This paper addresses a multi-period capacitated closed-loop supply chain (CLSC) network design problem subject to uncertainties in the demands and returns as well as the potential carbon emission regulations. Two promising regulatory policy settings are considered: namely, (a) a carbon cap and trade system, or (b) a tax on the amount of carbon emissions. A traditional CLSC network design model using stochastic programming is extended to integrate robust optimization to account for regulations of the carbon emissions caused by transportation. We propose a hybrid model to account for both regulatory policies and derive tractable robust counterparts under box and ellipsoidal uncertainty sets. Implications for network configuration, product allocation and transportation configuration are obtained via a detailed case study. We also present computational results that illustrate how the problem formulation under an ellipsoidal uncertainty set allows the decision maker to balance the trade-off between robustness and performance. The proposed method yields solutions that provide protection against the worst-case scenario without being too conservative.
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