Sharif University of Technology Scientia Iranica 1026-3098 32 12 2025 05 01 A modified Russell measure for estimating efficiency changes in the presence of the undesirable outputs and stochastic data 24151 10.24200/sci.2021.58051.5538 EN Seyedeh Sara Hosseini Department of Mathematics, Islamic Azad University, Qazvin Branch, Qazvin, Iran. Reza Farzipoor Saen Department of Operations Management and Business Statistics, College of Economics and Political Science, Sultan Qaboos University, Muscat, Oman. Reza Kazemi Matin Department of Mathematics, College of Science, Sultan Qaboos University, Muscat, Oman. Journal Article 2021 04 05 Although Data Envelopment Analysis (DEA) assumes deterministic data, a great volume of data might be stochastic. The Global Malmquist Productivity Index (GMPI) is a highly effective instrument for productivity analysis in DEA. This paper extends GMPI in the presence of stochastic data. Our new stochastic DEA model is a Chance-Constrained Programming (CCP) model, which is converted to a deterministic programming problem with a linear objective function and quadratic constraints. For efficiency evaluation purposes, in this paper, the weak disposability principle is used to model Russell’s measure in the presence of undesirable outputs. The main contribution of this paper is to develop a global Russell model with stochastic data. A case study is presented to illustrate the applicability of the proposed models. https://scientiairanica.sharif.edu/article_24151_9b6e62858e82a755fcce70013c328717.pdf