基于多阶段模拟仿真的生产决策问题  

Production Decision-making Problems Based on Multi-stage Simulation

作　　者：张汝坤 裘诚睿 何晨 李波[2] ZHANG Rukun;QIU Chengrui;HE Chen;LI Bo(College of Physical Science and Technology,Central China Normal University,Wuhan,Hubei 430079,China;School of Mathematics and Statistics,Central China Normal University,Wuhan,Hubei 430079,China)

机构地区：[1]华中师范大学物理科学与技术学院,湖北武汉430079 [2]华中师范大学数学与统计学学院,湖北武汉430079

出　　处：《数学建模及其应用》2025年第1期88-97,共10页Mathematical Modeling and Its Applications

摘　　要：本文探讨企业生产过程中的元件产品抽样检测问题和最大化生产收益问题,并在真实次品率未知的情况下制定出相应的生产决策.通过改进(n,c)抽样法,利用单边限制,消除了使用方风险的不确定性,得出判断拒收或接收一批产品的(n,c)方案.若已知使用方风险,本文改进模型得到了双边限制下的唯一方案.在最大化生产收益问题中,本文创新地将0-1决策转化为连续变量决策,让所有决策参数在0~1变动,再通过循环生产模型,收敛后得出一定数量的初始零件能够获取的最大净利润.在确定决策参数问题上,本文采用了线性模拟退火算法,迅速有效地得到了最优解.最后,在真实次品率未知的情况下,根据给出的(n,c)方案进行模拟,得出真实次品率的期望,将其重新代入生产决策模型,可以得到更新次品率后的生产决策.This paper discusses the sampling inspection of component products and the problem of maximizing production revenue in the production process of enterprises,and makes corresponding production decisions when the real defective rate is unknown.By improving the(n,c)sampling method and using unilateral restrictions,the uncertainty of the user′s risk is eliminated,and the(n,c)scheme for judging the rejection or acceptance of a batch of products is obtained.If the user risk is known,the improved model in this paper is the only solution under the two-sided constraint.In the problem of maximizing production benefits,this paper innovatively transforms the 0-1 decision into a continuous variable decision,so that all the decision parameters change at 0~1,and then through the circular production model,the maximum net profit that can be obtained by a certain number of initial parts is obtained after convergence.In this paper,a linear simulated annealing algorithm is used to determine the decision parameters,and the optimal solution is obtained quickly and effectively.Finally,in the case that the real defective rate is unknown,the simulation is carried out according to the(n,c)scheme given in the above method,and the expectation of the real defective rate is obtained,and it is re-substituted into the production decision model,and the production decision after the updated defective rate can be obtained.

关 键 词：生产决策 (n c)抽样 线性模拟退火 贝叶斯公式 

分 类 号：O29[理学—应用数学]