Optimization through multivariable calculus in intelligent industrial production systems
DOI:
https://doi.org/10.70577/asce.v5i2.879Keywords:
Management; Strategy; Optimization; Heuristics; Intelligent SystemsAbstract
This research analyzes the relevance of multivariable calculus optimization in the development and operation of smart industrial production systems. The main objective is to determine how advanced mathematical tools, such as stochastic gradient descent, Lagrange multipliers, and variational calculus, enhance operational efficiency and sustainability within the framework of Industry 4.0. Through a methodological review and quantitative data analysis, it is demonstrated that the integration of these models into cyber-physical environments facilitates real-time decision-making, achieving a 73% reduction in product rejection rates and increasing plant availability to 96.5%. The results highlight that the use of Pareto fronts and multi-objective optimization allows for a balance between economic profitability and carbon footprint reduction, achieving a 12.5% decrease in polluting emissions. It is concluded that multivariable calculus transcends its theoretical nature to become an indispensable practical pillar for industrial autonomy, providing robust solutions to the variability of modern processes. The research recommends the adoption of digital twins and edge computing architectures to maximize the benefits of these mathematical models in the management of smart and sustainable factories.
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Copyright (c) 2026 Jessica Paulina Gálvez Morocho, Rodrigo Patricio Toasa Jimenes, José Luis Cortés Llanganate, Andrés Joao Noguera Cundar
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