Abstract This paper considers a closed-loop supply chain production inventory model consisting of a virgin raw material supplier, a manufacturer, a retailer and a collector who collects the used product from consumers at a return rate depending on acceptance quality level of the used product. Here, two types of products are produced: manufactured product using virgin raw materials and remanufactured product using used manufactured product. So, to make the model more realistic, here, the manufacturer incorporates two separate remanufacturing and manufacturing infrastructures to process simultaneously to produce remanufactured and manufactured items due to overcome the lost sale situation arisen in several published model. Again, since the quality of a product from a remanufacturing process mostly depends upon the acceptance quality level of the used product, hence an acceptance quality level dependent development cost has been considered in remanufacturing process. Also, both demand of the remanufactured products and procurement cost of the used products from collector to manufacturer have been considered as a function of acceptance quality level of returned items. Moreover, remanufacturing and manufacturing processes produce some defective items which are reworked within the same cycle. With these considerations, a mathematical model has been developed (i) to find out optimum acceptance quality level of the used manufactured product for recycling, (ii) to overcome the lost sale situation due to unsatisfied demand of remanufactured (manufactured) product at the time of manufacturing (remanufacturing) process and (iii) to obtain optimum number of deliveries from supplier to manufacturer, from manufacturer to retailer and from collector to manufacturer that maximize total integrated profit. To get the optimum solutions of the proposed model, sequential and global optimizations methods have been used. Finally, the model has been analyzed numerically to study the feasibility taking several examples.

中文翻译：

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接受质量水平依赖于开发成本和需求的不完善生产系统中的可持续回收

摘要 本文考虑了一个由原始原材料供应商、制造商、零售商和收集者组成的闭环供应链生产库存模型，收集者根据所使用产品的接受质量水平以退货率从消费者那里收集使用过的产品。在这里，生产两种类型的产品：使用原始原材料制成的产品和使用使用过的制成品的再制造产品。因此，为了使模型更加逼真，制造商在这里合并了两个独立的再制造和制造基础设施，以同时处理生产再制造和制造物品，以克服多个已发布模型中出现的销售损失情况。再次，由于再制造过程中产品的质量主要取决于所用产品的验收质量水平，因此在再制造过程中考虑了与验收质量水平相关的开发成本。此外，再制造产品的需求和旧产品从收集者到制造商的采购成本都被视为退货项目验收质量水平的函数。此外，再制造和制造过程会产生一些在同一周期内返工的缺陷产品。考虑到这些因素，已经开发了一个数学模型 (i) 找出用于回收的已用制造产品的最佳接受质量水平，(ii) 克服由于在制造（再制造）过程中对再制造（制造）产品的需求未得到满足而造成的销售损失情况，以及 (iii) 获得从供应商到制造商、从制造商到零售商以及从收集者的最佳交货次数使总综合利润最大化的制造商。为了获得所提出模型的最佳解决方案，使用了顺序和全局优化方法。最后，对模型进行了数值分析，并举几个例子来研究其可行性。已使用顺序和全局优化方法。最后，对模型进行了数值分析，并举几个例子来研究其可行性。已使用顺序和全局优化方法。最后，对模型进行了数值分析，并举几个例子来研究其可行性。