Malmquist Productivity Index to a Two-Stage Structure in the Presence of Uncertain Data

Authors

  • Rita Shakouri * Department of Computer Engineering, Faculty of Mathematical Sciences, Technical and Vocational University (TVU), Tehran, Iran. https://orcid.org/0000-0003-2175-1519
  • Rosa Shakouri Math Teacher at The Ministry of Education of the republic of Iran.

https://doi.org/10.48314/anowa.v1i2.48

Abstract

Network Data Envelopment Analysis (NDEA) models assess the processes of the underlying system at a certain moment and disregard the dynamic effects inside the production process. Hence, distorted efficiency evaluation is gained that might give misleading information to Decision-Making Units (DMUs). However, the dynamic DEA model discusses the repetition of a single-period form over a long-term period, and it appears as a shape of time series one which includes a particular construction in each period. Malmquist 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 the uncertainty, we use the stochastic p-robust approach, and the weak disposability of Kuosmanen (2005) is utilized to take care of undesirable outputs. The proposed fractional models are linearized applying the Charnes and Cooper transformation, and they are applied to evaluate the efficiency of 11 oilfields 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 usage, especially forces and equipment, is inappropriate and investment is not sufficient. This specific attribute highlights the necessity to enhance the rate of investment to substitute the depreciated funds.

Keywords:

Data Envelopment Analysis, Stochastic p-robust, Network Data Envelopment Analysis, Malmquist Productivity Index, Oilfields

