Caputo-Based Numerical Modeling of Fractional Logistic Growth with Fractal Structures

Abstract

Transportation is one of the most important aspects of human activity, supporting various social and economic transactions. Meanwhile, in order to remain competitive, freight transportation businesses and logistics providers must deliver high-quality, dependable, and effective services. The effective design of the service network in this industry necessitates strategic and tactical decisions regarding service frequency, optimal route selection, and market share allocation among companies. In this study, we have examined the static competition between two transportation companies by utilizing a Mixed-Integer Nonlinear Programming (MINLP) model. The competition is studied by calculating entrant’s service frequency and each company’s market share using a logit function. In this type of competition, the incumbent’s decisions about route selection and frequency determination are known beforehand, and our goal is to maximize profits for the new market entrant. Additionally, a number of constraints have been taken into account, including route capacities, the maximum allowable frequency on each link, and penalty costs associated with the incomplete utilization of route capacities. To evaluate and validate the model, real-world data from the Iranian Road Maintenance and Transportation Organization has been employed. Furthermore, in the sensitivity analysis phase, the impacts of changing the values of important parameters on the model's outputs were evaluated. This investigation aims to improve understanding of the system's dynamics and clarify how these factors influence optimal decision-making processes.