OICC Press Mathematical Sciences 2251-7456 16 3 (September 2022) 2021 06 13 A modified semi-oriented radial measure to deal with negative and stochastic data: an application in banking industry 10.1007/s40096-021-00416-2 EN Hamidreza Babaie Asil Department of Mathematics, Qazvin Branch, Islamic Azad University, Qazvin, IR Reza Kazemi Matin Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, IR Mohsen Khounsiavash Department of Mathematics, Qazvin Branch, Islamic Azad University, Qazvin, IR Zohreh Moghadas Department of Mathematics, Qazvin Branch, Islamic Azad University, Qazvin, IR Journal Article 2021 06 13 Abstract 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.