Network data envelopment analysis (NDEA), one of the most important branches of recent DEA developments, has been developed for examining the decision making units (DMUs) of a system with complex and internal component divisions. In this study we apply a maximin strategy to network DEA at two levels. At the individual DMU level, we evaluate the system’s performance by maximizing the minimum of the divisions efficiencies, which is based on the weak-link approach. At the all DMUs level, we evaluate the system’s performance by maximizing the minimum of the DMUs’ efficiencies, which is based on the maximin ratio efficiency model. With such two-level maximin strategy, we propose the two-level maximin NDEA model to evaluate efficiencies of all divisions as well as all DMUs at the same time. The model will provide unique and unbiased efficiency scores for all divisions in a system and improve incomparable efficiency scores and weak discrimination power of traditional DEA models. In addition, we discuss the cross efficiency evaluation based on the two-level maximin NDEA model. The proposed models are applied to the efficiency evaluation of supply chains for illustrations.
Accepté le :
Première publication :
Publié le :
DOI : 10.1051/ro/2022090
Keywords: Data envelopment analysis, weak-link approach, maximin efficiency ratio model, cross efficiency, supply chains
@article{RO_2022__56_4_2543_0,
author = {Yang, Feng and Sun, Yu and Wang, Dawei and Ang, Sheng},
title = {Network data envelopment analysis with two-level maximin strategy},
journal = {RAIRO. Operations Research},
pages = {2543--2556},
year = {2022},
publisher = {EDP-Sciences},
volume = {56},
number = {4},
doi = {10.1051/ro/2022090},
mrnumber = {4469504},
language = {en},
url = {https://www.numdam.org/articles/10.1051/ro/2022090/}
}
TY - JOUR AU - Yang, Feng AU - Sun, Yu AU - Wang, Dawei AU - Ang, Sheng TI - Network data envelopment analysis with two-level maximin strategy JO - RAIRO. Operations Research PY - 2022 SP - 2543 EP - 2556 VL - 56 IS - 4 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/ro/2022090/ DO - 10.1051/ro/2022090 LA - en ID - RO_2022__56_4_2543_0 ER -
%0 Journal Article %A Yang, Feng %A Sun, Yu %A Wang, Dawei %A Ang, Sheng %T Network data envelopment analysis with two-level maximin strategy %J RAIRO. Operations Research %D 2022 %P 2543-2556 %V 56 %N 4 %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/ro/2022090/ %R 10.1051/ro/2022090 %G en %F RO_2022__56_4_2543_0
Yang, Feng; Sun, Yu; Wang, Dawei; Ang, Sheng. Network data envelopment analysis with two-level maximin strategy. RAIRO. Operations Research, Tome 56 (2022) no. 4, pp. 2543-2556. doi: 10.1051/ro/2022090
[1] , and , An ensemble approach for assessment of energy efficiency of agriculture system in Pakistan. Energ. Effic. 13 (2020) 683–696. | DOI
[2] , , , and , Target intermediate products setting in a two-stage system with fairness concern. Omega 73 (2017) 49–59. | DOI
[3] and , Pitfalls of decomposition weights in the additive multi-stage DEA model. Omega 58 (2016) 139–153. | DOI
[4] , and , Cross-ranking of decision making units in data envelopment analysis. Appl. Math. Modell. 37 (2013) 398–405. | MR | DOI
[5] , and , A classification of DEA models when the internal structure of the decision making units is considered. Ann. Oper. Res. 173 (2010) 207–235. | MR | DOI
[6] and , Programming with linear fractional functionals. Nav. Res. Logistics Q. 9 (1962) 181–186. | MR | DOI
[7] and , Preface to topics in data envelopment analysis. Ann. Oper. Res. 2 (1984) 59–94. | DOI
[8] , and , Measuring the efficiency of decision making units. Eur. J. Oper. Res. 2 (1978) 429–444. | MR | DOI
[9] , , and , Additive efficiency decomposition in two-stage DEA. Eur. J. Oper. Res. 196 (2009) 1170–1176. | DOI
[10] , , and , Efficiency evaluation of non-homogeneous DMUs with inconsistent input quality. Comput. Ind. Eng. 158 (2021) 107418. | DOI
[11] , and , Determining a common set of weights in a DEA problem using a separation vector. Math. Comput. Modell. 54 (2011) 2464–2470. | MR | DOI
[12] and , Data envelopment analysis (DEA)–Thirty years on. Eur. J. Oper. Res. 192 (2009) 1–17. | MR | DOI
[13] , , and . Network DEA: additive efficiency decomposition, Eur. J. Oper. Res. 207 (2010) 1122–1129. | DOI
[14] , and , RAM: a range adjusted measure of inefficiency for use with additive models, and relations to other models and measures in DEA. J. Prod. Anal. 11 (1999) 5–42. | DOI
[15] and , Fuzzy weak link approach to the two-stage DEA. RAIRO: Oper. Res. 55 (2021) 385. | MR | Numdam | DOI
[16] , and , The “weak-link” approach to network DEA for two-stage processes. Eur. J. Oper. Res. 254 (2016) 481–492. | DOI
[17] , and , A network DEA approach for series multi-stage processes. Omega 61 (2016) 35–48. | DOI
[18] and , Productivity and intermediate products: a frontier approach. Econ. Lett. 50 (1996) 65–70. | DOI
[19] and , Modelling bank performance: a network DEA approach. Eur. J. Oper. Res. 259 (2017) 721–732. | MR | DOI
[20] , , , and , Common weights in dynamic network DEA with goal programming approach for performance assessment of insurance companies in Iran. Manage. Res. Rev. (2018). DOI: . | DOI
[21] , , and , Decomposition weights and overall efficiency in two-stage additive network DEA. Eur. J. Oper. Res. 257 (2017) 896–906. | MR | DOI
[22] and , Evaluating sustainability of supply chains by two-stage range directional measure in the presence of negative data. Transp. Res. Part D: Transp. Environ. 49 (2016) 110–126. | DOI
[23] , , , and , Ranking of units by positive ideal DMU with common weights. Expert Syst. App. 37 (2010) 7483–7488. | DOI
[24] , Efficiency decomposition in network data envelopment analysis: a relational model. Eur. J. Oper. Res. 192 (2009) 949–962. | DOI
[25] , Network Data Envelopment Analysis: a review. Eur. J. Oper. Res. 239 (2014) 1–16. | MR | DOI
[26] , Network Data Envelopment Analysis: Foundations and Extensions. Springer, Berlin (2017). | MR | DOI
[27] and , 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
[28] and , Efficiency measurement for network systems: IT impact on firm performance. Decis. Support Syst. 48 (2010) 437–446. | DOI
[29] and , An integrated supplier selection methodology incorporating QFD and DEA with imprecise data. Expert Syst. App. 41 (2014) 6995–7004. | DOI
[30] and , A comprehensive common weights data envelopment analysis model: ideal and anti-ideal virtual decision making units approach. J. Ind. Syst. Eng. 11 (2018) 281–306.
