Research on Production Decision-Making Based on Sequential Sampling Inspection and Mixed Integer Programming

As modern manufacturing evolves, production decision-making has emerged as a pivotal concern for enterprises, with strategic sampling inspection and decision-making offering significant cost reductions. A supplier asserts that the defect rate of spare parts complies with the established standard, prompting the enterprise to undertake sampling verification at its own expense to inform decisions at each production stage. This paper endeavors to devise a sampling plan that minimizes inspections while maintaining quality, addressing the complexities of multiple processes and components. To this purpose, the study sequentially establishes both hypothesis testing and sequential testing models, comparing their efficacies. Based on the defect rate, four decision variables are considered: spare parts inspection, semi-finished product inspection, finished product inspection, and disassembly. Aiming to minimize costs, a mixed-integer programming model is formulated, with a simulated annealing algorithm employed to seek an approximate optimal solution. The findings indicate that, at the same confidence level, the sequential testing model can reduce the sample size by 41.0% to 57.1% compared to the hypothesis testing model, enabling enterprises to substantially decrease inspection costs while preserving inspection effectiveness. This study contributes to optimizing sampling inspection plans and multi-stage decision-making in multi-process and multi-component production environments, ultimately enhancing the economic benefits for enterprises.