Estimated model-based robust optimization of closed-loop supply chain under uncertain carbon tax rates and demand

Due to the growing interest in sustainable development, the importance of research on closed-loop supply chain is being emphasized more and more. The main objective of this study is to develop a robust optimization model for a closed-loop supply chain that reflects uncertain demand and the time-series patterns of uncertain carbon tax rates on the basis of historical data. This study incorporates the first-order autoregressive model into a set-based robust optimization model to find a less conservative solution. Two novel uncertainty sets reflecting the time series pattern using the historical data are proposed and tractable robust counterparts are developed. The results of numerical experiments conducted herein indicate that the optimal solutions of the proposed models are less conservative than those of the conventional robust optimization model, with a slight loss in robustness to the parameter uncertainty. Moreover, according to the experimental results, the stronger the autocorrelation of the uncertain parameter, the greater are the benefits of the proposed models. Furthermore, the smaller the size of the historical data, the higher are the conservatism and robustness of the proposed model. In addition, when the exact support set is known, the proposed model can be less conservative than that when it is not known, but both proposed models outperform the conventional robust optimization model.