The effect of weight control and weighing method of efficiency in data envelopment analysis

Document Type : Research Paper


1 Department of Mathematics, Tabriz Branch, Islamic Azad University, Tabriz, Iran

2 Department of Mathematics, Central Tehran Branch, Islamic Azad University, Tehran, Iran

3 Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran


Data Envelopment Analysis (DEA) determines the efficiency of decision-making units. Weight restrictions in a model with weight restrictions (WR) are considered to determine the efficiency of units, depending on the importance of indicators (inputs and outputs). Since weight plays an important role in the efficiency and ranking of options, in this paper we examine the effect of the type of weighting method of indices in the calculation of the efficiency of decision-making units. It should be noted that change is not applied in decision-making units but in the weighting method in order to understand the effect of different weighting methods in the calculation of efficiency: that is, the efficiency of a unit is calculated with a variety of weighting methods and the impact of the type of weighting method on the indicators is evaluated in the calculation of the efficiency of that unit. In this study, we showed that the efficiency of each unit is affected by weighting methods and that the efficiency of each unit at each change in the weighting method assigns a different value to itself.


[1] Y. Bian and F. Yang, Resource and environment efficiency analysis of provinces in China: A DEA approach based on Shannon’s entropy, Energy Policy 38 (2010), no. 4, 1909–1917.
[2] A. Charnes, W.W. Cooper and E. Rhodes, Measuring the efficiency of decision making units, Eur. J. Operat. Res. 2 (1978), no. 6, 429–444.
[3] C.I. Chiang, M.J. Hwang and Y.H. Liu, Determining a common set of weights in a DEA problem using a separation vector, Math. Comput. Model. 54 (2011), no. 9–10, 2464–2470.
[4] D. Ennen and I. Batool, Airport efficiency in Pakistan-A data envelopment analysis with weight restrictions, J. Air Transport Manag. 69 (2018), 205–212.
[5] F. Hosseinzadeh Lotfi, G.R. Jahanshahloo and M. Esmaeili, An alternative approach in the estimation of returns to scale under weight restrictions, Appl. Math. Comput. 189 (2007), no. 1, 719–724.
[6] A. Kumar, R. Shankar and R.M. Debnath, Analyzing customer preference and measuring relative efficiency in telecom sector: A hybrid fuzzy AHP/DEA study, Telemetr. Inf. 32 (2015), no. 3, 447–462.
[7] P.L. Lai, A.P. Potter, M. Beynon and A. Beresford, Evaluating the efficiency performance of airports an integrated AHP/DEA/AR technique, Transport Policy 42 (2015), 75–85.
[8] S.K. Lee, G. Mogi, Z. Li, K.S. Hui, S.K. Lee, K.N. Hui and J.W. Kim, Measuring the relative efficiency of hydrogen energy technologies for implementing the hydrogen economy: An integrated fuzzy AHP/DEA approach, Int. J. Hydrogen Energy 36 (2011), no. 20, 12655–12663.
[9] F.H.F. Liu and H.H. Peng, Ranking of units on the DEA frontier with common weights, Comput. Oper. Res. 35 (2008), no. 5, 1624–1637.
[10] V.V. Podinovski, Optimal weights in DEA models with weight restrictions, Eur. J. Oper. Res. 254 (2016), no. 3, 916–924.
[11] V.V. Podinovski and T. Bouzdine-Chameeva, Consistent weight restrictions in data envelopment analysis, Eur. J. Oper. Res. 244 (2015), no. 1, 201–209.
[12] T.L. Saaty, The analytic hierarchy process, McGraw Hill, New York, 1980.
[13] R.C. Silva and A.Z. Milioni, The adjusted spherical frontier model with weight restrictions, European J. Operat. Res. 220 (2012), no. 3, 729–735.
[14] M. Soleimani-Damaneh, G.R. Jahanshahloo, S. Mehrabian and M. Hasannasab, Returns to scale and scale elasticity in the presence of weight restrictions and alternative solutions, Knowledge-Based Syst. 23 (2010), no. 2, 86–93.
[15] M. Song, Q. Zhu, J. Peng and E.D.S. Gonzalez, Improving the evaluation of cross efficiencies: A method based on Shannon entropy weight, Comput. Indust. Eng. 112 (2017), 99–106.
[16] J. Wu, J. Sun, L. Liang and Y. Zha, Determination of weights for ultimate cross efficiency using Shannon entropy, Expert Syst. Appl. 38 (2011), no. 5, 5162–5165
Volume 14, Issue 3
March 2023
Pages 103-112
  • Receive Date: 06 July 2022
  • Revise Date: 06 September 2022
  • Accept Date: 13 September 2022
  • First Publish Date: 15 September 2022