A Lagrangian relaxation approach for algae-based biofuel supply chain network design under uncertainty and pricing issue

Biofuel has gained significant attention as a potential source to meet fuel demands instead of fossil fuel. The price of biofuel and alternative fuel have a considerable impact on biofuel demand. Thus, it is important to design a biofuel supply chain network that incorporates the biofuel price into an elastic demand. More precisely, a variable demand, including customer importance level (to the environment), biofuel price, and substituted fuel price, is considered in this research. Furthermore, this research presents a bi-objective mixed-integer quadratic formulation that aims to maximize the total profit of the supply chain and carbon absorption in harvesting areas. The problem is solved by the ε-constraint and lagrangian relaxation methods due to its complexity. Moreover, substituted fuel price uncertainty is addressed by two-stage stochastic programming. Finally, a real case study utilizing the data envelopment analysis approach is applied to assess the efficiency and currency of the addressed model. Several consequences are illustrated in the case study, such as rich areas for exporting algae, suggesting hub locations for biofuel production, etc.