Advertisement policy for dual-channel within emissions-controlled flexible production system

Nowadays, industrial firms are very much careful to build a green environment by reducing carbon emissions. The government imposes some rules and regulations to provide a better eco-friendly environment. In this study, the cap-and-trade mechanism has been considered in a production model to control the carbon emissions rate. The manufacturers invest in advanced green technology to reduce per unit emissions. As online and offline selling is crucial to any industry for increasing customer demand, the manufacturers sell their products by dual-channel and advertise their products by online channel to make more popular of their products. Keeping these in mind, a sustainable flexible production model with single-type substitutable product production is considered here by imposing a cap-and-tax policy, investing in green technology, and advertising for products. This model is divided into two cases: with and without investment in green technology. The demand of each manufacturer depends upon an online selling price, an offline selling price, and an online advertisement of the product. A classical optimization technique helps to get the optimum strategies for the online selling price, offline selling price, advertisement investment, green technology, cycle time, and production rate. From the numerical study, it is proved that the industry gets 6.97% more profit in the case of green technology investment and the proposed study gives 5.74% more profit than the traditional production system. Sensitivity analysis and managerial insights are performed.