# Sigmoidal Mathematical Models in the Planning and Control of Rigid Pavement Works
## 5 Discussion
Likewise, the polynomial models of [PERSON] [38] and [PERSON] [39], with R\({}^{2}\) between 0.90 and 0.98, are lower than those obtained in the research, where an R\({}^{2}\) of 0.9821 to 0.9848 was obtained with the sigmoidal models. [PERSON] et al. [19], using neuro-adaptive fuzzy logic, reported an MAE of 2.0198 and an MSE of 5.2017, higher values of error than the proposed models, where an MAE of 0.0278 to 0.0321 and an MSE of 0.0026 to 0.0028 were obtained, which are lower which indicating the reliability of the models. Models based on neural networks such as those of [PERSON] and [PERSON] [14; 16] and [PERSON] et al. [11] presented a low RMSE (0.0355 and 0.0552), comparable with the RMSE of sigmoidal models from 0.0506 to 0.0531, demonstrating that these have reliability levels similar to the models generated by artificial intelligence algorithms (see Table 7). Sigmoidal, polynomial, and artificial neural network models demonstrate significant discrepancies in terms of structure, requirements, and applicability in rigid pavement projects. Sigmoidal models are distinguished by their capacity to depict the temporal progression of construction activities. Their \"S\"-shaped structure adapts to the actual sequence of events, encompassing a gradual initiation, an accelerated intermediate phase, and a subsequent progression toward completion [11]. Their simple mathematical structure, in conjunction with moderate data requirements and high interpretability, positions them as an ideal tool for environments where decision-making must be efficient and traceable. Conversely, despite their simplicity of implementation, polynomial models are subject to limitations when extrapolating dynamic scenarios and are vulnerable to overfitting, which undermines their accuracy in real construction contexts [14]. Conversely, artificial neural networks boast high predictive capacity and adaptability; however, they require substantial data volumes and considerable computational resources. Moreover, their processes are opaque, which may impede their acceptance in engineering environments where the explanation and justification of results are paramount [16]. Consequently, sigmoidal models offer an optimal balance between adaptability, simplicity, and applicability, making them particularly well-suited for the planning and control of rigid pavement works in real construction industry contexts. Concerning other sigmoidal models studied, such as Von Bertalanffy (R\({}^{2}\) = 0.9844) and Gompertz (R\({}^{2}\) = 0.9832), the logistic model maintains a slight superiority in all met-rics, while the model proposed in this research, with an R\({}^{2}\) of 0.9821, presents the same error values (MAE and RMSE), which confirms its robustness and power for its application in large rigid pavement projects allowing greater accuracy. [PERSON] et al. [40] presented an innovative model that integrates techniques such as Earned Value Management (EVM), Activity-Based Costing (ABC), and BIM methodology. The objective of this integration is to optimize the cost structure and establish an equitable risk and reward distribution mechanism among the parties involved in the project. This model enables automation and enhances precision in cost control and activity scheduling. This approach bears resemblance to sigmoid models, which aim to accurately represent the cumulative growth and progress of complex projects or systems over time. [PERSON] et al. [41] developed a procedure and analysis using discrete event simulation to compare traditional scheduling methods with the Fixed Start Method (FSM) in repetitive projects. The findings indicate that FSM has a substantial impact on reducing variability in