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Origin and Evolution of Malmquist Productivity Index: Review of the Literature Cover

Origin and Evolution of Malmquist Productivity Index: Review of the Literature

Open Access
|Apr 2025

References

  1. Aigner, D., Lovell, C. A. K., & Schmidt, P. (1977). Formulation and Estimation of Stochastic Frontier Production Function Models. Journal of Econometrics, 6(1), 21–37. https://doi.org/10.1016/0304-4076(77)90052-5">https://doi.org/10.1016/0304-4076(77)90052-5
  2. Afsharian, M., Ahn, H., & Harms, S. G. (2018). A Non-Convex Meta-Frontier Malmquist Index for Measuring Productivity Over Time. IMA Journal of Management Mathematics, 29(4), 377–392. https://doi.org/10.1093/imaman/dpx007">https://doi.org/10.1093/imaman/dpx007
  3. Althin, R. (2001). Measurement of Productivity Changes: Two Malmquist Index Approaches. Journal of Productivity Analysis, 16(2), 107–128. https://doi.org/10.1023/A:1011682625976">https://doi.org/10.1023/A:1011682625976
  4. Álvarez, I. C., Barbero, J., & Zofío, J. L. (2020). A Data Envelopment Analysis Toolbox for MATLAB. Journal of Statistical Software, 95(3), 1–49. https://doi.org/10.18637/jss.v095.i03">https://doi.org/10.18637/jss.v095.i03
  5. Amirteimoori, A., Emrouznejad, A., & Khoshandam, L. (2013). Classifying Flexible Measures in Data Envelopment Analysis: A Slack-Based Measure. Measurement, 46(10), 4100–4107. https://doi.org/10.1016/j.measurement.2013.08.019">https://doi.org/10.1016/j.measurement.2013.08.019
  6. Asmild, M., Paradi, J. C., Aggarwall, V., & Schaffnit, C. (2004). Combining DEA Window Analysis With the Malmquist Index Approach in a Study of the Canadian Banking Industry. Journal of Productivity Analysis, 21(1), 67–89. https://doi.org/10.1023/B:PROD.0000012453.91326.ec">https://doi.org/10.1023/B:PROD.0000012453.91326.ec
  7. Balk, B. M. (1993). Malmquist Productivity Indexes and Fisher Ideal Indexes: Comment. The Economic Journal, 103(418), 680–682. https://doi.org/10.2307/2234540">https://doi.org/10.2307/2234540
  8. Balk, B. M. (2001). Scale Efficiency and Productivity Change. Journal of Productivity Analysis, 15(3), 159–183. https://doi.org/10.1023/A:1011117324278">https://doi.org/10.1023/A:1011117324278
  9. Balk, B. M., Barbero, J., & Zofío, J. L. (2020). A Toolbox for Calculating and Decomposing Total Factor Productivity Indices. Computers & Operations Research, 115, 104853. https://doi.org/10.1016/j.cor.2019.104853">https://doi.org/10.1016/j.cor.2019.104853
  10. Banker, R. D., Charnes, A., & Cooper, W. W. (1984). Some Models for Estimating Technical and Scale Inefficiencies in Data Envelopment Analysis. Management Science, 30(9), 1078–1092. https://doi.org/10.1287/mnsc.30.9.1078">https://doi.org/10.1287/mnsc.30.9.1078
  11. Bansal, P., & Mehra, A. (2022). Malmquist-Luenberger Productivity Indexes for Dynamic Network DEA With Undesirable Outputs and Negative Data. RAIRO - Operations Research, 56(2), 649–687. https://doi.org/10.1051/ro/2022023">https://doi.org/10.1051/ro/2022023
  12. Benitez, R., Coll Serrano, V., & Bolós, V. (2021). deaR-Shiny: An Interactive Web App for Data Envelopment Analysis. Sustainability, 13, 6774. https://doi.org/10.3390/su13126774">https://doi.org/10.3390/su13126774
