Multi-Stage Production Decision Optimization Model Based on Dynamic Programming and Monte Carlo Simulation

This study presents a multi-stage production decision optimization model based on dynamic programming and Monte Carlo simulation. The model aims to optimize quality control and cost-effectiveness for enterprises under different confidence levels. Initially, sampling inspection is conducted to determine if the defect rate of spare parts meets the standard, and decisions to accept or reject the entire batch are made accordingly. Two hypothesis testing models are established, corresponding to 95 % and 90 % confidence levels, to determine the minimum sample size. The inspection process is simulated using the binomial distribution, and Z -testing is applied for large samples to standardize the data. Furthermore, a multi-stage dynamic programming decision model is developed, taking into account factors such as part defect rates, finished product defect rates, purchase prices, inspection costs, and the replacement losses and disassembly costs of non-conforming finished products, to achieve optimal decisions throughout the production process. The model enumerates all possible strategy combinations and iteratively solves for the optimal strategy at each stage to maximize total profits in the production process. Additionally, a dynamic substandard rate feedback and production strategy adjustment model is proposed to consider the statistical characteristics of test results and cost factors at each stage, achieving optimal decisions at each stage. The study results indicate that the optimized strategy combinations outperform with a profit performance exceeding 90 % in all six production scenarios, with profit contribution rates even exceeding 100 % in some cases.