Estimation of inputs and outputs in the general production possibility set with negative data based on the inverse DEA
Subject Areas : International Journal of Data Envelopment Analysis
1 - عضو هیات علمی دانشگاه آزاد اسلامی واحد شیراز
Keywords: Data envelopment analysis, Inverse DEA, Negative data, Target efficiency.,
Abstract :
The primary models in data envelopment analysis (DEA), consider the inputs and outputs of the decision-making units (DMUs) as non-negative. However, in the real world, we face many cases where the data is negative. In this paper, we investigate the inverse DEA models to estimate the optimal level of inputs and outputs of DMUs based on target efficiency scores. We also assume that some input and output components are negative. In this way, we propose three different models in variable returns to scale (VRS) to determine optimal levels. In order to solve each model, we determine the counterpart DMU corresponding to the DMUs under evaluation. This DMU is obtain based on the additive model, and then we get the level of the target and the observed outputs corresponding to the DMU under evaluation to determine which of these three models to use to measure the efficiency of the DMU under evaluation. We apply the proposed approach with a numerical example and consider it to measure the optimal levels of inputs and outputs of bank branches. Also we propose the results of paper.
[1] Pastor J, Ruiz J. Variables with negative values in DEA. In Zhu, J., Cook, W.D. (Eds.) Modeling Data Irregularities and Structural Complexities in Data Envelopment Analysis. (Springer, NY). 2007 63-84.
[2] Banker RD, Charnes A, Cooper WW. Some models for estimating technical and scale efficiencies in data envelopment analysis. Management Science. 1984 30: 1078-1092.
[3] Seiford LM, Zhu J. Modeling undesirable factors in efficiency evaluation, European Journal of Operational Research, 2002 142: 16-20.
[4] Scheel H. Undesirable outputs in efficiency valuations. European Journal of Operational Research. 2001 132: 400-410.
[5] Halme M, Joro T, Koivu M. Dealing with interval scale data in data envelopment analysis. European Journal of Operational Research. 2002 137: 22-27.
[6] Emrouznejad A, Amin GR, Thanassoulis E, Anouze AL. On the boundedness of the SORM DEA models with negative data. European Journal of Operational Research. 2010 206: 265-268.
[7] Emrouznejad A, Anouze AL, Thanassoulis E. A semi-oriented radial measure for measuring the efficiency of decision making units with negative data, using DEA. European Journal of Operational Research. 2010 200: 297-304.
[8] Mehdiloozad M, Zhu J, Sahoo BK. Identification of congestion in data envelopment analysis under the occurrence of multiple projections: A reliable method capable of dealing with negative data. European Journal of Operational Research. 2018 265: 644-654.
[9] Sharp JA, Meng W, Liu W. A modified slacks-based measure model for data envelopment analysis with „natural‟ negative outputs and inputs, Journal of the Operational Research Society. 2007 58: 1672-1677.
[10] Aparicio J, Ruiz JL, Sirvent I. Closest targets and minimum distance to the Pareto-efficient frontier in DEA. Journal of Productivity Analysis. 2007 28: 209-218.
[11] Lin R, Yang W, Huang H. A modified slacks-based super-efficiency measure in the presence of negative data. Computers & Industrial Engineering. 2019 135: 39-52.
[12] Lo SF, Lu WM. An integrated performance evaluation of financial holding companies in Taiwan. European Journal of Operational Research. 2009 198: 341-350.
[13] Lin R, Liu Y. Super-efficiency based on the directional distance function in the presence of negative data. Omega 2019 85: 26-34.
[14] Portela MCAS, Thanassoulis E, Simpson G. Negative data in DEA: A directional distance approach applied to bank branches. Journal of the Operational Research Society. 2004 55: 1111-1121.
[15] Tavana M, Izadikhah M, Di Caprio, D, Saen RF. A new dynamic range directional measure for two-stage data envelopment analysis models with negative data. Computers & Industrial Engineering. 2018 115: 427-448.
