A Bounded Additive Model for Efficiency Evaluation in Two-Stage Production Systems With Negative Data

Subject Areas : Data Envelopment Analysis

حمیدرضا  بابائی اصیل ¹ (Department of Mathematics, Qazvin Branch, Islamic Azad University, Qazvin, Iran)
رضا  کاظمی متین ² (Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran)
محسن  خون سیاوش ³ (Department of Mathematics, Qazvin Branch, Islamic Azad University, Qazvin, Iran)
زهره  مقدس ⁴ (Department of Mathematics, Qazvin Branch, Islamic Azad University, Qazvin, Iran)

Received: 2022-03-13 Accepted : 2022-04-15 Published : 2022-03-01

Keywords: two-stage systems, Data Envelopment Analysis (DEA), Negative data, Efficiency, Additive models,

Abstract :

Data Envelopment Analysis (DEA) is a method for assessing the efficiency of Decision Making Units (DMUs). Traditional DEA models do not examine the potential differences between two stages caused by intermediate operations. As a result, DEA has been extended to evaluate the efficiency of two-stage processes. In these processes, all outputs of the first stage are intermediate operations that comprise the inputs of the second stage. The input data in real-world applications may have negative values. In this study, considering the importance of network production processes, we deal with the efficiency evaluation of two-stage production units with negative data. Also, we extend CRS (constant returns to scale) bounded additive model for the efficiency evaluation of the two-stage units in the presence of negative data. For illustration, we evaluate the efficiency and ranking of 36 airlines by applying the new model.

References:

Adler, N., &Golany, B.(2001). Evaluation of deregulated airline networks using data envelopment analysis combined with principal component analysis with an application to Western Europe, European Journal of Operational Research, 132, 260-273.

Chen, Y., & Zhu, J. (2004). Measuring information technology's indirect impact on firm performance. Information Technology and Management, 5, 9–22.

 

Chen, Y., Liang, L., & Zhu, J.(2009).Equivalence in two-stage DEA approaches. European Journal of Operational Research,193, 600–604.

Chen, Y., Cook, W. D., Li, N., &Zhu, J.(2009).Additive efficiency decomposition in two-stage DEA. European Journal of Operational Research, 196,1170–1176.

Chen, Y.,   Du, J.,  David Sherman,  H.,  & Zhu, J.(2010). DEA model with shared resources and efficiency decomposition.European Journal of Operational Research, 207(1), 339–349.

Chen, Y., Cook, W. D., & Zhu, J.(2010).Deriving the DEA frontier for two-stage processes.European Journal of Operational Research, 202, 138–142.

Cooper, W. W., & Pastor, T. P. (2011). BAM: a bounded adjusted measure of efficiency for use with bounded additive models. J Prod Anal,35,85–94.

Chen, Y., Cook, W.D., Kao, C., &Zhu, J. (2013).Network DEA pitfalls: Divisional efficiency and frontier projection under general network structures.European Journal of Operational Research, 226, 507–515.

Cheng, Y., Zhang, P., &Liu, X.(2020).Collaborative Autonomous Optimization of Interconnected Multi-Energy Systemswith Two-Stage Transactive Control Framework.Energies, 13, 171.

Fukuyama, H.,& Matousek, R. (2017).Modelling bank performance: A Network DEA approach. European Journal of Operational Research, 259(2), 721–732.

Gillen, D., & Lall, A. (1997). Developing Measures of Airport Productivity and Performance: An Application of Data Envelopment Analysis. Transportation Research Part E: Logistics and Transportation Review, 33(4), 261-273.

Halkos, G.E., & salamouris, D. S.(2004). Efficiency measurement of the Greek commercial banks with the use of financial ratios: a data envelopment analysis approach. Management Accounting Research, 15, 201–224.

 

Kazemi Matin, R., &Azizi, R. (2011). A two-phase approach for setting targets in DEA with negative data. Applied Mathematical Modelling, 35, 5794–5803.

Kao, C.(2014). Network data envelopment analysis: A review.European Journal of Operational Research, 239, 1–16.