References

  1. [1] Kuosmanen, T. (2005). Weak disposability in nonparametric production analysis with undesirable outputs. American journal of agricultural economics, 87(4), 1077–1082. https://doi.org/10.1111/j.1467-8276.2005.00788.x
  2. [2] Charnes, A., Cooper, W. W., & Rhodes, E. (1979). Measuring the efficiency of decision-making units. European journal of operational research, 3(4), 1–339. https://doi.org/10.1016/0377-2217(78)90138-8
  3. [3] Cook, W. D., & Zhu, J. (2014). Data envelopment analysis: A handbook of modeling internal structure and network. https://doi.org/10.1007/978-1-4899-8068-7
  4. [4] Malmquist, S. (1953). Index numbers and indifference surfaces. Trabajos de estadística, 4(2), 209-242. https://doi.org/10.1007/BF03006863
  5. [5] Xu, Y., Park, Y. S., Park, J. D., & Cho, W. (2021). Evaluating the environmental efficiency of the US airline industry using a directional distance function DEA approach. Journal of management analytics, 8(1), 1–18. https://doi.org/10.1080/23270012.2020.1832925
  6. [6] Li, M., Wang, X., Agyeman, F. O., Gao, Y., & Sarfraz, M. (2023). Efficiency evaluation and the impact factors of sustainable forestry development in China: Adoption of super-efficiency data envelopment analysis and malmquist index methods. Forests, 14(5), 909. https://doi.org/10.3390/f14050909
  7. [7] Diwan, R. K. (1968). On the cobb douglas production function. Southern economic journal, 410–414. https://doi.org/10.2307/1055504
  8. [8] Yang, L., & Zhang, X. (2018). Assessing regional eco-efficiency from the perspective of resource, environmental and economic performance in China: A bootstrapping approach in global data envelopment analysis. Journal of cleaner production, 173, 100–111. https://doi.org/10.1016/j.jclepro.2016.07.166
  9. [9] Nedaei, H., Naini, S. G. J., & Makui, A. (2021). A DEA approach to measuring teammate-adjusted efficiencies incorporating learning expectations: An application to Oil & Gas wells drilling. International journal of industrial engineering, 32(1), 47–64. https://www.sid.ir/fileserver/je/2005-275628-en-1117467.pdf
  10. [10] Mahmoudi, R., & Emrouznejad, A. (2023). A multi-period performance analysis of airlines: A game-SBM-NDEA and Malmquist Index approach. Research in transportation business & management, 46, 100801. https://doi.org/10.1016/j.rtbm.2022.100801
  11. [11] Tone, K., Kweh, Q. L., Lu, W. M., & Ting, I. W. K. (2019). Modeling investments in the dynamic network performance of insurance companies. Omega, 88, 237–247. https://doi.org/10.1016/j.omega.2018.09.005
  12. [12] Pittman, R. W. (1983). Multilateral productivity comparisons with undesirable outputs. The economic journal, 93(372), 883–891. https://doi.org/10.2307/2232753
  13. [13] Caves, D. W., Christensen, L. R., & Diewert, W. E. (1982). The economic theory of index numbers and the measurement of input, output, and productivity. Econometrica: journal of the econometric society, 1393–1414. https://doi.org/10.2307/1913388
  14. [14] Tone, K. (2015). Dealing with undesirable outputs in DEA: A slacks-based measure (SBM) approach. GRIPS discussion papers, 1. https://grips.repo.nii.ac.jp/?action=repository_action_common_download&item_id=955&item_no=1&attribute_id=20&file_no=1
  15. [15] Wang, C. N., Dang, T. T., Wang, J. W. (2022). Assessing Asian economies renewable energy consumption efficiency using DEA with undesirable output. Computer systems science & engineering, 43(1). https://openurl.ebsco.com
  16. [16] Zhu, J., & Lin, B. (2022). Economic growth pressure and energy efficiency improvement: Empirical evidence from Chinese cities. Applied energy, 307, 118275. https://doi.org/10.1016/j.apenergy.2021.118275
  17. [17] Li, Y., Wang, J., Liu, B., Li, H., Guo, Y., & Guo, X. (2023). Regional green total factor performance analysis of China’s construction industry based on a unified framework combining static and dynamic indexes. Environmental science and pollution research, 30(10), 26874–26888. https://doi.org/10.1007/s11356-022-23980-z
  18. [18] Tavana, M., Toloo, M., Aghayi, N., & Arabmaldar, A. (2021). A robust cross-efficiency data envelopment analysis model with undesirable outputs. Expert systems with applications, 167, 114117. https://doi.org/10.1016/j.eswa.2020.114117
  19. [19] Bhardwaj, B., Kaur, J., & Kumar, A. (2017). A new fuzzy CCR data envelopment analysis model and its application to manufacturing enterprises. In Soft computing applications for group decision-making and consensus modeling (pp. 345–368). Springer. https://doi.org/10.1007/978-3-319-60207-3_21
  20. [20] Toloo, M., & Hančlová, J. (2020). Multi-valued measures in DEA in the presence of undesirable outputs. Omega, 94, 102041. https://doi.org/10.1016/j.omega.2019.01.010
  21. [21] Lee, H.-S. (2021). An integrated model for SBM and Super-SBM DEA models. Journal of the operational research society, 72(5), 1174–1182. https://doi.org/10.1080/01605682.2020.1755900
  22. [22] Asanimoghadam, K., Salahi, M., Jamalian, A., & Shakouri, R. (2022). A two-stage structure with undesirable outputs: slacks-based and additive slacks-based measures DEA models. RAIRO-operations research, 56(4), 2513–2534. https://doi.org/10.1051/ro/2022117