[16] Cheng G, Zervopoulos P, Qian Z. A variant of radial measure capable of dealing with negative inputs and outputs in data envelopment analysis. European Journal of Operational Research. 2013 225: 100-105.
[17] Zhang X-S, Cui J-C. A project evaluation system in the state economic information system of China: An operations research practice in public sectors, International Transactions in Operational Research, 1999 6: 441–452.
[18] Wei Q, Zhang J, Zhang X. An inverse DEA model for inputs/outputs estimate. European Journal of Operational Research. 2000 121(1): 151–163.
[19] Hadi-Vencheh A, Foroughi AA, Soleimani-damaneh M. A DEA model for resource allocation, Economic Modelling. 2008 25(5): 983–993.
[20] Zhang M, Wang L-L, Cui J-C. Extra resource allocation: A DEA approach in the view of efficiencies, Journal of the Operations Research Society of China. 2018 6(1): 85–106.
[21] Jahanshahloo GR, Soleimani-damaneh M, Ghobadi S. Inverse DEA under inter-temporal dependence using multiple-objective programming., European Journal of Operational Research. 2015 240(2): 447–456.
[22] Ghobadi S, Jahangiri S. Inverse DEA: Review, extension and application. International Journal of Information Technology & Decision Making. 2015 14(04): 805–824.
[23] Lim, D.-J., 2016. Inverse DEA with frontier changes for new product target setting, European Journal of Operational Research, 254(2), 510–516.
[24] Eyni M, Tohidi G, Mehrabeian S. Applying inverse DEA and cone constraint to sensitivity analysis of DMUs with undesirable inputs and outputs. Journal of the Operational Research Society. 2017 68(1): 34–40.
[25] Ghiyasi M. Inverse DEA based on cost and revenue efficiency. Computers & Industrial Engineering., 2017 114: 258–263.
[26] Hassanzadeh A, Yousefi S, Saen R F, Hosseininia SSS. How to assess sustainability of countries via inverse data envelopment analysis? Clean Technologies and Environmental Policy. 2018 20(1): 29–40.
[27] Amin GR, Emrouznejad A, Gattouf S. Modelling generalized firms’ restructuring using inverse DEA. Journal of Productivity Analysis. 2017 48(1): 51–61.
[28] Gattoufi S, Amin GR, Emrouznejad A. A new inverse DEA method for merging banks. IMA Journal of Management Mathematics. 2014 25: 73–87.
[29] Emrouznejad A, Yang G, Amin G R. A novel inverse DEA model with application to allocate the 〖CO〗_2 emissions quota to different regions in Chinese manufacturing industries. Journal of the Operational Research Society. 2019 70(7): 1079–1090.
[30] Wegener M, Amin GR. Minimizing GHG emissions using inverse DEA with an application in oil and gas. Expert Systems with Applications. 2019 122, 369–375.
[31] Gerami J, Mozaffari MR, Wanke PF, Correa HL. A generalized inverse DEA model for firm restructuring based on value efficiency, IMA Journal of Management Mathematics, 2023 34(3): 541–580.
[32] Gerami J, Mozaffari MR, Wanke PF. A multi-criteria ratio-based approach for two-stage data envelopment analysis. Expert Systems with Applications. 2020 158: 113508.
[33] Gerami J, Kiani Mavi R, Farzipoor Saen R, Kiani Mavi N. A novel network DEA-R model for evaluating hospital services supply chain performance. Annals of Operations Research. 2020, 324, 1–2: 1041–1066.
[34] Gerami J. An interactive procedure to improve estimate of value efficiency in DEA. Expert Systems with Applications. 15 December 2019, 137 29-45.
[35] Gerami J, Mozaffari MR, Wanke PF, Correa H. A novel slacks-based model for efficiency and super-efficiency in DEA-R. Operations Research. 2021 22, 4: 3373–3410.
[36] Gerami J. Strategic alliances and partnerships based on the semi-additive production technology in DEA. Expert Systems with Applications. 1 October 2024 251: 123986.