Production Process Optimization Based on Statistical Sampling and Integer Linear Programming

This paper explores the optimization of the production process based on statistical sampling and integer linear programming. Initially, we designed a sampling inspection plan to help enterprises determine whether the defect rate of a batch of spare parts meets the claimed value of 10 % provided by the supplier, with the fewest number of inspections required to make acceptance or rejection decisions. Assuming that the defect rate of spare parts follows a binomial distribution, we can use statistical sampling theory to determine the sample size and ensure reasonable judgment under a given confidence level. By approximating with the normal distribution, we can estimate the confidence interval of the sample. We then determine the inspection plan under two confidence levels: 95 % and 90 %. Subsequently, we applied an Integer Linear Programming (ILP) model to optimize decisions in the production process of electronic products, aiming to minimize costs and maximize profits. We defined decision variables and established dual optimization objectives of cost minimization and profit maximization. By analyzing the defect rates of different parts and finished products, combined with sampling and non-testing strategies, we evaluated the costeffectiveness of each stage and assessed four main decision options based on the analysis results. Finally, we used dynamic programming considering finished product recovery to optimize inspection strategies and proposed analysis and decision-making programs for the treatment of nonconforming products in the production process of enterprises. By comprehensively considering replacement losses and the reprocessing of non-conforming products, we obtained the accumulation of costs and benefits under different schemes.