Implications of carbon policies for flexible demand and smart production with random lead time demand under a sustainable supply chain management

For a smart biofuel supply chain management, the idea of controllable lead time and variance is very crucial matter. Operational coordinations in a supply chain management, specially when the demand is advertise-dependent, can move in an efficient way in emission diminish. Carbon emissions control is one of the foremost imperative needs for the business division. This study concerns about three carbon emissions reduction regulation strategies, variable lead time, and variance within controllable flexible rate, which influences the plants to redesign their sustainable supply chain. Managers of any plants enhance their biofuel production execution by minimizing lead time and its variance always. This study discusses and inquires these conveniences of suchlike carbon regulation policies and lead time diminishing for commonly utilized advertisement cost, lot size quantity, safety factor, production rate, autonomation investment, and green investments for vendors and buyers to minimize carbon emissions. In place of prospective total cost equations, this article explores a proper total cost equation, constructed on an implicit relation within backorder and on-hand inventory. Carbon emissions are considered through manufacturing, transportation, and plants for both player. The aim of the study is to implement several regulatory policies (mainly cap and trade regulation policy, carbon taxation policy, and limited carbon emissions regulation) of emissions retrenchment which relieve the impact of carbon emissions by minimizing its volume through building three models. The terminal value exploration on lead time and its variance acquire much appropriate results and focus on making a trade-off between total generated cost and carbon emissions. The analytical results show that limited carbon emissions is 59.67% and 59.68% more beneficial compared to carbon taxation and cap and trade regulation, respectively. Finally, it is noticeable that limited carbon regulation is the best policy to minimize the total cost under carbon emissions.