Collaborative model for a two-echelon supply chain with uncertain demand under carbon tax policy

Consideration of carbon policies while optimizing supply chain operations has become imperative as governments and regulatory bodies throughout the world have implemented different carbon policies to reduce emissions of greenhouse gasses, especially CO2. “Carbon tax” is one of the major carbon policies, initiated by several governments to curtail emissions. In this study, we have considered this policy to optimize the total expected cost (TEC) of a two-echelon integrated supply chain with stochastic demand, where both backorders and lost sales are permitted. An unconstrained mixed integer non-linear programming (MINLP) problem is formulated and further solved to find the optimal production rate, order quantity, number of shipments and reorder point while minimizing the TEC. Emissions from all the major sources such as production, inventory and transportation have been taken into consideration. It is assumed that the emission from production is a function of production rate, and emission from transportation depends on payload and vehicle type. This study will help organizations to reduce cost and emissions, and regulatory bodies to decide proper tax rate on carbon emission.