Stochastic Sensitivity Analysis in Data Envelopment Analysis

Subject Areas : Fuzzy Optimization and Modeling Journal

Nasim Arabjazi ¹ , Mohsen Rostamy-Malkhalifeh ² , Farhad Hosseinzadeh Lotfi ³ , Mohammad Hasan Behzadi ⁴

1 - Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran
2 - Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran
3 - Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran
4 - Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran

Received: 2021-11-29 Accepted : 2021-12-26 Published : 2021-12-26

Keywords: Data envelopment analysis, stability region, Efficiency sensitivity analysis, Stochastic data,

Abstract :

Data Envelopment Analysis (DEA) is an impeccable approach based on mathematical programming for the efficiency measurement of homogeneous Decision-Making Units (DMUs). One of the topics of interest in data envelopment analysis (DEA) is the sensitivity and stability analysis of a specific DMU that determines ranges within which all data may be altered for any DMU before a reclassification from efficient to inefficient status (or vice versa) happens. In many real-world applications, the managers to estimate the under supervision DMUs encounter stochastic data and require a way to deal with the sensitivity analysis of DMUs with this special data. In DEA, efficient DMUs are of primary importance as they define the efficient frontier. The intent of this paper is to present the sensitivity analysis with stochastic data for efficient DMUs when inputs and outputs are stochastic and variations in the data are simultaneously considered for all DMUs. The models explained in this paper for treating sensitivity analysis in DEA are expanded by according them chance-constrained programming formulations. The ordinary route used in chance-constrained programming is followed here by replacing these stochastic models with their deterministic equivalents. The optimal solution of these models leads to allowable input/ output variations.