A novel robust fuzzy mean-UPM model for green closed-loop supply chain network design under distribution ambiguity

Abstract Green closed-loop supply chain (GCLSC) is a supply chain that encompasses forward and reverse flows of components and products in logistic networks with a focus on economic and environmental performance. In the decision-making process of GCLSC, the presence of uncertainty and risk originating from the size and complexity of network is crucial to consider, and the distribution of uncertain parameter may be ambiguous. To characterize the ambiguity caused by distributional perturbation, a novel ambiguity distribution set is proposed, and further a new upside risk: upper partial moment with power q is introduced to quantify the economic risk in the GCLSC. Subsequently, a distributionally robust fuzzy GCLSC network design model which attempts to optimize the worst-case performance of the network is developed with the perspective of a trade-off between upside risk and expectation of economic cost. To format a sustainable GCLSC paradigm, the policy of carbon cap is adopted to control carbon emissions in terms of environmental constraints. Furthermore, the tractable counterpart of the proposed model is obtained by transforming distributionally robust credibility objective and constraints into their equivalent forms under ambiguous distribution of uncertain parameter. Finally, a case study on Coca-Cola Company in Northeast China is investigated to test and verify the proposed model. The advantage of proposed model is demonstrated through comparative study on distribution ambiguity free and without environmental constraint problem. Computational results reveal that the proposed model has superior capability of immunity against the risk of distribution ambiguity.