  13. Berg, S. A., Førsund, F. R., & Jansen E. S. (1992). Malmquist Indices of Productivity Growth During the Deregulation of Norwegian Banking, 1980–89. Scandinavian Journal of Economics (Supplement), 94, 211–228. https://doi.org/10.2307/3440261">https://doi.org/10.2307/3440261
  14. Bjurek, H. (1996). The Malmquist Total Factor Productivity Index. The Scandinavian Journal of Economics, 98, 303. https://doi.org/10.2307/3440861">https://doi.org/10.2307/3440861
  15. Brennan, S., Haelermans, C., & Ruggiero, J. (2014). Nonparametric Estimation of Education Productivity with an Application to Dutch Schools. European Journal of Operational Research, 234(3), 809. https://doi.org/10.1016/j.ejor.2013.10.030">https://doi.org/10.1016/j.ejor.2013.10.030
  16. Brzezicki, Ł. (2017). Efektywność Działalności Dydaktycznej Polskiego Szkolnictwa Wyższego. Wiadomości Statystyczne. The Polish Statistician, 62(11), 56–73. https://doi.org/10.5604/01.3001.0014.1066">https://doi.org/10.5604/01.3001.0014.1066
  17. Brzezicki, Ł., & Łącka, I. (2022). Cost Efficiency of Administrative Service in Public Higher Education in Poland. Scientific Papers of Silesian University of Technology – Organization and Management, 156, 81–98. 10.29119/1641-3466.2022.156.6">http://dx.doi.org/10.29119/1641-3466.2022.156.6
  18. Brzezicki, Ł. (2025). Different Paths for Modification of the Malmquist Index: A Review of the Literature (Working Paper 1/2025). 10.13140/RG.2.2.20886.05449">http://dx.doi.org/10.13140/RG.2.2.20886.05449
  19. Camanho, A. S., & Dyson, R. G. (2006). Data Envelopment Analysis and Malmquist Indices for Measuring Group Performance. Journal of Productivity Analysis, 26(1), 35–49. https://doi.org/10.1007/s11123-006-0004-8">https://doi.org/10.1007/s11123-006-0004-8
  20. 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, 50, 1393–1414. https://doi.org/10.2307/1913388">https://doi.org/10.2307/1913388
  21. Chambers, R. G., Chung, Y., & Färe, R. (1996). Benefit and Distance Functions. Journal of Economic Theory, 70(2), 407–419. https://doi.org/10.1006/jeth.1996.0096">https://doi.org/10.1006/jeth.1996.0096
  22. Charnes, A., Cooper, W. W., & Rhodes, E. (1978). Measuring the Efficiency of Decision Making Units. European Journal of Operational Research, 2, 429–444. https://doi.org/10.1016/0377-2217(78)90138-8">https://doi.org/10.1016/0377-2217(78)90138-8
  23. Chen, Y. (2003). A Non-Radial Malmquist Productivity Index With an Illustrative Application to Chinese Major Industries. International Journal of Production Economics, 83(1), 27–35. https://doi.org/10.1016/S0925-5273(02)00267-0">https://doi.org/10.1016/S0925-5273(02)00267-0
  24. Chung, Y. H., Färe, R., & Grosskopf, S. (1997). Productivity and Undesirable Outputs: A Directional Distance Function Approach. Journal of Environmental Management, 51(3), 229–240. https://doi.org/10.1006/jema.1997.0146">https://doi.org/10.1006/jema.1997.0146
  25. Cooper, W. W., Seiford, L. M., & Tone, K. (2007). Data Envelopment Analysis: A Comprehensive Text With Models, Applications, References and DEA-Solver Software. New York: Springer.
