This paper discusses a basic dynamic lot-sizing model for a single item with rework of defectives. Due to the imperfect production process, some fraction of the generated items is not of sufficient quality. After rework, these goods serve the same demand as the initial perfect quality items; both are called serviceables.The internal processes production and rework are conducted independently from another at different or same periods. The basic model is proven to be NP-hard. We present three main unique characteristics that describe the specific model behavior observed in the optimal solutions: production only, multiple rework, and overproduction of serviceables. Different MIP formulations are derived to analyse the effects of these three characteristics on the optimal solutions that exclude each of these characteristics from the basic model. Afterward, computations for given data sets are conducted, using all different MIP formulations. It can be shown that production only occurs most frequently and has the highest effect on the total cost.