Constrained optimization plays a central role in transport and logistics location problems, such as depot siting under geometric or infrastructure-related constraints. In practice, the classification of constrained extrema by classical second-order methods, typically based on bordered Hessians and the explicit manipulation of the total differentials of the constraint functions, can be cumbersome and error-prone, especially in engineering-oriented applications. In this paper, we present algorithmic procedures for the classification of constrained extrema in low-dimensional problems (2D and 3D), with applications to transport location models. The proposed approach does not avoid the use of constraint derivatives, since first-order constraint information is necessary for any local constrained classification procedure. Rather, it avoids the explicit manipulation of the total differentials of the constraints during the application phase. The required constraint information is incorporated through first-order partial derivatives evaluated at the stationary point, leading to simple algebraic test coefficients derived from the second derivatives of the Lagrangian. The procedures apply to regular non-degenerate cases and require only the solution of Fermat-type systems together with the evaluation of low-order determinants. Their practical relevance is illustrated through a transport depot location problem with geometric constraints, showing how the proposed approach can provide a transparent and effective decision-support tool for transport and logistics engineering.

The transition of the automotive sector towards autonomous mobility requires a sophisticated amalgamation of cutting-edge hardware, redundant software frameworks, and accurate mathematical modeling. This research examines the technologies that facilitate autonomy in passenger vehicles, highlighting the shift from distributed to centralized zonal systems. The core focus of this study is the development of a unified modeling framework that integrates Kinematic and Dynamic Bicycle Models. Kinematic models prove sufficient for operations at low speeds, while dynamic models are essential for maintaining stability at high speeds, where tire slip and lateral forces gain prominence. This research provides a comprehensive classification of existing designs and introduces a mathematical framework that facilitates transitions between modeling paradigms based on the vehicle's state. A detailed numerical calculus experiment is performed, simulating the transition from a low-speed urban turn to a high-speed interstate lane change. This illustrates the necessity for an integrated modeling approach to ensure safe autonomous navigation.

The environmental problems, as well as the economic and health ones, are convincing enough for the design, production and deployment of clean, efficient and sustainable vehicles for transport. The idea of electrical vehicles for transportation is not recently, as a response for these environmental problems, but from the end of the XIX century. The aim of the paper is to show the evolution of this type of vehicles and the integration of electric vehicles in the actual development context. Electric vehicles (EV) are driven by an electric motor through a controller, being powered from an onboard energy source. This type of vehicle offers the possibility of having a cleaner environment and a more efficient and environmentally friendly transport system. Electric vehicles have practically no gas emissions, therefore they are able to reduce the problem of urban pollution in a very efficient way, so electric vehicles are the only zero-emission vehicles (ZEV).