An inverse DEA approach in the presence of undesirable outputs based on the directional distance function
محورهای موضوعی : International Journal of Data Envelopment Analysis
1 - عضو هیات علمی دانشگاه آزاد اسلامی واحد شیراز
کلید واژه: Data envelopment analysis, Inverse DEA, Directional distance function, Undesirable outputs.,
چکیده مقاله :
In many production systems, we can do acquisition and merge operations process to increase productivity. For this purpose, we can use the inverse data envelopment analysis (DEA) approach. In many cases, in addition to producing desirable outputs, we also have the simultaneous production of undesirable outputs. It is important to use a suitable approach in the acquisition and merge operations process. In this paper, we present a new model based on the directed distance function. The new model provides a new unit or a pre-determined target efficiency level by merging two decision-making units (DMUs). Based on this model, level for desirable and undesirable outputs is determined for the newly created unit. In the following, we will show the provided approach with a numerical example and apply it for real world data.
[1] Charnes A, Cooper WW, Rhodes E. Measuring the efficiency of decision-making units. European journal of operational research. 1978 Nov 1; 2(6): 429-44.
[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] Zhang M, Cui JC. The extension and integration of the inverse DEA method. Journal of the Operational Research Society. 2017 67(9): 1212-1220.
[4] Wei Q, Zhang J, Zhang X. An inverse DEA model for inputs/outputs estimate.’, European Journal of Operational Research. 2000 121 (1): 151–163.
[5] Amin, G. R., Emrouznejad, A. and Gattoufi, S. Modelling generalized firms’ restructuring using inverse DEA’, Journal of Productivity Analysis. 2017 48(1): 51–61.
[6] Hadi-Vencheh A, Foroughi AA, Soleimani-Damaneh M. A DEA model for resource allocation. Economic Modelling, 2008 25(5): 983–993.
[7] Ghiyasi M. Efficiency improvement and resource estimation: A tradeoff analysis. International Journal of Productivity and Quality Management 2018 25(2): 151–169.
[8] Ghobadi S, Jahangiri S. Inverse DEA: review, extension and application. International Journal Information Technology Decision Making. 2015 14 (4): 805–824.
[9] Gattoufi S, Amin GR, Emrouznejad A. A new inverse DEA method for merging banks. IMA Journal of Management Mathematics 2014 25(1): 73–87.
[10] 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.
[11] Lim DJ. Inverse DEA with frontier changes for new product target setting’, European Journal of Operational Research. 2016 254 (2): 510–516.
[13] 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.
[13] Ghiyasi M. Inverse DEA based on cost and revenue efficiency’, Computers & Industrial Engineering. 2017 114: 258–263.
[14] Amin GR., Al-Muharrami S, Toloo M. A combined goal programming and inverse DEA method for target setting in mergers. Expert Systems with Applications. 2019 115(2) 412–417.
[15] Amin GR, Oukil A. Flexible target setting in mergers using inverse data envelopment analysis. International Journal of Operational Research. 2019 35(3): 301–317.
[16] 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.
[17] Soltanifar M, Ghiyasi M, Sharafi H. Inverse DEA-R models for merger analysis with negative data. IMA Journal of Management Mathematics. 2023 34 (3): 491-510.
[18] Ghiyasi M, Soltanifar M, Sharafi H. A novel inverse DEA-R model with in application hospital efficiency. Socio-Economic Planning Sciences. 2023 84: 101427.
[19] Seiford LM, Zhu J. Modeling undesirable factors in efficiency evaluation, European Journal of Operational Research, 2002 142: 16-20.
[20] Sueyoshi T, Goto M. Weak and strong disposability vs. natural and managerial disposability in DEA environmental assessment: Comparison between Japanese electric power industry and manufacturing industries. Energy Economics, 2012 686-699.
[21] Halkos G, Petrou KN. Treating undesirable outputs in DEA: A critical review. Economic Analysis and Policy. 2019 62:97–104.
[22] Toloo M, Hanclova J. Multi-valued measures in DEA in the presence of undesirable outputs. Omega. 2019 94(C).
[23] Podinovski VV. Direct estimation of marginal characteristics of nonparametric production frontiers in the presence of undesirable outputs. European Journal of Operational Research. 2019 279 (1):258–276.
[24] Pishgar-Komleh SH, Zylowski T, Rozakis S, Kozyra J. Efficiency under different methods for incorporating undesirable outputs in an LCA+ DEA framework: A case study of winter wheat production in Poland. Journal of environmental management. 2020 260:110138.
[25] Scheel H. Undesirable outputs in efficiency valuations. European Journal of Operational Research. 2001 132: 400-410.
[26] Chung YH, Fare R, Grosskopf S. Productivity and undesirable outputs: A directional distance function approach. Journal of Environmental Management. 1997 51(3):229–240.
[27] Ball VE, Lovell CK, Luu H, Nehring R. Incorporating environmental impacts in the measurement of agricultural productivity growth. Journal of Agricultural and Resource Economics. 2004 29(3):436–460.
[28] Fare R, Grosskopf S, Lovell CAK, Pasurka C. Multilateral productivity comparisons when some outputs are undesirable: A nonparametric approach. Review of Economics and Statistics, 1989 71(1): 90–98.
[29] 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.
[30] 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.
[31] Gerami J. An interactive procedure to improve estimate of value efficiency in DEA. Expert Systems with Applications. 15 December 2019, 137 29-45.
[32] 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.
[33] Gerami J. Strategic alliances and partnerships based on the semi-additive production technology in DEA. Expert Systems with Applications. 1 October 2024 251: 123986.
[34] Zanella A, Camanho AS, Dias TG. Undesirable outputs and weighting schemes in composite indicators based on data envelopment analysis. European Journal of Operational Research. 2015 245(2): 517-530.
[35] Shirazi F, Mohammadi E. Evaluating efficiency of airlines: A new robust DEA approach with undesirable output. Research in Transportation Business & Management. 2019 33: 100467.
