project schedule is shortened to t₂ of 8 months.

Using the PNR equation, the initial effort 𝐸₁ and the revised effort 𝐸₂ can be calculated:

E₁ = ck^1/3(t₁)^4/3

E₁ = ck^1/3(t₂)^4/3

Since t₂ > t₁, 𝐸₂ will be significantly greater than 𝐸₁ , indicating that the total effort and cost have increased due to the reduced schedule. The exact increase in effort can be calculated by comparing the two equations.

Example Calculation:

Assume:

• C = 1
• k = 1
• Initial duration 𝑡₁ = 12
• New duration 𝑡₂ = 8

Initial Effort 𝐸₁: E₁ = 1⋅1^1/3 . 12^4/3 ≈ 22.63 person-months

Revised Effort 𝐸₂: E₂ = 1.1^1/3 . 8^4/3 ≈ 11.31 person-months

By shortening the schedule from 12 months to 8 months, the effort has increased significantly, illustrating the model's principle that compressing the schedule results in higher costs.

Conclusion

The Putnam Resource Allocation Model is very helpful to understand the time and effort-to-cost aspect of the process of software engineering. When using the Rayleigh curve and/or the PNR equation, project managers are more knowledgeable about needed resources and time. The model features the fact that shortening the time scale of a project results in high resource utilization, which should also be balanced to check for the best project.