Kao, N.,(2020).Measuring efficiency in a general production possibility set allowing for negative data. European Journal of Operational Research, 282, 980-988.

 

Lovell, C. A. K.(1995).Measuring the macroeconomic performance of the Taiwanese economy. Int. J. Prod. Econ.,39,165-178.

 

Lewis,H. F.,&Sexton,T.R.(2004).Network DEA:e(ciency analysis of organizations withcomplex internal structure.Computers & Operations Research, 31 ,1365 – 1410.

Lin, T. Y., & Chiu, S. H. (2013).Using independent component analysis and network DEA to improve bank performance evaluation.Economic Modelling, 32(1),608–616.

 

Liu, Z., Zhou, Z., Ma, C., Liu, D. & Shen, W.(2015). Two-stage DEA models with undesirable input-intermediate-outputs.Omega, 56, 74–87.

Lim, S.& Zhu, J.(2016).A note on two-stage network DEA model: Frontier projection and duality.European Journal of Operational Research 248,342–346.

Li, L., Dai, Q., Huang, H., &Wang, S.(2016).Efficiency decomposition with shared inputs and outputs in two-stage DEA.Journal of Systems Science and Systems Engineering, 25, 23–38.

Li, H., Chen, C., Cook, W. D., Zhang, J., & Zhu, J.(2018).Two-stage network DEA: Who is the leader?.Omega, 74, 15–19.

Lu, C. C., Dan, W., Chen, X., Tseng, C. K., & Chou, K. W.(2019). Evaluation of the operating performance of Taiwanese machine tool industry with the dynamic network DEA model. Enterprise Information Systems,15, 1751-7583.

 

Lin, R., Yang, W., & Huang,H.(2019).A modified slacks-based super-efficiency measure in the presence of negative data.Computers & Industrial Engineering, 135, 39–52.

Lin, R.(2019).Cross-efficiency evaluation capable of dealing with negative data: A directional distance function based approach.Journal of the Operational Research Society, 71, 505-516.

Pastor, J., T.(1994).How to discount environmental effects in DEA:an application to bank branches. Working paper N. 011/94, Depto.De Estadistica e Investigacion Operativa,Universidad de Alicante, Spain.

Portela,   S.,  Thanassoulis,  E., & Simpson, G. (2004).Negative data in DEA: a directional distance approach applied to bank branches. Journal of the Operational Research Society, 55,1111-1121.

[28] Prieto, A. M., & Zoflo, J. L.(2007).Network DEA efficiency in input–output models:With an application to OECD countries.European Journal of Operational Research, 178, 292–304.

Paradi, J. C., Rouatt, S., & Zhu, H.(2011).Two-stage evaluation of bank branch efficiency using data envelopment analysis. Omega, 39, 99–109.

Premachandra, I. M., Zhu, J., Watson, J., & Galagedera, D. U. A.(2012). Best-performing US mutual fund families from 1993 to 2008: Evidence

from a novel two-stage DEA model for efficiency decomposition.Journal of Banking & Finance, 36, 3302–3317.

Seiford, L. M., & Zhu, J.(2002).Modeling undesirable factors in efficiency evaluation.European Journal of Operational Research, 142, 16-20.

 

Sharp, J. A., Meng, W., &  Liu, W. (2007). A  Modified slacks-based measure model for data envelopment analysis with ‘natural’ negative outputs and inputs. Journal of the Operational Research Society, 58,1672-1677.

 

Tavana, M., Izadikhah, M.,  Caprio, D. D., Farzipoor  Saen, R. (2018). A new dynamic range directional measure for two-stage data envelopment analysis models with negative data .Computers & Industrial Engineering, 115, 427–448.

Vencheh, A. H., & Esmaeilzadeh, A.(2013). A new super-efficiency model in the presence of negative data.Journal of the Operational Research Society, 64, 396–401.

Wanke, P., &Barros, C. (2014).Two-stage DEA: An application to major Brazilian banks. Expert Systems with Applications, 41, 2337–2344.

Wanke, P.,  Blackburn, V., & Barros, C. P.(2016).Cost and learning efficiency drivers in Australian schools: a two-stage network DEA approach.Applied Economics, 48,1142656.