A Modified Russell Measure for Estimating Efficiency Changes in the Presence of the Undesirable Outputs and Stochastic Data

Document Type : Article


1 Department of Mathematics, Qazvin Branch, Islamic Azad University, Qazvin, Iran

2 Department of Operations Management & Business Statistics, College of Economics and Political Science, Sultan Qaboos University, Muscat, Oman

3 Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran


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 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.


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