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. Abstract 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.

My first debt of gratitude must go to my advisor, Dr. Sarah M. Ryan. She patiently provided the vision, encouragement and invaluable suggestions necessary for me to proceed through the doctoral program and complete my dissertation. She has been a supportive adviser to me throughout my Ph.D study, but she has always given me great freedom to pursue independent work. I could not have imagined having a better advisor and mentor for my Ph.D study.