A slacks-based measure approach for efficiency decomposition in multi-period two-stage systems
RAIRO - Operations Research - Recherche Opérationnelle, Tome 54 (2020) no. 6, pp. 1657-1671.

Two-stage production systems are often encountered in many real applications where the production process is divided into two processes. In contrast to the conventional data envelopment analysis (DEA) models, two-stage DEA models take the operations of the internal processes into account. A number of studies have used two-stage DEA models in order to evaluate the performance of decision making units (DMUs) having a network structure. In this paper, we use a non-radial DEA model called the network slacks-based measure (NSBM) model to measure the efficiency of a system with a multi-period two-stage structure. Then we describe the properties of the proposed model in details. Moreover, we shall decompose the overall efficiency of the system over a number of time periods as a weighted average of the efficiency in each period. The efficiency of the stages, in respect to the entire periods shall be decomposed in terms of the weighted average efficiency of the stages in each period. Finally, the real data of Mellat bank branches in Tehran extracted from extant literature is used to illustrate the proposed approach.

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Accepté le :
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Publié le :
DOI : 10.1051/ro/2019113
Classification : 90C05, 90Bxx, 90Cxx
Mots-clés : Data envelopment analysis, efficiency, two-stage system, multi-period, slacks-based measure 
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     author = {Esfidani, Samaneh and Hosseinzadeh Lotfi, Farhad and Razavyan, Shabnam and Ebrahimnejad, Ali},
     title = {A slacks-based measure approach for efficiency decomposition in multi-period two-stage systems},
     journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
     pages = {1657--1671},
     publisher = {EDP-Sciences},
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     doi = {10.1051/ro/2019113},
     mrnumber = {4150235},
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     url = {http://archive.numdam.org/articles/10.1051/ro/2019113/}
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Esfidani, Samaneh; Hosseinzadeh Lotfi, Farhad; Razavyan, Shabnam; Ebrahimnejad, Ali. A slacks-based measure approach for efficiency decomposition in multi-period two-stage systems. RAIRO - Operations Research - Recherche Opérationnelle, Tome 54 (2020) no. 6, pp. 1657-1671. doi : 10.1051/ro/2019113. http://archive.numdam.org/articles/10.1051/ro/2019113/

[1] S. Akther, H. Fukuyama and W.L. Weber, Estimating two-stage network Slacks-based inefficiency: an application to Bangladesh banking. Omega 41 (2013) 88–96. | DOI

[2] A. Amirteimoori, A DEA two-stage decision processes with shared resources. Cent. Eur. J. Oper. Res. 21 (2013) 141–151. | DOI | MR | Zbl

[3] A. Ashrafi, A.B. Jaafar, L.S. Lee and M.R. Abu Bakar, A slacks-based measure of efficiency in two-stage data envelopment analysis. Int. J. Math. Anal. 5 (2011) 1435–1444. | MR | Zbl

[4] S. Aviles-Sacoto, W.D. Cook, R. Imanirad and J. Zhu, Two-stage network DEA: when intermediate measures can be treated as outputs from the second stage. J. Oper. Res. Soc. 66 (2015) 1868–1877. | DOI

[5] F. Boloori, M. Afsharian and J. Pourmahmoud, Equivalent multiplier and envelopment DEA models for measuring efficiency under general network structures. Measurement 80 (2016) 259–269. | DOI

[6] A. Charnes, W.W. Cooper and E. Rhodes, Measuring the efficiency of decision making units. Eur. J. Oper. Res. 2 (1978) 429–444. | DOI | MR | Zbl

[7] Y. Chen, W.D. Cook, L. Ning and J. Zhu, Additive efficiency decomposition in two-stage DEA. Eur. J. Oper. Res. 196 (2009) 1170–1176. | DOI | Zbl

[8] W.D. Cook, J. Zhu, G. Bi and F. Yang, Network DEA: additive efficiency decomposition. Eur. J. Oper. Res. 207 (2010) 1122–1129. | DOI

