Modelo matemático para la optimización de los tiempos muertos. Una aplicación en el sector transporte de San José de Cúcuta

The absence of technical studies aimed at optimizing public transportation in Norte de Santander can lead to increased traffic congestion, operational inefficiency of existing routes, user dissatisfaction due to lack of coverage, poor infrastructure, and long wait times. If research-based planning tools are not implemented, responsible entities could continue to make reactive and disjointed decisions, prolonging the structural problems of the mobility system. This research designed a mathematical allocation model to minimize dead time (delay or lead time). Initially, a diagnosis was conducted based on historical information collected by the company in question, followed by the creation of a time sheet to identify patterns in driver arrival times at stations. Finally, these data were analyzed, and performance indicators were created and strategic profiles defined. The results of the model's simulation showed improvements in the daily operation of the system, reducing the time drivers were not using during their work shifts by 14%. Experimentation with different scenarios within the model demonstrated its adaptability and usefulness in situations where the system is being expanded or modified. This finding validates that the proposed model is functional and a solid tool for supporting decision-making in daily logistics. Furthermore, the model allows drivers to be classified efficiently based on their average time, which helps organize shifts more strategically.