Is the advertisement policy for dual-channel profitable for retailing and consumer service of a retail management system under emissions-controlled flexible production system?

Presently, by reducing carbon emissions, biorefineries are very much careful to build a green environment. Several rules and regulations are imposed by the government to provide a comparatively better eco-friendly environment. To control the carbon emission rate, the cap-and-trade policy is intimated in this flexible biofuel production model. To reduce per unit carbon emission, manufacturers impose the advanced green technology. As online and offline selling is crucial to any industry for increasing customer demand, manufacturers sell their products by dual-channel and advertise to promote their products through online channel to make their biofuel products more popular. Keeping these in mind, a study on a sustainable flexible production of biofuel is considered here by imposing an investment in green technology cap-and-tax policy, and advertising for biofuels. A smart inspection, known as autonomation policy, is considered such that the quantity of impure biofuel is reduced. An offline selling price, online selling price, and online advertisement of biofuel-depended demand are considered for each manufacturer. This study is divided into two cases: with and without investment in green technology. The main goal of this research is to manage a dual-channel retailing for biofuel production systems under multiple manufacturers for gaining more profit. To get global optimality of profit function and decision variables, a classical optimization technique is applied. In addition, numerical experiments are carried out along with sensitivity analysis and graphical representation to show the applicability and optimality of this study. Numerical experiments prove that industries achieve 4.37% more profit when green technology is invested. The flexible production system shows 7.09% more profit than the traditional production system. In case of advertisement policy for dual-channel investment, the proposed model provides 2.55% more profit than the without investment. Numerical results indicate that industries receive 2.56% more profit when autonomation policy is applied for an error-free inspection. Finally, it can be stated that the advertisement policy based on a sustainable flexible biofuel production system with controlled-emissions is the best retailing strategy for the dual-channel supply chain.