A Unified Mathematical Model for Stochastic Data Envelopment Analysis

A Unified Mathematical Model for Stochastic Data Envelopment Analysis

Basma E. El-Demerdash, Assem A. Tharwat, Ihab A. A. El-Khodary
Copyright: © 2021 |Pages: 15
DOI: 10.4018/IJSSMET.2021010108
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Abstract

Efficiency measurement is one aspect of organizational performance that managers are usually interested in determining. Data envelopment analysis (DEA) is a powerful quantitative tool that provides a means to obtain useful information about the efficiency and performance of organizations and all sorts of functionally similar, relatively autonomous operating units. DEA models are either with a constant rate of return (CRS) or variable return to scale (VRS). Furthermore, the models could be input-oriented or output-oriented. In many real-life applications, observations are usually random in nature; as a result, DEA efficiency measurement may be sensitive to such variations. The purpose of this study was to develop a unified stochastic DEA model that handles different natures of variables independently (random and deterministic) and can be adapted to model both input/output-oriented problems, whether it is CRS or VRS. The chance-constrained approach was adopted to handle the stochastic variables that exist in the model. The developed model is implemented through an illustrative example.
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Literatures Review

There are good efforts that have been made recently to handle the randomness in data. Several output-oriented stochastic DEA models were developed that consider all data have same random nature (Cooper et al. 2004; Razavyan and Tohidi 2008; Kao and Liu 2009; Khodabakhshi 2010; Azadi and Saen 2011; Azadeh et al. 2015; Liu et al. 2017) or consider all output variables have random nature and all inputs are deterministic (Desai et al. 2005; Wu et al. 2012; Chebil et al. 2014). As for input-oriented stochastic DEA models, some developed models considered all output variables to have random nature and all inputs are deterministic (Talluri et al. 2006) or consider all input variables to have random nature and all outputs are deterministic (El-Khodary et al. 2010).

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