Physics-Informed Neural Networks (PINNs) represent a transformative approach to solving partial differential equation (PDE)-based boundary value problems by embedding physical laws into the learning process, addressing challenges such as non-physical solutions and data scarcity, which are inherent in traditional neural networks. This review analyzes critical challenges in PINN development, focusing on loss function design, geometric information integration, and their application in engineering modeling. We explore advanced strategies for constructing loss functions—including adaptive weighting, energy-based, and variational formulations—that enhance optimization stability and ensure physical consistency across multiscale and multiphysics problems. We emphasize geometry-aware learning through analytical representations—signed distance functions (SDFs), phi-functions, and R-functions—with complementary strengths: SDFs enable precise local boundary enforcement, whereas phi/R capture global multi-body constraints in irregular domains; in practice, hybrid use is effective for engineering problems. We also examine adaptive collocation sampling, domain decomposition, and hard-constraint mechanisms for boundary conditions to improve convergence and accuracy and discuss integration with commercial CAE via hybrid schemes that couple PINNs with classical solvers (e.g., FEM) to boost efficiency and reliability. Finally, we consider emerging paradigms—Physics-Informed Kolmogorov–Arnold Networks (PIKANs) and operator-learning frameworks (DeepONet, Fourier Neural Operator)—and outline open directions in standardized benchmarks, computational scalability, and multiphysics/multi-fidelity modeling for digital twins and design optimization.

In a system of distribution of products are involved in different factors that determine their efficiency, profitability or optimal state, among these factors is the type of goods to be collected or delivered, it must also be considered the physical-chemical composition, hazard index to transport etc., in this sense, exist different standards for collection, delivery and transportation of such material causing with it an increase in operating costs associated with territory design and planning of distribution routes, the current paper present a general model based in mixed integer programming which integrates both problems, seeking to minimize the total distance traveled by the vehicle in each territory. It should be noted that one of the main features of this model is that it only considers the collection of goods in the distribution network which gives us the opportunity to offer low-cost solutions in terms of time and quality, addressing the specific and general characteristics of the emerging markets in Mexico

Fluidity models in the supply chain privilege the sustainable integration of capabilities and collaboration among its members in order to guarantee an efficient and safe flow of resources throughout all its processes. This research proposes a fluidity model for the agroindustry supply chain as a solution with regard to the sector’s needs of supply chain processes, and opportunities to collaborate within the field of innovation and sustainability through of traceability and proactive risk management as a tool for creating resilient systems. The model is based on a holistic vision that will allow it to adapt to an ever more complex and continuously transformed global environment that demands solutions to assess the global impact of local decision-making in the supply chain over a period of time, considering its implications and contributions to the agroindustry and agro-logistics sector. Finally, pertinent research areas are identified in the integration of agroindustry supply chain echelons.

This work considers the application of a mathematical model using mixed-integer linear programming for the vehicle routing problem. The model aims at establishing the distribution routes departing from a distribution center to each customer in order to reduce the transport cost associated with these routes. The study considers the use of a fleet of different capacities in the distribution network, which presents the special characteristic of a star network and which must meet different efficiency criteria, such as the fulfillment of each customer’s demand, the vehicle carrying capacity, work schedule, and sustainable use of resources. The intention is to find the amount of equipment suitable to satisfy the demand, thus improving the level of customer service, optimizing the use of both human and economic resources in the distribution area, and leveraging maximum vehicle capacity usage. The MILP mixed-integer linear programming mathematical model of the case study is presented, as well as the corresponding numerical study.

Sphere packing consists of placing several spheres in a container without mutual overlapping. While packing into regular-shape containers is well explored, less attention is focused on containers with nonlinear boundaries, such as ellipsoids or paraboloids. Packing n-dimensional spheres into a minimum-height container bounded by a parabolic surface is formulated. The minimum allowable distances between spheres as well as between spheres and the container boundary are considered. A normalized Φ-function is used for analytical description of the containment constraints. A nonlinear programming model for the packing problem is provided. A solution algorithm based on the feasible directions approach and a decomposition technique is proposed. The computational results for problem instances with various space dimensions, different numbers of spheres and their radii, the minimal allowable distances and the parameters of the parabolic container are presented to demonstrate the efficiency of the proposed approach.

Se contextualiza la importancia de las herramientas de manufactura esbelta mediante su aplicación para evaluar un proceso de fabricación de alarmar para disminuir sus costos y tener un menor número de retrabajos, scrap, y aumentar la calidad de los productos. En este estudio se recopila información de la situación problemática como indicadores actuales de scrap de un 0.49% y defectos un 36.2%, se diseña un plan de control para reducir significativamente el consumo de puntas de cautín, así como mantener las mejoras en otros indicadores de calidad. Los resultados del estudio muestran una disminución del consumo de puntas de cautín, alcanzando un 72% en el tipo de punta A y un 52% en el tipo B; teniendo un beneficio económicamente de 11,471.25 USD para finales del año. Se enfatiza la necesidad de mantener una comunicación efectiva y estrategias de gestión del talento humano para garantizar el éxito continuo de estas propuestas de mejora. Además, se descata la relevancia de Kaizen como un enfoque centrado en las personas y la estandarización de procesos, resaltando la participación activa de equipos multidisciplinarios en la implementación de estas prácticas para lograr mejoras sostenibles en los procesos de producción.