  26. Daraio, C., Kerstens, K. H. J., Nepomuceno, T. C. C., & Sickles, R. (2019). Productivity and Efficiency Analysis Software: An Exploratory Bibliographical Survey of The Options. Journal of Economic Surveys, 33(1), 85–100. https://doi.org/10.1111/joes.12270">https://doi.org/10.1111/joes.12270
  27. Daraio, C., Kerstens, K., Nepomuceno, T., & Sickles, R. C. (2020). Empirical Surveys of Frontier Applications: A Meta-Review. International Transactions in Operational Research, 27, 709–738. https://doi.org/10.1111/itor.12649">https://doi.org/10.1111/itor.12649
  28. Ding, L., Yang, Y., Wang, W., & Calin, A. C. (2019). Regional Carbon Emission Efficiency and its Dynamic Evolution in China: A Novel Cross Efficiency-Malmquist Productivity Index. Journal of Cleaner Production, 241, 118260. https://doi.org/10.1016/j.jclepro.2019.118260">https://doi.org/10.1016/j.jclepro.2019.118260
  29. Dorri, N. M., & Rostamy-Malkhalifeh, M. (2017). Malmquist Productivity Index in Ratio Data Envelopment Analysis. Data Envelopment Analysis and Decision Science, 2017, 7–13.
  30. Emrouznejad, A., & Thanassoulis, E. (2010). Measurement of Productivity Index With Dynamic DEA. International Journal of Operational Research, 8(2), 247–260. https://doi.org/10.1504/IJOR.2010.033140">https://doi.org/10.1504/IJOR.2010.033140
  31. Emrouznejad, A., Rostamy-Malkhalifeh, M., Hatami-Marbini, A., Tavana, M., & Aghayi, N. (2011). An Overall Profit Malmquist Productivity Index with Fuzzy and Interval Data. Mathematical and Computer Modelling, 54(11), 2827–2838. https://doi.org/10.1016/j.mcm.2011.07.003">https://doi.org/10.1016/j.mcm.2011.07.003
  32. Emrouznejad, A., Tavana M., & Hatami-Marbini, A. (2014). The State of the Art in Fuzzy Data Envelopment Analysis. In A. Emrouznejad & M. Tavana (Eds.), Performance Measurement with Fuzzy Data Envelopment Analysis (pp. 1–45). Berlin: Springer. https://doi.org/10.1007/978-3-642-41372-8_1">https://doi.org/10.1007/978-3-642-41372-8_1
  33. Emrouznejad, A., Brzezicki, Ł., & Lu, C. (2025). The Development and Evolution of Slacks-Based Measure Models in Data Envelopment Analysis: A Comprehensive Review of the Literature. Journal of Economic Surveys. https://doi.org/10.1111/joes.12682">https://doi.org/10.1111/joes.12682
  34. Seyed Esmaeili, F. S., Rostamy-Malkhalifeh, M., & Hosseinzadeh Lotfi, F. (2022). Interval Network Malmquist Productivity Index for Examining Productivity Changes of Insurance Companies under Data Uncertainty: A Case Study. Journal of Mathematical Extension, 16(8), 1–7. https://doi.org/10.30495/JME.2022.1503">https://doi.org/10.30495/JME.2022.1503
  35. Essid, H., Ouellette, P., & Vigeant, S. (2014). Productivity, Efficiency, and Technical Change of Tunisian Schools: A Bootstrapped Malmquist Approach with Quasi-Fixed Inputs. Omega, 42(1), 88–97. https://doi.org/10.1016/j.omega.2013.04.001">https://doi.org/10.1016/j.omega.2013.04.001
  36. Fallahnejad, R., Mozaffari, M. R., Wanke, P. F., & Tan, Y. (2024). Nash Bargaining Game Enhanced Global Malmquist Productivity Index for Cross-Productivity Index. Games, 15(1), 3. https://doi.org/10.3390/g15010003">https://doi.org/10.3390/g15010003
  37. Färe, R., & Lovell, C. A. K. (1978). Measuring the Technical Efficiency of Production. Journal of Economic Theory, 19(1), 150–162. https://doi.org/10.1016/0022-0531(78)90060-1">https://doi.org/10.1016/0022-0531(78)90060-1
  38. Färe, R., Grosskopf, S., & Lovell, C. A. K. (1985). The Measurement of Efficiency of Production. Dordrecht: Springer.
