Effects of green innovation and advertisement in an imperfect production-based competitive supply chain under two-tier credit facility

This article investigates game-theoretic approaches in a competitive supply chain model with imperfect production and a two-tier credit facility under the environment of carbon emissions. In this environment, we incorporate a manufacturer and two rival retailers who compete against one another for selling price and advertisement of a product, where the members offer trade credit facilities to the downstream players. We consider that the manufacturer invests in green technology to curtail the emission during the production and rework process. The retailers provide advertisements to expand their businesses, where market demands are dependent on their selling prices, advertisement frequencies, and the green innovation level. Here, we analyze the model under the cap-and-trade policy for various subcases of the centralized and decentralized systems and discuss a solution algorithm for the optimal results. For the practical feasibility test of the model, numerical analysis is examined, and the impact of variations of the critical parameters is studied. The study's primary motive is to figure out the optimal operative strategies and collaborative actions on the decision variables, which leads to the profits of the supply chain to a lofty extent. We observe that the offered credit periods are highly responsive to the profit functions so that the chain members have to be more careful and draw a compact plan for credit policy. Moreover, the manufacturer has to invest in green technology up to a certain level, as, after that level, high investment costs will hamper the optimal profit. Besides, the retailers must have adequate policies for selling prices and advertisement frequencies to acquire a higher yield.