Stochastic p-robust approach to two-stage network DEA model

Rita Shakouri; Maziar Salahi; Sohrab Kordrostami; Rita Shakouri; Maziar Salahi; Sohrab Kordrostami

doi:10.3934/QFE.2019.2.315

Quantitative Finance and Economics

2019, Volume 3, Issue 2: 315-346. doi: 10.3934/QFE.2019.2.315

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Research article

Stochastic p-robust approach to two-stage network DEA model

1.
Department of Mathematics, Lahijan Branch, Islamic Azad University, Lahijan, Iran
2.
Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran

Received: 02 April 2019 Accepted: 23 May 2019 Published: 03 June 2019
JEL Codes: D81, D85, C71, C72

Data Envelopment Analysis (DEA) is a method for evaluating the performance of a set of homogeneous Decision Making Units (DMUs). When there are uncertainties in problem data, original DEA models might lead to incorrect results. In this study, we present two stochastic p-robust two-stage Network Data Envelopment Analysis (NDEA) models for DMUs efficiency estimation under uncertainty based on Stackelberg (leader-follower) and centralized game theory models. This allows a deleterious effect to the objective function to better hedge against the uncertain cases those are commonly ignored in classical NDEA models. In the sequel, we obtained an ideal robustness level and the maximum possible overall efficiency score of each DMU over all permissible uncertainties, and also the minimal amount of uncertainty level for each DMU under proposed models. The applicability of the proposed models is shown in the context of the analysis of bank branches performance.
- data envelopment analysis,
- p-robustness,
- discrete uncertain data,
- NDEA,
- stochastic p-robust optimization
Citation: Rita Shakouri, Maziar Salahi, Sohrab Kordrostami. Stochastic p-robust approach to two-stage network DEA model[J]. Quantitative Finance and Economics, 2019, 3(2): 315-346. doi: 10.3934/QFE.2019.2.315

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Abstract

Data Envelopment Analysis (DEA) is a method for evaluating the performance of a set of homogeneous Decision Making Units (DMUs). When there are uncertainties in problem data, original DEA models might lead to incorrect results. In this study, we present two stochastic p-robust two-stage Network Data Envelopment Analysis (NDEA) models for DMUs efficiency estimation under uncertainty based on Stackelberg (leader-follower) and centralized game theory models. This allows a deleterious effect to the objective function to better hedge against the uncertain cases those are commonly ignored in classical NDEA models. In the sequel, we obtained an ideal robustness level and the maximum possible overall efficiency score of each DMU over all permissible uncertainties, and also the minimal amount of uncertainty level for each DMU under proposed models. The applicability of the proposed models is shown in the context of the analysis of bank branches performance.

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