(untitled) (Web of Teachers: Inderscience Research, 2025)
This article systematically examines the theoretical and practical foundations of mathematical modeling of production processes. It provides a detailed analysis of the main concepts, methodologies, and approaches related to modeling production processes. Special attention is given to various types of production functions, their applications in economic and industrial processes, and their role in improving efficiency. The relevance of the article lies in the fact that in modern production systems, the optimal allocation of available resources and the enhancement of production efficiency are of critical importance for any enterprise or industrial entity. Therefore, mathematical modeling of production processes allows for forecasting their behavior in advance, improving efficiency indicators, and ensuring the optimal use of resources. Moreover, the article presents mathematical representations of production functions, their analysis, and practical applications. This facilitates the optimization of production processes and enables accurate and well-founded decision-making. The article focuses on issues such as increasing production efficiency, conserving resources, and advancing production systems to a more digital and controllable level, contributing to a deeper understanding of economic and industrial processes.