[9] D.K. Despotis, D. Sotiros and G.R. Koronakos, A network DEA approach for series multi-stage Processes. Omega 61 (2015) 35–48. | DOI

[10] D.K. Despotis, D. Sotiros and G.R. Koronakos, Composition versus decomposition in two-stage network DEA: a reverse approach. J. Prod. Anal. 45 (2016) 71–87. | DOI

[11] A. Ebrahimnejad, M. Tavana, F. Hosseinzadeh Lotfi, R. Shahverdi and M. Yousefpour, A three-stage data envelopment analysis model with application to banking industry. Measurement 49 (2014) 308–319. | DOI

[12] S. Esfidani, F. Hosseinzadeh Lotfi, S.H. Razavyan and A. Ebrahimnejad, Efficiency changes index in the network data envelopment analysis with non-radial model. Asian-Eur. J. Math. 13 (2018) 2050031. | DOI | MR

[13] A. Esmaeilzadeh and A. Hadi-Vencheh, A super-efficiency model for measuring aggregative efficiency of multi-period production systems. Measurement 46 (2013) 3988–3993. | DOI

[14] A. Esmaeilzadeh and R. Kazemi Matin, Multi-period efficiency measurement of network production systems. Measurement 134 (2019) 835–844. | DOI

[15] M.J. Farrell, The measurement of productive efficiency. J. R. Stat. Soc. Ser. A. 120 (1957) 253–290. | DOI

[16] H. Fukuyama and S.M. Mirdehghan, Identifying the efficiency status in network DEA. Eur. J. Oper. Res. 220 (2012) 85–92. | DOI | MR | Zbl

[17] C. Guo and J. Zhu, Non-cooperative two-stage network dea model: linear vs. parametric linear. Eur. J. Oper. Res. 258 (2017) 398–400. | DOI | MR | Zbl

[18] S.H.R. Hajiagha, S.H. Hashemi, H.A. Mahdiraji and J. Azaddel, Multi-period data envelopment analysis based on Chebyshev inequality bounds. Expert Syst. App. 42 (2015) 7759–7767. | DOI

[19] M.A. Hinojosa, S. Lozano and A.M. Mármol, Nash decomposition for process efficiency in multi-stage production systems. Expert Syst. App. 55 (2016) 480–492. | DOI

[20] F. Hosseinzadeh Lotfi and M. Abravesh, Evaluation of efficiency and effectiveness of Mellat bank branch in Tehran by using data envelopment analysis method. In: The First International Conference on Management and Accounting with Value Creation Approach (2015).

[21] M. Izadikhah, M. Tavana, D.D. Caprio and J.S.-A. Francisco, A novel two-stage DEA production model with freely distributed initial inputs and shared intermediate outputs. Expert Syst. App. 99 (2018) 213–230. | DOI

[22] M.A. Jianfeng, A two-stage DEA model considering shared inputs and free intermediate measures. Expert Syst. App. 42 (2015) 4339–4347. | DOI

[23] C. Kao, Efficiency decomposition in network data envelopment analysis with slacks based measures. Omega 45 (2014) 1–6. | DOI

[24] C. Kao, Efficiency decomposition for general multi-stage systems in data envelopment analysis. Eur. J. Oper. Res. 232 (2014) 117–124. | DOI | MR | Zbl

[25] C. Kao, Network data envelopment analysis: a review. Eur. J. Oper. Res. 239 (2014) 1–16. | DOI | MR | Zbl

[26] C. Kao, A classification of slacks-based efficiency measures in network data envelopment analysis with an analysis of the properties possessed. Eur. J. Oper. Res. 270 (2018) 1109–1121. | DOI | MR | Zbl

[27] C. Kao and S.N. Hwang, Efficiency decomposition in two-stage data envelopment analysis: an application to non-life insurance companies in Taiwan. Eur. J. Oper. Res. 185 (2008) 418–429. | DOI | Zbl

