企业生产过程中的决策问题研究——以2024年全国大学生数学建模竞赛B题为例
南阳师范学院, 数学与统计学院, 河南南阳 473061
| 摘 要： | 在现代制造业全流程生产体系中，不仅需要考虑零配件的生产状况以及产品最终的完成度情况，还必须要把产品的合格率这一关键因素纳入考量范围来进行企业生产。根据消费者的需求市场需要对成品的价格以及质量进行测试，通过分析检测成本、拆卸成本、调换成本等多个不同维度的成本因素来权衡是否对成品进行各种操作。本研究主要是借助合理的算法，充分运用假设性检验、置信区间、拒绝域等得出最优结果，得到如何对零配件进行检测以及对成品进行合格率测试来使企业获得最大利润。与此同时，本研究还会结合具体的实际情况，给出具有针对性和可操作性的决策方案，以便企业能够根据这些方案更好地开展生产和经营活动。 |
| 关 键 词： | 假设性检验; 正态分布; 拒绝域; 置信区间 |
| DOI： | 10.57237/j.wjms.2026.01.001 |
View:
Downloads:
收稿日期: 2024-12-28
接受日期: 2025-12-26
在线出版日期: 2026-01-14
Research on Decision-making Problems in the Production Process of Enterprises
School of Mathematics and Statistics, Nanyang Normal University, Nanyang 473061, China
| Abstract: | In modern manufacturing’s end-to-end production system, it is essential not only to take into account the production status of components and the final completion level of products, but also to incorporate the crucial factor of product qualification rate into the scope of consideration for enterprise production. According to consumer demand, the market requires that both the price and quality of finished goods be tested. This necessitates a comprehensive evaluation of whether to carry out various operations on finished products by analyzing cost factors across multiple dimensions - including inspection costs, disassembly costs, and replacement costs. The present study primarily utilizes well‑designed algorithms and fully applies statistical methods such as hypothesis testing, confidence intervals, and rejection regions to derive optimal solutions. These approaches enable the determination of how to inspect components and how to conduct qualification‑rate testing on finished products, thereby helping firms achieve maximum profit. Furthermore, the research takes specific practical conditions into account and proposes targeted, actionable decision schemes. By following these schemes, enterprises can more effectively plan and execute their production and operational activities, enhancing overall efficiency and competitiveness. In summary, integrating component-level inspection strategies with finished‑product qualification assessments within a cost‑benefit analytical framework provides a systematic pathway for manufacturers to align product quality assurance with economic objectives under real‑world constraints. This methodology supports data‑driven decision making and facilitates sustainable growth in increasingly demanding markets. |
| Keywords: | Hypothesis Testing; Normal Distribution; Rejection Region; Confidence Interval |
参考文献
| [1] | 孟庆瑜, 刘婷婷. 生态环境法典视域下生产者责任延伸制度的规范供给和配套完善 [J], 2022第4期: 175-184. |
| [2] | 谢家平, 迟琳娜, 梁玲. 基于产品质量内生的制造/再制造最优生产决策 [J], 2012, 第15卷第8期: 12-13. |
| [3] | Fine C H. Quality improvement and learning in productive systems [J]. Management Science, 1986, 32(10): 1301-1315. |
| [4] | Gal-Or E. Quality and quantity competition [J]. The Bell Journal of Economics, 1983, 14(2): 590-600. |
| [5] | 茆诗松, 程依明, 濮晓龙. 概率论与数理统计教程 (第三版) [M], 北京: 高等教育出版社, 2019. 11 (2023.4重印). |
| [6] | 杨波, 胡钊. 浅议假设检验中原假设的设置 [J], 2023, 第38卷第3期: 91-95. |
| [7] | 卢亚丽, 假设检验中两类错误分析与实验, 河南教育学院学报 (自然科学版) [J], 2011, 第20卷第3期: 10-12. |
| [8] | 徐永朋, 某电子产品抽检方案探讨, 航空兵器 [J]. 1995, 第3期: 23-24. |
| [9] | 沈维军, 沈少军. 企业成本管理与经营决策研究,中国电子情[J], 2024, 第21卷: 16-18. |
| [10] | 梁海洲, 王佳璐, 袁欣, 等. 基于改良模拟退火算法和统计方法的生产过程决策,天府数学 [J], 2025, 第03卷: 22-29. |
| [11] | 全国大学生数学建模竞赛组委会. 2024年高教社杯全国大学生数学建模竞赛赛题 [EB/OL]. (2024-09-05) [2025-03-03]. https://www.mcm.edu.cn/html_cn/node/a0c1fb5c31d43551f08cd8ad16870444.html |
| [12] | 姜启源,谢金星,数学建模案例选集, [M]], 北京: 高等教育出版社. 2006. |
| [13] | 李泰新, 靳析函, 基于动态规划和顺序概率比检验的企业生产决策优化研究, 市场瞭望 [J], 2024, 第24卷: 7-9. |
| [14] | 潘蓉蓉; 罗建强; 杨子超, 数字技术赋能制造企业服务化转型: 理论分析与展望[J]. 系统工程理论与实践, 2023, 第11期, 22-27. |
| [15] | 吴鹏; 吕有厂, 随机需求下考虑半成品库存的多周期生产决策优化. 运筹与管理 [J], 2014, 第02卷: 11-17. |
