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.

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In this article, an imperfect production inventory model consisting of a manufacturer and a retailer with quality improvement effort and the promotional effort sensitive demand pattern is investigated under a two-tier credit policy. We study the model for deteriorating items where the deterioration occurs at different rates in the manufacturer’s and the retailer’s level considering a fixed lifetime of the product. Discussing the six possible cases of credit policy analytically, we analyze the behavior of the model under an integrated system concerning production lot-size, quality effort and promotional effort such that the integrated average profit is maximum. To obtain the optimal solutions of the model, we design an operative solution algorithm. A numerical example is provided to test feasibility of the model, and the effect of the variation of the key parameters is also studied. The outcomes of this proposed model show that the manufacturer and the retailer have to be more careful about their offered credit periods in aspect of the profit. It is observed that the integrated profit is maximum when both credit periods provided by the manufacturer and the retailer belong to the manufacturer’s cycle. Moreover, we identify that the extended product lifetime does not meet with higher profit all times. This study directs that quality effort and promotional effort stimulate the market demand while it is not always economically profitable for the supply chain.

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