Abstract This paper investigates an impact of random defective rates in an imperfect production system with multiple products and planned backorders in a single-stage production system. The purpose of this study is to control a single-stage cleaner production system with a random defective rate for multiple products. Considering these, the model becomes a non-linear constraint problem. Based on different distribution functions of random defective rates, to eliminate the defective items from the system, five special cases for effective system management are considered. A non-linear optimization technique is utilized to solve the model and obtain the global optimum solution of cleaner production system with multiple products and a global optimum solution. Numerical examples, graphical representations, and sensitivity analysis are given to illustrate the model. Numerical studies prove that the cost related with a Chi-square distribution gives the least cost and cost related with a beta distribution gives the maximum cost, whereas the literature shows a triangular distribution gives the minimum cost.

中文翻译：

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具有随机不良率和再制造的单级清洁生产系统

摘要 本文研究了在单阶段生产系统中具有多个产品和计划延期交货的不完善生产系统中随机缺陷率的影响。本研究的目的是控制具有多个产品随机缺陷率的单级清洁生产系统。考虑到这些，模型变成了一个非线性约束问题。基于随机缺陷率的不同分布函数，为了从系统中消除缺陷项目，考虑了有效系统管理的五种特殊情况。利用非线性优化技术对模型进行求解，得到多产品清洁生产系统的全局最优解和一个全局最优解。数值示例、图形表示、并给出敏感性分析来说明该模型。数值研究证明，与卡方分布相关的成本最低，与贝塔分布相关的成本最高，而文献显示三角分布的成本最低。