Due to legislation and economic reasons, firms in most industries are forced to be responsible and manage their products at the end of their lives. Management of product returns is critical for the stability and profitability of a reverse supply chain. Forecasting the return amounts and timing is beneficial. The purpose of this paper is to develop a forecasting system for discarded end-of-life vehicles and to predict the number of end-of-life vehicles that will be generated in the future. To create the forecasting system, grey system theory, which uses a small amount of the most recent data, is employed. The accuracy of the grey model is improved with parameter optimization, Fourier series and Markov chain correction. The proposed models are applied to the case of Turkey and data sets of twelve regions in Turkey are considered. The obtained results show that the proposed forecasting system can successfully govern the phenomena of the data sets, and high accuracy can be provided for each region in Turkey. The proposed forecasting system can be used as a strategic tool in similar forecasting problems, and supportive guidance can be achieved. (C) 2016 Elsevier Inc. All rights reserved.