Transient sensitivity and Monte Carlo spectral analy- sis in stage-structured manufacturing systems

Abstract

This study presents a mathematical modeling and simulation scheme for optimizing multi-stage production systems with dormancy effects, transition dynamics, and rework mechanisms. A staged structured approach is employed to capture the interplay between production flow, storage capacities, and material recovery. Sensitivity and elasticity analyses are conducted to evaluate the impact of transition rates on total production output. The results indicate that an increase in transition rate γ2 significantly enhances production efficiency, as demonstrated by a sensitivity of 1007.36 and an elasticity of 5.44. However, an unregulated increase in transition rates can create bottlenecks in downstream stages, necessitating capacity adjustments and strategic control measures. The study concludes that a balanced optimization of transition dynamics, dormancy effects, and storage capacities is critical for enhancing overall system efficiency. Future work will focus on integrating stochastic optimization techniques and adaptive control strategies to refine decision-making in real-time manufacturing systems.