Recently, finding sustainable solutions to deal with the environmental and social problems emerging from the combustion of fossil fuels in the transportation sector has attracted much interest. This paper proposes an integrated, multiperiod, mixed-integer, nonlinear programming model to design a biodiesel supply-chain network under uncertainty. To deal with the uncertainty of the parameters of the proposed model, a novel formulation of a possibilistic programming model based on possibilistic mean and absolute deviation of fuzzy numbers is proposed. The proposed model, called the possibilistic mean-absolute deviation model, utilizes not only the advantages of previous possibilistic programming methods, such as simultaneously handling the uncertainty and the flexibility in goals and constraints, but also balances mean and risk values of an objective function, including uncertain coefficients according to Decision-Maker's (DM) preferences. A real case study is conducted in Iran to evaluate the performance and efficiency of the proposed model. The proposed approach has better performance than a pure possibilistic programming model, and its results are justified by the robust possibilistic programming approaches.