  39. Färe, R., Grosskopf, S., Lindgren, B., & Roos, P. (1989a). Productivity Developments in Swedish Hospitals: A Malmquist Output Index Approach (Discussion Paper 89–3). Department of Economics, Southern Illinois University, Carbondale.
  40. Färe, R., Grosskopf, S., Lovell, C., & Pasurka, C. (1989b). Multilateral Productivity Comparisons When Some Outputs Are Undesirable: A Nonparametric Approach. The Review of Economics and Statistics, 71, 90–98. https://doi.org/10.2307/1928055">https://doi.org/10.2307/1928055
  41. Färe, R., Grosskopf, S., Yaisawarng, S., Li, S. K., & Wang, Z. (1990). Productivity Growth in Illinois Electric Utilities. Resources and Energy, 12(4), 383–398. https://doi.org/10.1016/0165-0572(90)90030-M">https://doi.org/10.1016/0165-0572(90)90030-M
  42. Färe, R., & Grosskopf, S. (1992). Malmquist Productivity Indexes and Fisher Ideal Indexes. The Economic Journal, 102(410), 158–160. https://doi.org/10.2307/2234861">https://doi.org/10.2307/2234861
  43. Färe, R., Grosskopf, S., Lindgren, B., & Roos, P. (1992). Productivity Changes in Swedish Pharamacies 1980–1989: A Non-Parametric Malmquist Approach. The Journal of Productivity Analysis, 3, 85–101. https://doi.org/10.1007/BF00158770">https://doi.org/10.1007/BF00158770
  44. Färe, R., Grosskopf, S., Lindgren, B., & Roos, P. (1994a). Productivity Change in Swedish Hospitals: A Malmquist Output Index Approach. In: A. Charnes, W. W. Cooper, A. Y. Lewin, & M. L. Seiford (Eds.), Data Envelopment Analysis: Theory, Methodology and Applications (pp. 253–272). Boston: Kluwer Academic Publishers.
  45. Färe, R., Grosskopf, S., Norris, M., & Zhang, Z. (1994b). Productivity Growth, Technical Progress, and Efficiency Change in Industrialized Countries. The American Economic Review, 84(1), 66–83.
  46. Färe, R., Grosskopf, S., & Roos, P. (1995). Productivity and Quality Changes in Swedish Pharmacies. International Journal of ProductionEconomics, 39(1), 137– 144. https://doi.org/10.1016/0925-5273(94)00063-G">https://doi.org/10.1016/0925-5273(94)00063-G
  47. Färe, R., & Grosskopf, S. (1996). Intertemporal Production Frontiers: With Dynamic DEA. Dordrecht: Kluwer Academic Publishers. https://doi.org/10.1007/978-94-009-1816-0">https://doi.org/10.1007/978-94-009-1816-0
  48. Färe, R., Grifell-Tatje, E., Grosskopf, S., & Lovell, C.A.K. (1997). Biased Technical Change and the Malmquist Productivity Index. Scandinavian Journal of Economics, 99(1), 119–127. https://doi.org/10.1111/1467-9442.00051">https://doi.org/10.1111/1467-9442.00051
  49. Färe, R., Grosskopf, S., & Roos, P. (1998). Malmquist Productivity Indexes: A Survey of Theory and Practice. In R. Färe, S. Grosskopf, R. R. Russell (Eds.), Index Numbers: Essays in Honour of Sten Malmquist. Dordrecht: Springer. https://doi.org/10.1007/978-94-011-4858-0_4">https://doi.org/10.1007/978-94-011-4858-0_4
