Analysis of Green Production System with Control of Emission, Replacement and Rework Policies under Emission Tax

In today's saturated market, chemical-based products often harm human health and the environment, while carbon emissions from production pose a significant challenge to sustainable manufacturing. Simultaneously, companies face competitive pressure to attract consumers through various offers. Against this backdrop, this study develops an optimal policy for an imperfect production system of green products, incorporating emission reduction, replacement, and rework strategies. Motivated by realistic business practices, the model treats an item's greening index as a time-dependent function. It also considers that the replacement period for faulty items has a non-linear impact on the system's total revenue. The model is subsequently analysed under two distinct cases based on the emission reduction policy applied. The time-dependent greening index presents a major challenge, as it reduces the average profit maximisation task to two distinct singular control problems. Due to the high non-linearity of these profit functions, six well-established metaheuristic algorithms are applied to solve the problems numerically. The key findings indicate that emission reduction leads to higher profitability. Furthermore, the greening index is shown to positively influence pricing while inversely affecting the optimal replacement duration. Finally, a sensitivity analysis provides several valuable managerial insights.