Sustainable optimal production policies for an imperfect production system with trade credit under different carbon emission regulations

Production systems are subject to imperfect processes among other factors that may produce items of imperfect quality. To avoid further losses, regular preventive maintenance, and system breakdowns, firms can make changes in their production planning decisions or invest in a green inventory management. Every manufacturing system generates some harmful by-products which are the causes of environmental pollution, and it is increasing day by day. As a result, one of the goals of this research is to develop a sustainable smart manufacturing model with less waste and controlled pollution. Moreover, permissible delay in payment is a popular payment method and important proportion of company finance. This research proposes a manufacturing plan for products by controlling pollution through sustainable and smart production under warranty and preventive maintenance performed with trade credits. Two different sustainable production models are presented here by considering pollution control costs. A sustainable production model with variable pollution costs is examined under the influence of three pollution control mechanisms to improve the model's applicability. The paper's novelty lies in introducing pollution control costs and pollution control mechanisms together in a flexible, sustainable production system. In comparison with the other models, the model with a variable pollution cost appears to be more sustainable as, in this case, there is a 27.76% reduction in the pollution level compared to the other models. Implementing three pollution-controlling strategies, such as pollution cap, pollution cap & trade, and pollution tax, resulted in reductions of 32.52%, 1.72%, and 0.84% in pollution levels, respectively. A sensitivity analysis of the obtained results is also carried out to show the model's strength and robustness.