The paper analyses properties of a large class of "path-based" Data Envelopment Analysis models through a unifying general scheme. The scheme includes the well-known oriented radial models, the hyperbolic distance function model, the directional distance function models, and even permits their generalisations. The modelling is not constrained to non-negative data and is flexible enough to accommodate variants of standard models over arbitrary data. Mathematical tools developed in the paper allow systematic analysis of the models from the point of view of ten desirable properties. It is shown that some of the properties are satisfied (resp., fail) for all models in the general scheme, while others have a more nuanced behaviour and must be assessed individually in each model. Our results can help researchers and practitioners navigate among the different models and apply the models to mixed data.

翻译：本文通过一个统一的通用框架，分析了“基于路径”数据包络分析模型中一大类模型的性质。该框架包括经典的有向径向模型、双曲距离函数模型、方向距离函数模型，并允许对其进行推广。该建模方法不局限于非负数据，且足够灵活，能够适应标准模型在任意数据上的变体。本文发展的数学工具允许从十个理想性质的角度对模型进行系统分析。结果表明，通用框架中的所有模型均满足（或不满足）某些性质，而其他性质则表现出更细微的行为，需针对每个模型单独评估。我们的研究结果有助于研究人员和实践者在不同模型间进行选择，并将模型应用于混合数据。