[31] and , Common set of weights and efficiency improvement on the basis of separation vector in two-stage network data envelopment analysis. Math. Sci. 14 (2020) 53–65. | MR | DOI
[32] , and , Reformulation of Network Data Envelopment Analysis models using a common modelling framework. Eur. J. Oper. Res. 278 (2019) 472–480. | MR | DOI
[33] , and , Modelling a multi-period production process: evidence from the Japanese regional banks. Eur. J. Oper. Res. 294 (2021) 327–339. | MR | DOI
[34] , , and , DEA models for extended two-stage network structures. Omega 40 (2012) 611–618. | DOI
[35] , , and , A balanced data envelopment analysis cross-efficiency evaluation approach. Expert Syst. App. 106 (2018) 154–168. | DOI
[36] and , Units invariant and translation invariant DEA models. Oper. Res. Lett. 18 (1995) 147–151. | MR | DOI
[37] , and , Joint analysis of eco-efficiency and eco-innovation with common weights in two-stage network DEA: a big data approach. Technol. Forecasting Soc. Change 144 (2019) 553–562. | DOI
[38] , and , A generalized multiplicative directional distance function for efficiency measurement in DEA. Eur. J. Oper. Res. 232 (2014) 679–688. | MR | DOI
[39] , Cross efficiency evaluation of decision-making units using the maximum decisional efficiency principle. Comput. Ind. Eng. 145 (2020) 106550. | DOI
[40] , , and , Efficiency under different methods for incorporating undesirable outputs in an LCA + DEA framework: a case study of winter wheat production in Poland. J. Environ. Manage. 260 (2020) 110138. | DOI
[41] and , An algorithm for determining common weights by concept of membership function. J. Linear Topol. Algebra (JLTA) 4 (2015) 165–172. | MR
[42] , and , Cost, revenue and profit efficiency measurement in DEA: a directional distance function approach. Eur. J. Oper. Res. 237 (2014) 921–931. | MR | DOI
[43] , , , and , An Alternative Approach to Dealing with the Composition Approach for Series Network Production Processes. Asia-Pac. J. Oper. Res. 38 (2021) 2150004. | MR | DOI
[44] and , Profitability and marketability of the top 55 US commercial banks. Manage. Sci. 45 (1999) 1270–1288. | DOI
[45] , and , Dominance at the divisional efficiencies level in network DEA: the case of two-stage processes. Omega 85 (2019) 144–155. | DOI
[46] , and , An integrated data envelopment analysis and mixed integer non-linear programming model for linearizing the common set of weights. Cent. Eur. J. Oper. Res. 27 (2019) 887–904. | MR | DOI
[47] , A slacks-based measure of efficiency in data envelopment analysis. Eur. J. Oper. Res. 130 (2001) 498–509. | MR | DOI
[48] , Derivation of the maximin efficiency ratio model from the maximum decisional efficiency principle. Ann. Oper. Res. 73 (1997) 323–338. | DOI
[49] and , Enhanced bisection strategies for the Maximin Efficiency Ratio model. Eur. J. Oper. Res. 144 (2003) 545–553. | MR | DOI
[50] and , Assess and prognosticate green house gas emissions from agricultural production of EU countries, by implementing, DEA Window analysis and artificial neural networks. Renew. Sustain. Energy Rev. 76 (2017) 155–162. | DOI
[51] , , and , Assessing sustainability performance of global supply chains: an input-output modeling approach. Eur. J. Oper. Res. 285 (2020) 393–404. | DOI
[52] , and , Efficiency evaluation for supply chains using maximin decision support. IEEE Trans. Syst. Man Cybern. Syst. 44 (2014) 1088–1097. | DOI
[53] , , , , and , Joint optimization for coordinated configuration of product families and supply chains by a leader-follower Stackelberg game. Eur. J. Oper. Res. 246 (2015) 263–280. | MR | DOI
[54] and , Two-stage cooperation model with input freely distributed among the stages. Eur. J. Oper. Res. 205 (2010) 332–338. | DOI
[55] , and , Regulation adaptive strategy and bank efficiency: a network slacks-based measure with shared resources. Eur. J. Oper. Res. 295 (2021) 348–362. | MR | DOI
Cité par Sources :
