Managing complex projects, especially in IT, requires a clear understanding and balance between three fundamental factors, known as the 3Cs:
From these three pillars stem time planning, budget, and risk management. The purpose of this publication is to provide a model that shows:
The heart of the model is based on the regime formula:
Where \(R\) represents the state of "regime" (equilibrium). If Cost, Capacity, and Complexity remain coherent, the project proceeds within the expected timeframe. If something becomes unbalanced, a deviation occurs and time begins to grow non-linearly.
Under optimal conditions:
In this situation, the project remains in regime. If Complexity turns out to be much higher than estimated, or Capacity is lower, the actual Cost may overrun and/or Time extends.
When the ratio between Cost and Capacity, at equal Complexity, becomes unbalanced (deviation \(E\)), time extends in a non-linear manner:
Where:
Rationale: In project management, delays and overruns generate overhead, rework, and confusion, which accumulate logarithmically. It's not an immediate explosion (exponential), but a progressively more onerous extension.
To calculate project Capacity transparently, we introduce the FTEC (Full Time Equivalent Container):
Objective: avoid naive summation of "person-days" (which would inflate capacity), and consider that, in fact, "real time" is singular.
Different roles work in sequence within the FTEC:
If you allocate 10 hours to BA, 20 to Dev, 10 to QA in the week, the sum is 40. There's no "parallel" between different roles.
Internal scalability: If you have 2 developers (duplicated Dev role), in that 1-hour slot, 2 Devs work simultaneously, producing 2 "person-hours" of development.
Formally:
where \(c_i\) is the number of parallel resources in role \(i\), and \(T_i\) the clock hours allocated to that role.
If role \(i\) has hourly cost \(\rho_i\) and counts \(c_i\) people, and \(T_i\) clock hours are dedicated to it within the FTEC:
A project may require "\(H_i\) person-hours" to complete tasks for role \(i\). For 1 FTEC to be sufficient, we need:
If these conditions are not met, 2 FTEC, 3 FTEC, etc., are needed. In fact, you can represent the function "how many FTECs are needed" based on complexity (total person-hours).
Adding governance roles (Architect, PMO/Scrum Master, BA/QA Lead) doesn't increase the 40 weekly hours, but can:
Formally, you can introduce a "Lead" role with time \(T_{\text{Lead}}\) that reduces \(H_{\text{Dev}}, H_{\text{QA}}, H_{\text{BA}}\), improving efficiency. It's a trade-off within the same 40 hours.
We can imagine a cube diagram where the three axes represent Cost (C), Capacity (K), Complexity (X):
Where we position ourselves on the "plane" defined by K and C, and Complexity shifts the "height" of the regime. If Complexity increases at equal Capacity, Cost must rise or Time dilates.
If the maximum capacity of 1 FTEC (distributing the 40 hours optimally among roles) is, for example, 64 person-hours, then the function that returns "FTEC_needed" based on Complexity results in:
The presented model provides an integrated approach covering several fundamental aspects of project management:
The balance between Cost, Capacity, and Complexity is crucial. Any deviation produces a non-linear delay that follows a logarithmic curve, potentially compromising project success if not managed appropriately.
The introduction of the FTEC concept as a 40-hour weekly container helps avoid the additive overestimates typical of the "person-day" approach. Role serialization, with the possibility of internal scaling for specific roles, offers a more realistic model of the team's actual capacity.
The model provides a clear structure for cost estimation, considering both scenarios with internal teams and mixed situations with external consultants, through the role and FTEC cost formula.
The mathematical formalization of the relationship between capacity and complexity allows objective determination of when scaling with additional FTECs is necessary, avoiding overload and maintaining work quality.
The integration of governance and architecture figures represents a strategic investment that, while remaining within the same FTEC container, can significantly improve overall efficiency by reducing errors and overhead.
Understanding the logarithmic effect on time in case of imbalances emphasizes the importance of maintaining the project in regime, highlighting how small initial deviations can lead to significant temporal dilations in later phases.
In conclusion, this model offers a comprehensive framework for planning and controlling IT projects, avoiding common traps of capacity overestimation and complexity underestimation. Its practical application can significantly improve the accuracy of estimates and resource management.