The implementation of scrap recovery activities has been shown to improve the financial performance of many firms, and this kind of circular economy (CE) is particularly evident in industries with green manufacturing (GM). In this paper, we consider an imperfect multiple-stage production system that manufactures paired products made from mixed materials containing scrap returns, in which the scrap returns are converted from defective products. The feed rates of scrap returns for two products are different, and the product with the higher feed rate is placed in the second order of the process to avoid unlimited accumulation of scrap returns. The proposed problem is formulated as a joint economic order quantity (EOQ) and economic production quantity (EPQ) model aimed at cost minimization. The decision variables of the proposed model include the production run time of two products, order quantity of new material, and the extent of investment in converted equipment. We also prove that the optimal solution exists uniquely and provide an algorithm for the computation of the optimal solution. Finally, a numerical example involving the pulp and paper manufacturing industry is provided to illustrate the solution process, and the results of its sensitivity analysis are also presented to show some managerial implications.

中文翻译：

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基于循环经济的包含废料回收的混合材料的不完善生产-库存模型

废钢回收活动的实施已被证明可以改善许多公司的财务业绩，这种循环经济 (CE) 在绿色制造 (GM) 行业尤为明显。在本文中，我们考虑了一个不完善的多阶段生产系统，该系统制造由包含废料退货的混合材料制成的配对产品，其中废料退货是从缺陷产品转换而来的。两种产品的报废回料进料速度不同，进料速度高的产品排在工序的第二个顺序，避免报废回料无限累积。所提出的问题被表述为旨在使成本最小化的联合经济订单数量 (EOQ) 和经济生产数量 (EPQ) 模型。所提出模型的决策变量包括两种产品的生产运行时间、新材料的订单数量以及转换设备的投资程度。我们还证明了最优解是唯一存在的，并提供了计算最优解的算法。最后，提供了一个涉及纸浆和造纸制造业的数值例子来说明求解过程，并给出其敏感性分析的结果以显示一些管理意义。