Ideal buy-back pricing and product-quality strategies for any carbon-conscious closed-loop supply chain

Abstract The present study addresses a closed-loop supply chain under various carbon emission regulation policies. This article involves four key chain partners viz. a single supplier of raw materials, single manufacturer, single retailer, and single collector of the used products from the end users. Depending on the returned goods quality, the collector procures used items from customers. Unlike the existing articles, the manufacturer has two different setups for the production of both items made from newly sourced components and returned goods. A specified portion of fresh and used items goes through the same reworking cycle because the production process for both is flawed. This model has been framed under the carbon tax and the strict carbon cap regulations in order to maintain better environmental stability. A newly developed metaheurestic method namely Atomic orbital search algorithm has been implemented to determine the optimal replenishment planning and acceptance quality level, along with the corresponding numbers of deliveries among the four different chain partners and to improve the supply chain net profit. To assess how carbon regulatory policies affect the best course of action, a numerical analysis of the mathematical models is conducted, followed by a sensitivity analysis of key parameters. This study proposes that the manufacturer should consider implementing a strategy wherein they provide collectors with better rates for used products. By doing so, this is anticipated that the demand rate for these items will increase, leading to improved profitability and raw materials sustainability for the suggested model.