The majority of data envelopment analysis (DEA) models can be linearized via the classical Charnes–Cooper transformation. Nevertheless, this transformation does not apply to sum-of-fractional DEA efficiencies models, such as the secondary goal I (SG-I) cross efficiency model and the arithmetic mean two-stage network DEA model. To solve a sum-of-fractional DEA efficiencies model, we convert it into bilinear programming. Then, the obtained bilinear programming is relaxed to mixed-integer linear programming (MILP) by using a multiparametric disaggregation technique. We reveal the hidden mathematical structures of sum-of-fractional DEA efficiencies models, and propose corresponding discretization strategies to make the models more easily to be solved. Discretization of the multipliers of inputs or the DEA efficiencies in the objective function depends on the number of multipliers and decision-making units. The obtained MILP provides an upper bound for the solution and can be tightened as desired by adding binary variables. Finally, an algorithm based on MILP is developed to search for the global optimal solution. The effectiveness of the proposed method is verified by using it to solve the SG-I cross efficiency model and the arithmetic mean two-stage network DEA model. Results of the numerical applications show that the proposed approach can solve the SG-I cross efficiency model with 100 decision-making units, 3 inputs, and 3 outputs in 329.6 s. Moreover, the proposed approach obtains more accurate solutions in less time than the heuristic search procedure when solving the arithmetic mean two-stage network DEA model.

大多数数据包络分析（DEA）模型都可以通过经典的Charnes-Cooper变换线性化。但是，此转换不适用于分数和DEA效率模型，例如次要目标I（SG-I）交叉效率模型和算术平均两阶段网络DEA模型。为了解决分数和DEA效率模型，我们将其转换为双线性规划。然后，使用多参数分解技术将获得的双线性规划放宽为混合整数线性规划（MILP）。我们揭示了分数和DEA效率模型的隐藏数学结构，并提出了相应的离散化策略，以使模型更易于求解。输入乘数或目标函数中DEA效率的离散化取决于乘数和决策单元的数量。所获得的MILP为解决方案提供了一个上限，可以通过添加二进制变量来根据需要进行收紧。最后，开发了一种基于MILP的算法来寻找全局最优解。通过解决SG-I交叉效率模型和算术平均两阶段网络DEA模型，验证了所提方法的有效性。数值应用结果表明，该方法可以在329.6 s内求解100个决策单元，3个输入和3个输出的SG-I交叉效率模型。而且，