Development and Application of a Stochastic Model for Optimizing Production Cycles Aimed at Sustainable Production

This paper analyzed the importance of applying modern concepts and tools for monitoring production processes in order to improve effectiveness, efficiency, and sustainable manufacturing. The aim of the study was to develop and apply a stochastic model based on a modified real-time observation method to optimize production cycles in the metalworking industry. The research was conducted over several years in real industrial conditions using instantaneous observations, and the collected data were statistically analyzed using control charts and flow coefficient functions. The results showed a significant reduction in production cycle times and improved efficiency, particularly when the batch size was optimized to 10 units. The analyzed working time elements and flow coefficients enabled a comprehensive analysis and influenced trends in subsequent years, thereby improving production management. A comparative analysis of the results reveals a downward trend in average PC time per unit over the years—56.2, 37.7, 31.5, and 44.8 min from phases I to IV—until the introduction of a new operation. The corresponding flow coefficient functions are y1 = 297.54/x + 2; y2 = 239/x − 7.36; y3 = 192/x + 0.65; and y4 = 438.2/x − 11.3. These findings suggest that the optimal batch size for the enterprise under consideration is 10 units. The findings confirmed that the integration of Lean principles and Industry 4.0 methods contributes to the reduction of non-productive time and better process control. The study provided a simple and effective model for cycle time optimization that can be implemented even in small and medium-sized enterprises.