  50. Färe, R., & Grosskopf, S. (2000). Network DEA. Socio-Economic Planning Sciences, 34(1), 35–49. https://doi.org/10.1016/S0038-0121(99)00012-9">https://doi.org/10.1016/S0038-0121(99)00012-9
  51. Färe, R., Førsund, F. R., Grosskopf, S., Hayes, K., & Heshmati, A. (2001). A Note on Decomposing the Malmquist Productivity Index by Means of Subvector Homotheticity. Economic Theory, 17(1), 239–245. https://doi.org/10.1007/PL00004101">https://doi.org/10.1007/PL00004101
  52. Färe, R., & Zelenyuk, V. (2003). On Aggregate Farrell Efficiencies. European Journal of Operational Research, 146(3), 615–620. https://doi.org/10.1016/S0377-2217(02)00259-X">https://doi.org/10.1016/S0377-2217(02)00259-X
  53. Färe, R., Grosskopf, S., Forsund, F. R., Hayes, K., & Heshmati, A. (2006). Measurement of Productivity and Quality in Non‐Marketable Services. Quality Assurance in Education, 14(1), 21–36. https://doi.org/10.1108/09684880610643593">https://doi.org/10.1108/09684880610643593
  54. Färe, R., Grosskopf, S., & Margaritis, D. (2008). Efficiency and Productivity: Malmquist and More. In H. O. Fried, C. A. K. Lovell, & S. S. Schmidt (Eds.), The Measurement of Productive Efficiency and Productivity Change (pp. 522–621). Oxford: Oxford University Press.
  55. Färe, R., Grosskopf, S., Margaritis, D., & Weber, W. L. (2018). Dynamic Efficiency and Productivity. In E. Grifell-Tatjé, C. A. K. Lovell, & R. C. Sickles (Eds.), The Oxford Handbook of Productivity Analysis (pp. 183–210). New York: Oxford University Press. https://doi.org/10.1093/oxfordhb/9780190226718.013.5">https://doi.org/10.1093/oxfordhb/9780190226718.013.5
  56. Färe, R., & Zelenyuk, V. (2021). On Aggregation of Multi-Factor Productivity Indexes. Journal of Productivity Analysis, 55(2), 107–133. https://doi.org/10.1007/s11123-021-00598-w">https://doi.org/10.1007/s11123-021-00598-w
  57. Farrell, M. J. (1957). The Measurement of Productive Efficiency. Journal of Royal Statistical Society, Series A, 120(III), 253–290. https://doi.org/10.2307/2343100">https://doi.org/10.2307/2343100
  58. Fixler, D., & Zieschang, K. D. (1992). Incorporating Ancillary Measures of Process and Quality Change into a Superlative Productivity Index. Journal of Productivity Analysis, 2(4), 245–267. https://doi.org/10.1007/BF00156469">https://doi.org/10.1007/BF00156469
  59. Førsund, F. R. (1998). The Rise and Fall of Slacks: Comments on Quasi-Malmquist Productivity Indices. Journal of Productivity Analysis, 10(1), 21–34. https://doi.org/10.1023/A:1018342214700">https://doi.org/10.1023/A:1018342214700
  60. Førsund, F. R. (2016). Productivity Interpretations of the Farrell Efficiency Measures and the Malmquist Index and its Decomposition. In: J. Aparicio, C. Lovell, & J. Pastor, (Eds.), Advances in Efficiency and Productivity (pp. 121–147). Cham: Springer.
