Bi-level supply chain model with price and time-dependent demand under carbon emission tax regulation

In today’s world, controlling environmental pollution presents a significant challenge because as many manufacturing industries and supply chain systems contribute to carbon emissions and produce non-environmentally friendly products. As a consequence, the governments of responsible countries have instituted carbon taxes and regulatory measures to mitigate environmental pollution. In response to this situation, a retailer–manufacturer supply chain model under carbon tax regulations is developed. In this supply chain model, the manufacturer produces products and fulfils customer demand through retailers. Additionally, it is assumed that both retailer and customer demand demend on time and the retail price of the item. Moreover, it is presumed that the government collects a carbon tax from the retailers and the manufacturer due to carbon emissions during transportation and production, respectively. This study primarily aims to determine the optimal selling price and the manufacturer’s production duration to maximise the average profit of the integrated system. Subsequently, a numerical experiment is conducted to verify the validity of the proposed model. Furthermore, the impact of the model parameters on the optimal policy is examined through a sensitivity analysis to derive valuable insights from this study.