In Brazil, the National School Feeding Program (PNAE) seeks to contribute to the socio-economic development of smallholder farmers, prioritizing them in supplying their products for preparing daily meals in public schools. However, farmers face challenges in determining which school calls to bid for and the potential benefits from their participation, due to the multiple quantitative and qualitative decision criteria involved. This paper presents a novel Data Envelopment Analysis (DEA)-based method for bidding priority setting, to support the decision making. The model was applied for a case study in Brazil. The academic contribution lies in the innovation of using a Double-Frontier Slack-Based Measure (SBM) DEA model for Hierarchical Network systems, i.e., applied to multiple levels and followed by a tie-breaking method. The practical contribution lies in the decision support of farmers by presenting the results at three levels, the first of which is a ranking by the town or urban cluster priority, the second by the school, and the third by the products. Thus, using the rankings of calls, farmers can make informed decisions regarding the feasibility of bidding for each PNAE public call. At the same time, the objective rankings can alleviate friction and conflict within co-operatives during the decision-making process.