Peter John Ezhilarasan, Mishra Umakanta
Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore, 632014, India.
Environ Sci Pollut Res Int. 2023 May;30(21):59963-59990. doi: 10.1007/s11356-023-26243-7. Epub 2023 Apr 5.
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.
地球母亲拥有完全可持续的循环生命周期模式。在其生命周期中，不会对任何生物或环境造成危害。本文为一家遵循与我们星球相同循环模式的LED灯泡公司开发了一种可持续的循环经济生产和消费系统。该模型引入了循环经济概念、绿色技术和碳排放权交易政策，以控制LED公司的碳排放率和资源消耗。通过拉格朗日乘数法和卡鲁什-库恩-塔克（KKT）条件使利润函数最大化。本文确定了用于明智制造过程的LED灯泡的最优产量和循环指数。利用海森矩阵法证明了最优利润函数的凹性。讨论了需求和利润函数的不同线性和非线性组合。本文认为，LED灯泡的循环水平影响了它们的售价、成本和需求。绿色技术和碳排放权交易政策提高了LED灯泡公司的可持续性。提供了数值示例、结果讨论和最优解表，以展示该模型对LED灯泡公司的意义。对关键参数进行了敏感性分析。根据所得结果解释了管理启示。结论部分给出了该模型的局限性和可能的未来扩展。
