We address an extension of the economic lot-sizing problem with remanufacturing, in which the returns are assumed of heterogeneous quality. Costs for remanufacturing and holding inventory depend on the quality of the returns. For the problem with general cost functions, we provide a network flows formulation and a dynamic programming algorithm of pseudopolynomial time. Then, we consider the problem under stationary costs and different set-up schemes for manufacturing and remanufacturing. For the case of a joint set-up scheme, we derive certain properties related to the form of the optimal solutions. Based on these theoretical results, a polynomial-time algorithm is presented for the particular case of a large quantity of low-cost returns. For the case of separate set-up scheme, we show that the problem is NP-hard and present several lot-sizing rules specially designed for the problem. An extensive numerical experimentation was conducted to evaluate the suggested rules under different combinations of inventory and set-up costs. From the results obtained, we can extract several managerial insights, such as in general it is profitable to remanufacture all the available returns of the same quality in certain periods, but not necessarily those of the highest quality.

我们通过再制造解决了经济批量问题的扩展，其中假设收益具有异质性。再制造和持有库存的成本取决于退货的质量。对于一般成本函数的问题，我们提供了网络流公式和伪多项式时间的动态规划算法。然后，我们考虑固定成本和制造和再制造的不同设置方案下的问题。对于联合设置方案的情况，我们推导出与最优解的形式相关的某些属性。基于这些理论结果，针对大量低成本回报的特殊情况，提出了一种多项式时间算法。对于单独设置方案的情况，我们证明了这个问题是 NP 难的，并提出了几个专门为这个问题设计的批量规则。进行了广泛的数值实验，以评估不同库存和设置成本组合下的建议规则。从获得的结果中，我们可以提取一些管理见解，例如，一般来说，在某些时期再制造相同质量的所有可用回报是有利可图的，但不一定是最高质量的回报。