Sustainable circular economy production system with emission control in LED bulb companies

Mother Earth has a completely sustainable circular life cycle pattern. In its life cycle, there is no harm created to any living creature or to the environment. In this paper, a sustainable circular economic production and consumption system for a LED bulb firm that follows the same cycle pattern as our planet is developed. The circular economy concept, green technology, and carbon cap-and-trade policy are introduced in this model to control the carbon emission rate and resource depletion in LED firms. The profit function is maximized by Lagrange's multipliers method and Karush-Kuhn-Tucker (KKT) criteria. This paper determined the optimal production quantity and circularity index of the LED bulb for a wise manufacturing process. The concavity of the optimal profit function is proved by using the Hessian matrix method. Different linear and non-linear combinations of demand and profit functions were discussed. This article claims that the circularity level of LED bulbs has influenced their selling price, cost, and demand. Green technology and carbon cap-and-trade policies improved the sustainability of LED bulb companies. Numerical examples, results discussions, and an optimal solution table are provided to show the implication of this model for LED bulb companies. Sensitivity analysis is presented for key parameters. Managerial implication explained in terms of arrived results. Limitations and possible future extensions of this model are given in the conclusion section.