Modelling low-carbon closed-loop supply chain considering channel power structures and cross-shareholding

Under the background of low-carbon economy, cross-shareholding is introduced into the low-carbon closed-loop supply chain (CLSC) composed of a manufacturer and a retailer, a centralized and three decentralized decision-making models with different channel power structures are constructed. The recovery, emission reduction, and pricing decisions of low-carbon CLSC are studied, and a two-part-tariff contract is proposed to coordinate the low-carbon CLSC. The results indicate that under three channel power structures, the improvement of the cross-shareholding ratio and consumers’ low-carbon awareness are beneficial to improve recovery rate, carbon emission reduction and increase market demand. Under Nash Game, the profit of low-carbon CLSC can reach the centralized level which means cross-shareholding can realize the coordination of low-carbon CLSC. Under Stackelberg Game, the enterprise with larger channel power can always obtain higher profit. Cross-shareholding cannot coordinate the retailer-led low-carbon CLSC, however it can realize the partial coordination of the manufacturer-led low-carbon CLSC. Two-part-tariff contract can realize the coordination of low-carbon CLSC under both situations.