  61. Fukuyama, H., & Weber, W. L. (2001). Efficiency and Productivity Change of Non-Life Insurance Companies in Japan. Pacific Economic Review, 6, 129– 146. https://doi.org/10.1111/1468-0106.00122">https://doi.org/10.1111/1468-0106.00122
  62. Grifell-Tatjé, E., & Lovell, C. A. K. (1995). A Note on the Malmquist Productivity Index. Economics Letters, 47(2), 169–175. https://doi.org/10.1016/0165-1765(94)00497-P">https://doi.org/10.1016/0165-1765(94)00497-P
  63. Grifell-Tatjé, E., Lovell, C. A. K., & Pastor, J. T. (1998). A Quasi-Malmquist Productivity Index. Journal of Productivity Analysis, 10(1), 7–20. https://doi.org/10.1023/A:1018329930629">https://doi.org/10.1023/A:1018329930629
  64. Grosskopf, S. (2003). Some Remarks on Productivity and its Decompositions. Journal of Productivity Analysis, 20, 459–474. https://doi.org/10.1023/A:1027364119672">https://doi.org/10.1023/A:1027364119672
  65. Hatami-Marbini, A., & Toloo, M. (2019). Data Envelopment Analysis Models With Ratio Data: A Revisit. Computers & Industrial Engineering, 133, 331–338. https://doi.org/10.1016/j.cie.2019.04.041">https://doi.org/10.1016/j.cie.2019.04.041
  66. Hosseinzadeh Lotfi, F., Jahanshahloo, G. R., Shahverdi, R., & Rostamy-Malkhalifeh, M. (2007). Cost Efficiency and Cost Malmquist Productivity Index With Interval Data. International Mathematical Forum, 2(9), 441–453
  67. Kao, C. (2014). Network Data Envelopment Analysis: A Review. European Journal of Operational Research, 239(1), 1–16. https://doi.org/10.1016/j.ejor.2014.02.039">https://doi.org/10.1016/j.ejor.2014.02.039
  68. Kao, C., & Hwang, S. -N. (2014). Multi-Period Efficiency and Malmquist Productivity Index in Two-Stage Production Systems. European Journal of Operational Research, 232(3), 512–521. https://doi.org/10.1016/j.ejor.2013.07.030">https://doi.org/10.1016/j.ejor.2013.07.030
  69. Kao, C. (2017). Measurement and Decomposition of the Malmquist Productivity Index for Parallel Production Systems. Omega, 67, 54–59. https://doi.org/10.1016/j.omega.2016.04.001">https://doi.org/10.1016/j.omega.2016.04.001
  70. Khalili-Damghani, K., & Haji-Sami, E. (2018). Productivity of Steam Power-Plants Using Uncertain DEA-Based Malmquist Index in the Presence of undesirable outputs. International Journal of Information and Decision Sciences, 10(2), 162–180. https://dx.doi.org/10.1504/IJIDS.2018.092422
  71. Khoshroo, A., Izadikhah, M., & Emrouznejad, A. (2022). Total Factor Energy Productivity Considering Undesirable Pollutant Outputs: A New Double Frontier Based Malmquist Productivity Index. Energy, 258, 124819. https://doi.org/10.1016/j.energy.2022.124819">https://doi.org/10.1016/j.energy.2022.124819
  72. Koronakos, G. (2019). A Taxonomy and Review of the Network Data Envelopment Analysis Literature. In G. Tsihrintzis, M. Virvou, E. Sakkopoulos, & L. Jain (Eds.), Machine Learning Paradigms. Learning and Analytics in Intelligent Systems (pp. 255–311). Cham: Springer. https://doi.org/10.1007/978-3-030-15628-2_9">https://doi.org/10.1007/978-3-030-15628-2_9
  73. Łącka, I., & Brzezicki, Ł. (2023). The Efficiency of Scientific Activities and Technology Transfer in Higher Education in Poland. Social Inequalities and Economic Growth, (75), 62–89. https://doi.org/10.15584/nsawg.2023.3.4">https://doi.org/10.15584/nsawg.2023.3.4
  74. Lovell, C. A. K., Grosskopf, S., Ley, E., Pastor, J. T., Prior, D., & Vanden Eeckaut, P. (1994). Linear Programming Approaches to the Measurement and Analysis of Productive Efficiency. Top, 2(2), 175–248. https://doi.org/10.1007/BF02574810">https://doi.org/10.1007/BF02574810