[28] C. Kao and S.N. Hwang, Multi-period efficiency and Malmquist productivity index in two-stage production systems. Eur. J. Oper. Res. 232 (2014) 512–521. | DOI | MR | Zbl

[29] C. Kao and S.T. Liu, Multi-period efficiency measurement in data envelopment analysis: the case of Taiwanese commercial banks. Omega 47 (2014) 90–98. | DOI

[30] H.Y. Kao, C.Y. Chan and D.J. Wu, A multi-objective programming method for solving network DEA. Appl. Soft Comput. 24 (2014) 406–413. | DOI

[31] Y.H. Kao, D.J. Wu and C.H. Huang, Evaluation of cloud service industry with dynamic and network DEA models. Appl. Math. Comput. 315 (2017) 188–202.

[32] M. Kou, K. Chen, S.R. Wang and Y. Shao, Measuring efficiencies of multi-period and multi-division systems associated with DEA: an application to OECD countries’ national innovation systems. Expert Syst. App. 46 (2016) 494–510. | DOI

[33] S. Kordrostami and M.J.S. Noveiri, Evaluating the efficiency of firms with negative data in multi-period systems. Int. J. Ind. Math. 9 (2017) 27–35.

[34] S. Kordrostami and M.J.S. Noveiri, Evaluating the multi-period systems efficiency in the presence of fuzzy data. Fuzzy Inf. Eng. 9 (2017) 281–298. | DOI | MR

[35] D. Liu, Evaluating the multi-period efficiency of East Asia airport companies. J. Air Trans. Manage. 59 (2017) 71–82. | DOI

[36] S. Lozano, Slacks-based inefficiency approach for general networks with bad outputs: an application to the banking sector. Omega 60 (2016) 73–84. | DOI

[37] S. Lozano, E. Gutiérrez and P. Moreno, Network DEA approach to airports performance assessment considering undesirable outputs. Appl. Math. Model. 37 (2013) 1665–1676. | DOI

[38] M.J.S. Noveiri and S. Kordrostami, Detecting the multi-period performance and efficiency changes of systems with undesirable outputs. Discrete Math. Algorithms App. 10 (2018) 1850034. | DOI | MR | Zbl

[39] K. Park, measurement of multi-period aggregative efficiency. Eur. J. Oper. Res. 193 (2009) 567–580. | DOI | MR | Zbl

[40] L. Parte and P. Alberca, A multi-stage model to evaluate the efficiency the bar industry. Int. J. Hospitality Manage. 77 (2019) 512–522. | DOI

[41] L.M. Seiford and J. Zhu, Profitability and marketability of the top 55 US commercial banks. Manag. Sci. 45 (1999) 1270–1288. | DOI

[42] M. Tavassoli, G.R. Faramarzi and R. Farzipoor Saen, Efficiency and effectiveness in airline performance using a SBM-NDEA model in the presence of shared input. J. Air Trans Manage. 34 (2014) 146–153. | DOI

[43] K. Tone, Theory and methodology A slacks-based measure of efficiency in data envelopment analysis. Eur. J. Oper. Res. 130 (2001) 498–509. | DOI | MR | Zbl

[44] K. Tone and M. Tsutsui, Network DEA: a slacks-based measure approach. Eur. J. Oper. Res. 197 (2009) 243–252. | DOI | Zbl

[45] J. Wu, Q. Zhu, J. Xiang, J. Chu and L. Liang, Two-stage network processes with shared resources and resources recovered from undesirable outputs. Eur. J. Oper. Res. 251 (2016) 182–197. | DOI | MR

[46] X. Zhou, Z. Xu, J. Chai, L. Yao, S. Wang and B. Lev, Efficiency evaluation for banking systems under uncertainty: a multi-period three-stage DEA model. Omega 85 (2019) 68–82. | DOI

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