Investigating a closed-loop dual-channel green supply chain with stochastic demand rate and collection ratio using the distribution-free approach

Abstract

This paper investigates a dual-channel closed-loop supply chain in an uncertain market environment consisting of a manufacturer, a retailer, and a collector, where the manufacturer can produce green products by utilizing recycling components from the collector and raw materials from an outside source. According to our analysis, market demand is stochastic and strongly influenced by channels’ selling prices, the level of green innovation, and retail service. Additionally, the collection rate of used-obsolete products is also random and affected by green innovation levels and refund prices. We analyze the model by dividing it into three scenarios based on players’ collaborative and non-collaborative behavior and then solve the problem in centralized and decentralized cases through a distribution-free approach. Using vertical Nash and Stackelberg game approaches, the interaction between players is modeled in the decentralized scenario. The model’s findings are illustrated with a numerical example, and a sensitivity analysis is also performed to provide insights into management by determining how different parameters will impact profits. Results suggest that the higher expected value of demand randomness is linked to increased market scale but that random variables with higher variance levels are more uncertain, leading to lower channel profitability. Moreover, a collaborative effort between manufacturer and collector could improve both prices and greenness, ultimately boosting the fraction collected. In addition, results reveal that the retailer Stackelberg frameworks will most adversely affect players, whereas the manufacturer Stackelberg frameworks will generate profits almost every time.