LOGISTICS MODEL VS GOMPERTZ MODEL IN APPROXIMATION OF “S” CURVES IN WATER SUPPLY SYSTEMS PROJECTS

Abstract

Much of the success of an engineering project depends on good planning. Most engineers use an S curve to estimate the relationship between the execution time variables and the financial resources available for construction. Mathematically speaking, the functions that can be used for said estimation are those that pass through the origin of the Cartesian plane, given that at the initial time of the project the cost used is zero, they are also increasing and upon reaching the estimated execution time it is expected to have used the total amount assigned for the work. This investigation began in 2019 where the forms of several executed water supply systems were taken and with this data, the planning curve was modeled with a logistic equation adjusted with least squares and validated with new projects to analyze its effectiveness. Now in 2023, data from new projects is added and a new model was made based on the Gompertz curve that has a graph similar to the logistic curve, but with the difference that the curvature at the beginning and end of the time interval it is not always the same, as is the case with the logistic equation model, and it is expected that this characteristic will improve the approximation to the real execution curve of the project. It is concluded that the Gompertz model is indeed better than the logistic equation model for this type of approach and a tool is presented that is used for decision making.