  23. [23] Salahi, M., Jamalian, A., Shakouri, R., & Asanimoghadam, K. (2022). Additive slack-based measure for a two-stage structure with shared inputs and undesirable feedback. Advances in operations research, 2022(1), 7596736. https://doi.org/10.1155/2022/7596736
  24. [24] Shakouri, R., Salahi, M., & Kordrostami, S. (2020). Stochastic p-robust DEA efficiency scores approach to banking sector. Journal of modelling in management, 15(3), 893–917. https://doi.org/10.1108/JM2-01-2019-0014
  25. [25] Zhang, X., Li, R., & Zhang, J. (2022). Understanding the green total factor productivity of manufacturing industry in China: analysis based on the super-SBM model with undesirable outputs. Sustainability, 14(15), 9310. https://doi.org/10.3390/su14159310
  26. [26] Kuang, B., Lu, X., Zhou, M., & Chen, D. (2020). Provincial cultivated land use efficiency in China: Empirical analysis based on the SBM-DEA model with carbon emissions considered. Technological forecasting and social change, 151, 119874. https://doi.org/10.1016/j.techfore.2019.119874
  27. [27] Arabi, B., Doraisamy, S. M., Emrouznejad, A., & Khoshroo, A. (2017). Eco-efficiency measurement and material balance principle: An application in power plants Malmquist Luenberger Index. Annals of operations research, 255(1), 221–239. https://doi.org/10.1007/s10479-015-1970-x
  28. [28] Peykani, P., Hosseinzadeh Lotfi, F., Sadjadi, S. J., Ebrahimnejad, A., & Mohammadi, E. (2022). Fuzzy chance-constrained data envelopment analysis: a structured literature review, current trends, and future directions. Fuzzy optimization and decision making, 21(2), 197–261. https://doi.org/10.1007/s10700-021-09364-x
  29. [29] Khaksar, M., & Malakoutian, M. M. A. (2020). Productivity evaluation for banking system in developing countries: DEA malmquist productivity index based on CCR, BCC, CCR-BCC (a case study). Eng transactions, 1, 186. https://hal.science/hal-03221338/
  30. [30] Salahi, M., Torabi, N., & Amiri, A. (2016). An optimistic robust optimization approach to common set of weights in DEA. Measurement, 93, 67–73. https://doi.org/10.1016/j.measurement.2016.06.049
  31. [31] Salahi, M., Toloo, M., & Hesabirad, Z. (2019). Robust Russell and enhanced Russell measures in DEA. Journal of the operational research society, 70(8), 1275–1283. https://doi.org/10.1080/01605682.2018.1489353
  32. [32] Salahi, M., Toloo, M., & Torabi, N. (2021). A new robust optimization approach to common weights formulation in DEA. Journal of the operational research society, 72(6), 1390–1402. https://doi.org/10.1080/01605682.2020.1718016
  33. [33] Soltanzadeh, E., & Omrani, H. (2018). Dynamic network data envelopment analysis model with fuzzy inputs and outputs: An application for Iranian Airlines. Applied soft computing journal, 63, 268–288. https://doi.org/10.1016/j.asoc.2017.11.031
  34. [34] Akbarian, D. (2020). Overall profit Malmquist productivity index under data uncertainty. Financial innovation, 6(1), 6. https://doi.org/10.1186/s40854-020-0170-0
  35. [35] Shakouri, R., Salahi, M., & Kordrostami, S. (2019). Stochastic p-robust approach to two-stage network DEA model. Quantitative finance and economics, 3(2), 315–346. https://www.aimspress.com/fileOther/PDF/QFE/QFE-03-02-315.pdf
  36. [36] Mehdizadeh, S., Amirteimoori, A. R., Behzadi, M. H., & Kordrostami, S. (2020). Stochastic two-stage network-structures under P-models: a DEA based approach. International journal of industrial mathematics, 12(3), 1332. https://www.researchgate.net
  37. [37] Chavas, J. P., & Cox, T. L. (1997). Production analysis: A non-parametric time series application to US agriculture. Journal of agricultural economics, 48(1–3), 330–348. https://doi.org/10.1111/j.1477-9552.1997.tb01158.x
  38. [38] Hailu, A., & Veeman, T. S. (2001). Non-parametric productivity analysis with undesirable outputs: an application to the Canadian pulp and paper industry. American journal of agricultural economics, 83(3), 605–616. https://doi.org/10.1111/0002-9092.00181
  39. [39] Kuosmanen, T., & Matin, R. K. (2011). Duality of weakly disposable technology. Omega, 39(5), 504–512. https://doi.org/10.1016/j.omega.2010.10.008
  40. [40] Fakhru’l-Razi, A., Pendashteh, A., Abdullah, L. C., Biak, D. R. A., Madaeni, S. S., & Abidin, Z. Z. (2009). Review of technologies for oil and gas produced water treatment. Journal of hazardous materials, 170(2–3), 530–551. https://doi.org/10.1016/j.jhazmat.2009.05.044
  41. [41] Snyder, L. V, & Daskin, M. S. (2006). Stochastic p-robust location problems. Iie transactions, 38(11), 971–985. https://doi.org/10.1080/07408170500469113

Downloads

Published

2025-05-27

Issue

Vol. 1 No. 2 (2025): Annals of Optimization With Applications (ANOWA)

Section

Articles

How to Cite

Shakouri, R. ., & Shakouri, R. . . (2025). Malmquist Productivity Index to a Two-Stage Structure in the Presence of Uncertain Data. Annals of Optimization With Applications, 1(2), 119-140. https://doi.org/10.48314/anowa.v1i2.48

Similar Articles

1-10 of 11

You may also start an advanced similarity search for this article.