Conventional models of data envelopment analysis (DEA) are based on the constant and variable returns-to-scale production technologies. Any optimal input and output weights of the multiplier DEA models based on these technologies are interpreted as being the most favorable for the decision making unit (DMU) under the assessment when the latter is benchmarked against the set of all observed DMUs. In this paper we consider a very large class of DEA models based on arbitrary polyhedral technologies, which includes almost all known convex DEA models. We highlight the fact that the conventional interpretation of the optimal input and output weights in such models is generally incorrect, which raises a question about the meaning of multiplier models. We address this question and prove that the optimal solutions of such models show the DMU under the assessment in the best light in comparison to the entire technology, but not necessarily in comparison to the set of observed DMUs. This result allows a clear and meaningful interpretation of the optimal solutions of multiplier models, including known models with a complex constraint structure whose interpretation has been problematic and left unaddressed in the existing literature.

数据包络分析 (DEA) 的传统模型基于恒定和可变的规模收益生产技术。基于这些技术的乘数 DEA 模型的任何最优输入和输出权重都被解释为对评估下的决策单元 (DMU) 最有利，当后者以所有观察到的 DMU 的集合为基准时。在本文中，我们考虑了一大类基于任意多面体技术的 DEA 模型，其中包括几乎所有已知的凸 DEA 模型。我们强调这样一个事实，即对此类模型中最佳输入和输出权重的传统解释通常是不正确的，这引发了关于乘法器模型含义的问题。我们解决了这个问题，并证明此类模型的最佳解决方案与整个技术相比以最佳方式显示了评估下的 DMU，但不一定与观察到的 DMU 集相比。该结果允许对乘法模型的最优解进行清晰而有意义的解释，包括具有复杂约束结构的已知模型，其解释在现有文献中存在问题且未解决。