Emission reduction investment for green products of a manufacturing system via optimal control theory and artificial hummingbird algorithm

Abstract

Now, due to the global industrialization, carbon emission from the industrial section imposes a severe impact on the current environment. Due to the increasing awareness of environmental and sustainability issues, green products, also known as eco-friendly, include a considerable impact on the today’s market economy. Keeping mind of these two important issues of the current scenario, a production inventory model is developed in which time-dependent production rate is considered. In this work, the level of greenness of the products, selling price and time, influences the customers’ demand rate. Again, two different cases are considered due to the business assimilation of defectively manufactured items: rework and salvage policies. Additionally, the company uses pollution reduction technologies to lower emissions from the manufacturing firms in order to lower emission taxes. The Euler-Lagrange equation is used to solve an optimal control problem that arises in the model as time-dependent production rate is taken into the account. The optimisation problem corresponding to the proposed model is solved with the help of artificial hummingbird algorithm (AHA) as the system's average profit functions for both of the considered scenarios are highly nonlinear in nature w. r. to its decision variables. Further, the results obtained from AHA are compared with the help of other well-known metaheuristics. Finally, sensitivity analysis is conducted to arrive at meaningful conclusions and implications for the competent manager of the manufacturing firm.