Dynamic Lot-Sizing with Imperfect Production and Rework of Defectives

Lot-sizing models are a vital part of the inventory management literature. Especially dynamic lot-sizing models are the basis of many industrial applications. Besides the basic single-item model, many extensions exist. Among them, remanufacturing models are important concerning aspects of quality and sustainability. They focus on the handling of product returns from customers and thus combine the processes of manufacturing and remanufacturing into a single model. Whereas many models are focusing on this aspect of external product returns, comparatively little attention has been paid to internal product returns. While quality management aims to optimise production towards zero defects, this is not always possible. Therefore, this paper contributes to the literature by introducing a basic model that assumes an imperfect production process and rework of the resulting defective items. We compare this model to the closely related models, namely the basic single-item model with perfect production and the remanufacturing model. In addition, a numeric study will compare the computation efforts for them and will also highlight hard cases of the rework model. It will be shown, that the model formulations are very similar but the computation times differ strongly for the three models. The rework model shows the largest runtimes and increases strongly with increasing lengths of the planning horizon. Also, there are specific cost parameter combinations that cause multiples of the average computation times.