In most standard data envelopment analysis (DEA) models, data are deterministic. However, real-world applications are subject to stochastic data as production costs, which depend on many factors such as environmental and social elements. So, this shortcoming requires the generalization of DEA models to stochastic data. Also, the standard DEA models are often used for positive inputs and outputs, while in many real-world situations, inputs or outputs may take negative values. This article is intended to extend the semi-oriented radial measure model for dealing with negative and stochastic data in the DEA framework. Some new chance-constrained optimization models and their deterministic equivalent models are introduced to evaluate the production units. Besides, some numerical examples, including an empirical application on 61 bank branches, were used to evaluate the proposed approach.

在大多数标准数据包络分析 (DEA) 模型中，数据是确定性的。然而，现实世界的应用程序受制于作为生产成本的随机数据，这取决于许多因素，例如环境和社会因素。因此，这个缺点需要将 DEA 模型推广到随机数据。此外，标准 DEA 模型通常用于正输入和输出，而在许多实际情况中，输入或输出可能取负值。本文旨在扩展半定向径向测度模型，用于处理 DEA 框架中的负数据和随机数据。引入了一些新的机会约束优化模型及其确定性等效模型来评估生产单元。此外，一些数值例子，包括对 61 家银行分行的实证应用，