Export file:


  • RIS(for EndNote,Reference Manager,ProCite)
  • BibTex
  • Text


  • Citation Only
  • Citation and Abstract

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

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.
  Article Metrics


1.Akther S, Fukuyama H, Weber WL (2013) Estimating two-stage network slacks-based inefficiency: An application to Bangladesh banking. Omega 41: 88–96.    

2.Alimohammadi AM, Hoseininasab H, Khademizare H, et al. (2016) A robust two-stage data envelopment analysis model for measuring efficiency: Considering Iranian electricity power production and distribution processes. Int J Eng 29: 646–653.

3.Ang S, Chen CM (2016) Pitfalls of decomposition weights in the additive multi-stage DEA model. Omega 58: 139–153.    

4.Avkiran NK (2009) Opening the black box of efficiency analysis: An illustration with UAE banks. Omega 37: 930–941.    

5.Ben-Tal A, Nemirovski A (1999) Robust solutions of uncertain linear programs. Oper Res Lett 25: 1–13.    

6.Ben-Tal A, Nemirovski A (2000) Robust solutions of linear programming problems contaminated with uncertain data. Math Program 88: 411–424.    

7.Bertsimas D, Sim M (2003) Robust discrete optimization and network flows. Math Program 98: 49–71.    

8.Bertsimas D, Sim M (2004) The price of robustness. Oper Res 52: 35–53.    

9.Bertsimas D, Thiele A (2006) A robust optimization approach to inventory theory. Oper Res 54: 150–168.    

10.Charnes A, Cooper WW, Rhodes E (1978) Measuring the efficiency of decision making units. Eur J Oper Res 2: 429–44.    

11.Chen Y, Cook WD, Li N, et al. (2009) Additive efficiency decomposition in two-stage DEA. Eur J Oper Res 196: 1170–1176.    

12.Cooper WW, Seiford LM, Tone K (2007) Data envelopment analysis: a comprehensive text with models applications references and DEA-solver software, 2nd Edition, Springer, New York.

13.Cook WD, Liang L, Zha Y, et al. (2009) A modified super-efficiency DEA model for infeasibility. J Oper Res Soc 60: 276–281.    

14.Cook WD, Liang L, Zhu J (2010) Measuring performance of two-stage network structures by DEA: A review and future perspective. Omega 38: 423–430.    

15.Cook WD, Zhu J (2014) Data envelopment analysis: a handbook of modeling internal structure and networks, Springer, New York, 261–284.

16.Despotis DK, Smirlis YG (2002) Data envelopment analysis with imprecise data. Eur J Oper Res 140: 24–36.    

17.Despotis DK, Sotiros D, Koronakos G (2016) A network DEA approach for series multi-stage processes. Omega 61: 35–48.    

18.Fukuyama H, Weber WL (2010) A slacks-based inefficiency measure for a two-stage system with bad outputs. Omega 38: 398–409.    

19.Guo C, Zhu J (2017) Non-cooperative two-stage network DEA model: Linear VS-parametric linear. Eur J Oper Res 258: 398–400.    

20.Gutierrez GL, Kouvelis P, Kurawarwala AA (1996) A robustness approach to incapacitated network design problems. Eur J Oper Res 94: 362–376.    

21.Hatefi SM, Jolai F, Torabi SA, et al. (2016) Integrated forward reverse logistics network design under uncertainty and reliability consideration. Sci Iran 23: 2721–735.

22.Huang TH, Chen KC, Lin CL (2018) An extension from network DEA to Copula-based network SFA: Evidence from the U. S. commercial banks in 2009. Q Rev Econ Financ 67: 51–62.

23.Izadikhah M, Tavana M, Caprio DD, et al. (2018) A novel two-stage DEA production model with freely distributed initial inputs and shared intermediate outputs. Expert Syst Appl 99: 213–230.    

24.Kao C, Hwang SN (2008) Efficiency decomposition in two stage data envelopment analysis: An application to non-life insurance companies in Taiwan. Eur J Oper Res 185: 418–429.    

25.Kao C, Liu S (2009) Stochastic data envelopment analysis in measuring the efficiency of Taiwan commercial banks. Eur J Oper Res 196: 312–322.    

26.Kao C, Liu ST (2011) Efficiencies of two-stage systems with fuzzy data. Fuzzy Set Syst 176: 20–35.    

27.Kouvelis P, Kurawarwala AA, Gutierrez GJ (1992) Algorithms for robust single and multiple period layout planning for manufacturing systems. Eur J Oper Res 63: 287–303.    

