生产过程中的决策问题研究

Research on Decision-making Issues in the Production Process

摘要

针对生产过程中供应链次品率问题,基于假设检验、目标规划及贝叶斯统计等方法,构建了质量控制和决策优化模型.首先,通过简单随机抽样和序贯抽样,基于二项分布-ICDF的假设检验模型,确定了不同置信水平下的最小样本量和临界次品数量.对比分析表明,序贯抽样在检测效率上更优,在95%置信水平下,样本量为98,次品数大于等于5时拒绝该批零件;在90%置信水平下,样本量为60,次品数小于9时接收.随后,构建了双目标规划模型,综合考虑采购、装配、检测、调换和拆解等成本因素,优化了在不同次品率条件下的质量控制与成本效益策略.通过蒙特卡洛模拟生成随机样本,并结合贝叶斯更新方法估计次品率的后验分布,进一步分析不同情境下的利润率变化.最终,模型有效提升了生产效率、利润率和财务稳健性,验证了其在生产质量控制中的适应性和实用性.

Abstract

This paper addresses the issue of defect rates in the supply chain during the production process by constructing a quality control and decision optimization model based on hypothesis testing, goal programming, and Bayesian statistics. First, using simple random sampling and sequential sampling, a hypothesis testing model based on the Binomial Distribution ICDF was applied to determine the minimum sample size and critical defect quantity at different confidence levels. Comparative analysis showed that sequential sampling is more efficient. At a 95% confidence level, a sample size of 98 was required, and the batch was rejected if the number of defects was greater than or equal to 5. At a 90% confidence level, a sample size of 60 was required, and the batch was accepted if the number of defects was fewer than 9. Subsequently, a dual objective programming model was developed, considering factors such as procurement, assembly, inspection, replacement, and dismantling costs, to optimize quality control and cost efficiency strategies under different defect rate conditions. Using Monte Carlo simulation to generate random samples and combining Bayesian updating to estimate the posterior distribution of the defect rate, the model further analyzed profit rate variations under different scenarios. Although the profit rates fluctuated, the optimal decision strategy remained unchanged. Ultimately, the model effectively improved production efficiency, profitability, and financial stability, demonstrating its adaptability and practicality in production quality control.

关键词

二项分布-ICDF模型 / 双目标规划 / 贝叶斯统计 / 蒙特卡洛模拟

Key words

binomial distribution ICDF model / dual objective programming / Bayesian statistics / Monte Carlo simulation

参考文献

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基金资助

湖北省哲学社会科学研究一般项目(24Y092)