Malmquist–Luenberger Productivity Index for a Two-Stage Structure in the Presence of Undesirable Outputs and Uncertainty
Network Data Envelopment Analysis (NDEA) models assess the processes of the underlying system at a certain moment and disregard the dynamic effects in the production process. Hence, distorted efficiency evaluation is gained that might give misleading information to decision-making units (DMUs). Malm...
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| Published in: | Advances in Operations Research Vol. 2024; pp. 1 - 22 |
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| Abstract | Network Data Envelopment Analysis (NDEA) models assess the processes of the underlying system at a certain moment and disregard the dynamic effects in the production process. Hence, distorted efficiency evaluation is gained that might give misleading information to decision-making units (DMUs). Malmquist–Luenberger Productivity Index (MPI) assesses efficiency changes over time, which are measured as the product of recovery and frontier-shift terms, both coming from the DEA framework. In this study, a form of MPI involving network structure for evaluating DMUs in the presence of uncertainty and undesirable outputs in two periods of time is presented. To cope with uncertainty, we use the stochastic p-robust approach and the weak disposability of Kuosmanen (American Journal Agricultural Economics 87 (4):1077–1082, 2005) proposed to take care of undesirable outputs. The proposed fractional models for stages and overall system are linearized by applying the Charnes and Cooper transformation. Finally, the proposed models are applied to evaluate the efficiency of 11 petroleum wells to identify the main factors determining their productivity, utilizing the data from the 2020 to 2021 period. The results show that the management of resource consumption, especially equipment and capital, is not appropriate and investment is inadequate. Although the depreciation rate of capital facilities in this industry is high, the purpose of the investment is not to upgrade the level of technology. |
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| AbstractList | Network Data Envelopment Analysis (NDEA) models assess the processes of the underlying system at a certain moment and disregard the dynamic effects in the production process. Hence, distorted efficiency evaluation is gained that might give misleading information to decision-making units (DMUs). Malmquist-Luenberger Productivity Index (MPI) assesses efficiency changes over time, which are measured as the product of recovery and frontier-shift terms, both coming from the DEA framework. In this study, a form of MPI involving network structure for evaluating DMUs in the presence of uncertainty and undesirable outputs in two periods of time is presented. To cope with uncertainty, we use the stochastic p-robust approach and the weak disposability of Kuosmanen (American Journal Agricultural Economics 87 (4):1077-1082, 2005) proposed to take care of undesirable outputs. The proposed fractional models for stages and overall system are linearized by applying the Charnes and Cooper transformation. Finally, the proposed models are applied to evaluate the efficiency of 11 petroleum wells to identify the main factors determining their productivity, utilizing the data from the 2020 to 2021 period. The results show that the management of resource consumption, especially equipment and capital, is not appropriate and investment is inadequate. Although the depreciation rate of capital facilities in this industry is high, the purpose of the investment is not to upgrade the level of technology. |
| Audience | Academic |
| Author | Salahi, Maziar Shakouri, Rita |
| Author_xml | – sequence: 1 givenname: Rita orcidid: 0000-0003-2175-1519 surname: Shakouri fullname: Shakouri, Rita organization: Department of Computer EngineeringFaculty of Mathematical SciencesTechnical and Vocational University (TVU)TehranIran – sequence: 2 givenname: Maziar orcidid: 0000-0002-0430-3063 surname: Salahi fullname: Salahi, Maziar organization: Department of Applied MathematicsFaculty of Mathematical SciencesUniversity of GuilanP.O. Box 1914RashtIranguilan.ac.ir |
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| Cites_doi | 10.1080/01605682.2018.1489353 10.1186/s40854-020-0170-0 10.1111/j.1467-8276.2005.00788.x 10.3934/qfe.2019.2.315 10.3390/f14050909 10.1007/bf03006863 10.3390/su14159310 10.1016/j.omega.2010.10.008 10.1042/bj2120791 10.1002/nav.3800090303 10.24200/sci.2018.5259.1173 10.1016/0377-2217(78)90138-8 10.1080/07408170500469113 10.2307/2232257 10.1016/j.iref.2019.01.004 10.1016/j.measurement.2016.06.049 10.1007/s10479-019-03491-w 10.1016/j.apenergy.2021.118275 10.1155/2022/1133882 10.1016/j.omega.2019.01.010 10.1111/0002-9092.00181 10.1051/ro/2022117 10.1016/j.asoc.2017.11.031 10.1016/j.jairtraman.2023.102403 10.21203/rs.3.rs-1161479/v1 10.1016/j.rtbm.2020.100467 10.1007/s10479-015-1970-x 10.1016/j.jclepro.2020.123110 10.1016/j.eneco.2019.03.022 10.1108/jm2-01-2019-0014 10.1007/s40953-021-00247-x 10.1016/j.cie.2020.106434 10.1016/j.eswa.2020.113938 10.1016/j.jclepro.2016.07.166 10.1155/2022/7596736 10.1007/s10479-019-03173-7 10.1111/j.1477-9552.1997.tb01158.x 10.1016/j.cie.2017.06.005 10.1002/nav.20308 10.1016/j.omega.2018.09.005 10.1016/j.jhazmat.2009.05.044 10.1016/j.rtbm.2022.100801 10.1016/j.eap.2019.01.005 10.1080/01605682.2020.1718016 |
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| Copyright | Copyright © 2024 Rita Shakouri and Maziar Salahi. COPYRIGHT 2024 John Wiley & Sons, Inc. Copyright © 2024 Rita Shakouri and Maziar Salahi. This is an open access article distributed under the Creative Commons Attribution License (the “License”), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. https://creativecommons.org/licenses/by/4.0 |
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| References | 22 44 23 24 46 25 47 26 48 27 28 29 M. Salahi (33) 2019; 70 30 31 10 32 11 12 34 13 35 H. Nedaei (9) 2020; 144 36 15 37 16 38 17 18 19 K. Tone (14) 1 3 4 A. Charnes (45) 1962; 9 5 6 7 8 W. D. Cook (2) 2014 S. Mehdizadeh (39) 2020; 12 40 41 20 42 21 43 |
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| SubjectTerms | Airlines Banking industry Commercial banks Data envelopment analysis Decision-making Efficiency Evaluation Operations research Performance evaluation Productivity Time measurement Uncertainty Upgrading |
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| Title | Malmquist–Luenberger Productivity Index for a Two-Stage Structure in the Presence of Undesirable Outputs and Uncertainty |
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