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Highlights • Developing a possibilistic MILP model to design a second-generation biodiesel supply chain network under epistemic uncertainty. • Employing a credibility-based possibilistic programming approach to convert the original possibilistic programming model into a crisp counterpart. • Proposing an accelerated benders decomposition algorithm using efficient acceleration mechanisms to deal with the computational complexity of solving the proposed model. • Verification and validation of the proposed approach through investigating a real case study in Iran. Abstract This paper proposes a possibilistic programming model in order to design a second-generation biodiesel supply chain network under epistemic uncertainty of input data. The developed model minimizes the total cost of the supply chain from supply centers to the biodiesel and glycerin consumer centers. Waste cooking oil and Jatropha plants, as non-edible feedstocks, are considered for biodiesel production. To cope with the epistemic uncertainty of the parameters, a credibility-based possibilistic programming approach is employed to convert the original possibilistic programming model into a crisp counterpart. An accelerated benders decomposition algorithm using efficient acceleration mechanisms is devised to deal with the computational complexity of solving the proposed model in an efficient manner. The performance of the proposed possibilistic programming model and the efficiency of the developed accelerated benders decomposition algorithm are validated by performing a computational analysis using a real case study in Iran. [ABSTRACT FROM AUTHOR]