# Sigmoidal Mathematical Models in the Planning and Control of Rigid Pavement Works
## 1 Introduction  
The construction industry exerts a significant influence on global economies, with road projects being the most in demand. These projects contribute to the enhancement of trade, the effective connection of cities, and the facilitation of the transportation of goods and people [1]. In this context, meticulous planning and effective construction control are indispensable for the success of engineering projects, which involve a multitude of resources, including labor, equipment, materials, logistics, and transportation [2]. The role of the project manager is to ensure the timely delivery of projects through cost control, the identification and measurement of deviations between planned and actual work performance, and the coordination and supervision of resources to avoid interference between theconstruction site configuration and work [3]. Project delays are a significant challenge, and effective planning and scheduling are critical to ensure project delivery and control costs, which vary significantly between countries due to factors such as topography, climate, wage levels, availability of materials, energy resources, and economic and institutional conditions [4]. Conventional methodologies employed in the realm of road project planning are characterized by their protracted nature and susceptibility to inaccuracies. This inherent variability gives rise to unreliable S-curves, which, under their representation, are prone to misrepresenting the project's status at a given juncture [5]. This phenomenon often gives rise to cost overruns, which, in turn, impede the meticulous planning and modeling of construction operations. Cost estimation is imperative during the planning and scheduling stages for effective decision-making. Consequently, the development of mathematical models has been proposed as a means to enhance the precision and dependability of cost estimations in the road construction industry [6]. The utilization of planning optimization models has been put forth; nevertheless, these possess inherent limitations in their scope, as they have been developed for small-scale case studies with predefined exercises, which hinders the consideration of the dynamic nature of the construction process throughout its life cycle. Conversely, although sigmoidal models, including the logistic and Gompertz models, have been extensively employed to represent the cumulative progress of construction projects, their direct application to rigid pavement works is constrained. This phenomenon can be attributed to their inability to effectively adapt to the planning curves that are characteristic of road projects. These planning curves typically exhibit a more accelerated dynamic range compared to that of building works [2; 4; 7]. In response to this challenge, researchers have proposed the utilization of non-linear regression models for the analysis of multifactor data. These models facilitate the S-curve modeling of project status and subsequent prediction of project progress. S-curves are graphical representations that have gained widespread popularity in the field of project management. These representations are employed to depict the progression of costs, labor hours, percentage of work, and other metrics as a function of the elapsed time. The characteristic pattern of these curves is marked by a gradual onset, a rapid acceleration, and a subsequent decline, culminating at the point of project completion [8]. Furthermore, it encapsulates the intrinsic characteristics of projects, where the preliminary configuration necessitates resource allocation. Large-scale projects commence with a limited number of tasks but rapidly transition to concurrently managing multiple activities, which results in elevated expenses compared to the initial stages. These tools have evolved into essential instruments for project planning, control, and execution.