The economic lot-sizing problem with remanufacturing and heterogeneous returns: formulations, analysis and algorithms

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.