28.Lewis HF, Sexton TR (2004) Network DEA: Efficiency an analysis of organizations with complex internal structure. Comput Oper Res 31: 1365–1410.    

29.Liang L, Yang F, Cook WD et al. (2006) DEA models for supply chain efficiency evaluation. Ann Oper Res 145: 35–49.

30.Liang L, Wu J, Cook WD, et al. (2008) The DEA game cross-efficiency model and its Nash equilibrium. Oper Res 56: 1278–1288.    

31.Liang L, Cook WD, Zhu J (2008) DEA models for two-stage processes: Game approach and efficiency decomposition. Nav Res Log 55: 643–653.    

32.Li WH, Liang L, Cook WD (2017c) Measuring efficiency with products, by-products and parent-offspring relations: a conditional two-stage DEA model. Omega 68: 95–104.

33.Li H, Chen C, Cook WD, et al. (2018) Two-stage network DEA: Who is the leader? Omega 74: 15–19.    

34.Liu ST (2014) Restricting weight flexibility in fuzzy two-stage DEA. Comput Ind Eng 74: 149–160.    

35.Lu CC (2015) Robust data envelopment analysis approaches for evaluating algorithmic performance. Comput Ind Eng 81: 78–89.    

36.Mo Y, Harrison TP (2005) A conceptual framework for robust supply chain design under demand uncertainty. Supply Chain Opt 243–263.

37.Moreno P, Andrade GN, Meza LA, de Mello JCS (2015) Evaluation of Brazilian electricity distributors using a network DEA model with shared inputs. IEEE Latin Am Trans 13: 2209–2216.    

38.Mulvey JM, Vanderbei RJ, Zenios SA (1995) Robust optimization of large-scale systems. Oper Res 43: 264–281.

39.Paradi JC, Zhu H (2013) A survey on bank branch efficiency and performance research with data envelopment analysis. Omega 41: 61–79.    

40.Sadjadi SJ, Omrani H (2008) Data envelopment analysis with uncertain data: An application for Iranian electricity distribution companies. Energ Policy 36: 4247–4254.    

41.Salahi M, Torabi N, Amiri A (2016) An optimistic robust optimization approach to common set of weights in DEA. Measurement 93: 67–73.    

42.Salahi M, Toloo M, Hesabirad Z (2018) Robust Russell and enhanced Russell measures in DEA. J Oper Res Soc, 1–9.

43.Seiford LM, Zhu J (1999) Profitability and marketability of the top 55 US commercial banks. Manage Sci 45: 1270–1288.    

44.Snyder LV, Daskin MS (2006) Stochastic p-robust location problems. IIE Trans 38: 971–985.    

45.Soyster AL (1973) Convex programming with set inclusive constraints and applications to inexact linear programming. Oper Res 21: 1154–1157.    

46.Thanassoulis E, Kortelainen M, Johnes G, et al. (2011) Costs and efficiency of higher education institutions in England: a DEA analysis. J Oper Res Soc 62: 1282–1297.    

47.Tavana M, Khalili-Damghani K (2014) A new two-stage Stackelberg fuzzy data envelopment analysis model. Measurement 53: 277–296.    

48.Wu J, Liang L (2010) Cross-efficiency evaluation approach to Olympic ranking and benchmarking: the case of Beijing 2008. Inter J App Mngt Sci 2: 76–92.

49.Wu J, Zhu Q, Chu J, et al. (2016a) Measuring energy and environmental efficiency of transportation systems in China based on a parallel DEA approach. Transp Res D Transp Environ 48: 460–472.

50.Wu J, Zhu Q, Ji X, et al. (2016b) Two-stage network processes with shared resources and resources recovered from undesirable outputs. Eur J Oper Res 251: 182–197.

51.Wu D, Ding W, Koubaa A, et al. (2017) Robust DEA to assess the reliability of methyl methacrylate-hardened hybrid poplar wood. Ann Oper Res 248: 515–529.    

52.Yu Y, Shi Q (2014) Two-stage DEA model with additional input in the second stage and part of intermediate products as final output. Expert Syst Appl 41: 6570–6574.    

53.Zhou Z, Lin L, Xiao H, et al. (2017) Stochastic network DEA models for two-stage systems under the centralized control organization mechanism. Comput Ind Eng 110: 404–412.    

© 2019 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

Download full text in PDF

Export Citation

Article outline

Show full outline
Copyright © AIMS Press All Rights Reserved