  75. Lovell, C. A. K. (2003). The Decomposition of Malmquist Productivity Indexes. Journal of Productivity Analysis, 20, 437–458. https://doi.org/10.1023/A:1027312102834">https://doi.org/10.1023/A:1027312102834
  76. Lu, W. -M., Kweh, Q. L., & Ting, I. W. K. (2024). Overlooked Effect of Negative Data on Efficiency Analysis. OPSEARCH. https://doi.org/10.1007/s12597-024-00797-7">https://doi.org/10.1007/s12597-024-00797-7
  77. Malmquist, S. (1953). Index Numbers and Indifference Surfaces. Trabajos de Estatistica, 4, 209– 242. https://doi.org/10.1007/BF03006863">https://doi.org/10.1007/BF03006863
  78. Maniadakis, N., & Thanassoulis, E. (2004). A Cost Malmquist Productivity Index. European Journal of Operational Research, 154, 396–409. https://doi.org/10.1016/S0377-2217(03)00177-2">https://doi.org/10.1016/S0377-2217(03)00177-2
  79. Mariz, F. B., Almeida, M. R., & Aloise, D. (2018). A Review of Dynamic Data Envelopment Analysis: State of the Art and Applications. International Transactions in Operational Research, 25, 469–505. https://doi.org/10.1111/itor.12468">https://doi.org/10.1111/itor.12468
  80. Mergoni, A., Emrouznejad, A., & De Witte, K. (2025). Fifty Years of Data Envelopment Analysis. European Journal of Operational Research, 1–25. https://doi.org/10.1016/j.ejor.2024.12.049">https://doi.org/10.1016/j.ejor.2024.12.049
  81. Meeusen, W., & van Den Broeck, J. (1977). Efficiency Estimation from Cobb-Douglas Production Functions with Composed Error. International Economic Review, 18, 435–444. 10.2307/2525757">http://dx.doi.org/10.2307/2525757
  82. Mohammadi, N., & Yousefpour, A. (2014). The Biennial Malmquist Index in The Of Negative Data. Journal of Mathematics and Computer Science, 12(1), 1–11. 10.22436/jmcs.012.01.01">http://dx.doi.org/10.22436/jmcs.012.01.01
  83. Nankali, P., Alirezaee, M., & Rakhshan, F. (2022). Malmquist Productivity Index Using the Concept of Loyalty Factor in Bank Branches. Journal of Industrial and Systems Engineering, 14(3), 69–83.
  84. Navanbakhsh, M., Jahanshahloo, G. R., Hosseinzadeh Lotfi, F., & Taeb, Z. (2006). Revenue Malmquist Productivity Index and Application in Bank Branch. International Mathematical Forum, 1(25), 1233– 1247. 10.12988/imf.2006.06102">http://dx.doi.org/10.12988/imf.2006.06102
  85. O’Donnell, C. J., Rao, D. S. P., & Battese, G. E. (2008). Metafrontier Frameworks for the Study of Firm-Level Efficiencies and Technology Ratios. Empirical Economics, 34(2), 231–255. https://doi.org/10.1007/s00181-007-0119-4">https://doi.org/10.1007/s00181-007-0119-4
  86. Oh, D. -h., & Lee, J. -d. (2010). A Metafrontier Approach for Measuring Malmquist Productivity Index. Empirical Economics, 38(1), 47–64. https://doi.org/10.1007/s00181-009-0255-0">https://doi.org/10.1007/s00181-009-0255-0
  87. Pastor, J. T., & Lovell, C. K. (2005). A Global Malmquist Productivity Index. Economics Letters, 88(2), 266–271. https://doi.org/10.1016/j.econlet.2005.02.013">https://doi.org/10.1016/j.econlet.2005.02.013
  88. Pastor, J. T., & Lovell, C. A. K. (2007). Circularity of the Malmquist Productivity Index. Economic Theory, 33(3), 591–599. https://doi.org/10.1007/s00199-006-0169-4">https://doi.org/10.1007/s00199-006-0169-4
  89. Pastor, J. T., Asmild, M., & Lovell, C. (2011). The Biennial Malmquist Productivity Change Index. Socio-Economic Planning Sciences, 45(1), 10–15. https://doi.org/10.1016/j.seps.2010.09.001">https://doi.org/10.1016/j.seps.2010.09.001
  90. Pastor, J. T., Aparicio, J., & Zofío, J. L. (2022). Benchmarking Economic Efficiency. Technical and Allocative Fundamentals. Cham: Springer.
