Pricing and carbon reduction decisions for a new uncertain dual-channel supply chain under cap-and-trade regulation

This study concentrates on the pricing issue in a low-carbon dual-channel (DC) supply chain, where the upper-level manufacturer is regulated by the cap-and-trade (CAT) mechanisms. Market demand is a key factor affecting pricing decision and demand uncertainty complicates the pricing problem. To deal with the challenge that only partial demand distribution information is available, this paper proposes a novel ambiguity distribution set to depict the uncertain demand. Under the proposed ambiguity distribution set, a robust fuzzy bi-level optimization pricing model is developed for the low-carbon DC supply chain. Three CAT regulation mechanisms, no CAT regulation, grandfathering (GF) mechanism and benchmarking (BM) mechanism, are considered to address the manufacturer’s CAT regulation. The analytically tractable counterpart of the proposed model is derived and the corresponding robust equilibrium solutions are obtained under three CAT mechanisms. Numerical analyses are carried out to explore the impact of the demand uncertainty on the manufacturer’s selection of the CAT regulation mechanism. The numerical results indicate that the uncertainty degree can change the manufacturer’s selection of the regulated mechanisms. Specifically, when the uncertainty degree is smaller, the BM mechanism is beneficial for the manufacturer comparing with the GF mechanism; when the uncertainty degree is bigger, the manufacturer prefers to GF mechanism rather than BM mechanism.