Analysis of methods and algorithms for optimizing production capacity planning

The key objective of this study is to find optimal solutions in the field of production capacity allocation and determining the optimal batch size. Methods are considered to minimize the costs associated with transportation, storage and production, as well as maximize the efficiency of resource use. The analysis of methods and algorithms used to optimize production capacity utilization is presented: Johnson's algorithm, the method of branches and boundaries, and the genetic algorithm. Each of the methods is being investigated in terms of their applicability, accuracy, computational complexity, and adaptability to different production conditions. Attention is paid to comparing the strengths and weaknesses of each approach, which makes it possible to evaluate their effectiveness depending on the specifics of production processes. The results of the analysis show that classical methods remain relevant for tasks with well-defined parameters and stable conditions, while modern technologies such as neural networks, genetic algorithms and optimization methods based on big data demonstrate high efficiency in conditions of uncertainty, dynamically changing requirements and complex production systems. Based on the conducted research, possible directions for further development are proposed, including the integration of classical and modern methods, the development of hybrid approaches combining the advantages of various technologies.