  91. Peykani, P., & Seyed Esmaeili, F. S. (2021). Malmquist Productivity Index under Fuzzy Environment. Fuzzy Optimization and Modelling Journal, 2(4), 10–19. https://doi.org/10.30495/FOMJ.2021.1940660.1038">https://doi.org/10.30495/FOMJ.2021.1940660.1038
  92. Peykani, P., Farzipoor Saen, R., Seyed Esmaeili, F. S., & Gheidar-Kheljani, J. (2021). Window Data Envelopment Analysis Approach: A Review and Bibliometric Analysis. Expert Systems, 38(7), e12721. https://doi.org/10.1111/exsy.12721">https://doi.org/10.1111/exsy.12721
  93. Portela, M., Thanassoulis, E., & Simpson, G. (2004). Negative Data in DEA: A Directional Distance Approach Applied to Bank Branches. Journal of the Operational Research Society, 55(10), 1111–1121. https://doi.org/10.1057/palgrave.jors.2601768">https://doi.org/10.1057/palgrave.jors.2601768
  94. Portela, M. C. A. S., & Thanassoulis, E. (2010). Malmquist-Type Indices in the Presence of Negative Data: An Application to Bank Branches. Journal of Banking & Finance, 34(7), 1472–1483. https://doi.org/10.1016/j.jbankfin.2010.01.004">https://doi.org/10.1016/j.jbankfin.2010.01.004
  95. Ray, S. C., & Desli, E. (1997). Productivity Growth, Technical Progress and Efficiency Change in Industrialized Countries: Comment. The American Economic Review, 87, 1033–1039.
  96. Russell, R. R. (2018). Theoretical Productivity Indices. In E. Grifell-Tatjé, C. A. K. Lovell, & R. C. Sickles (Eds.), The Oxford Handbook of Productivity Analysis (pp. 153–182). New York: Oxford University Press. https://doi.org/10.1093/oxfordhb/9780190226718.013.4">https://doi.org/10.1093/oxfordhb/9780190226718.013.4
  97. Shahkooeei, M., Balf, F. R., Rabbani, M., & Jelodar, M. F. (2022). Role of Flexible Data in Evaluation Productivity and Cost Efficiency Using Data Envelopment Analysis. RAIRO-Operations Research, 56(6), 4113–4127. https://doi.org/10.1051/ro/2022181">https://doi.org/10.1051/ro/2022181
  98. Shephard, R. W. (1953). Cost and Production Functions. Princeton: Princeton University Press.
  99. Shestalova, V. (2003). Sequential Malmquist Indices of Productivity Growth: An Application to OECD Industrial Activities. Journal of Productivity Analysis, 19(2), 211–226. https://doi.org/10.1023/A:1022857501478">https://doi.org/10.1023/A:1022857501478
  100. Sickles, R., & Zelenyuk, V. (2019). Measurement of Productivity and Efficiency: Theory and Practice. Cambridge: Cambridge University Press.
  101. Simar, L., & Wilson, P. W. (1998). Sensitivity Analysis of Efficiency Scores: How to Bootstrap in Nonparametric Frontier Models. Management Science, 44(1), 49–61. https://doi.org/10.1287/mnsc.44.1.49">https://doi.org/10.1287/mnsc.44.1.49
  102. Simar, L., & Wilson, P. W. (1999). Estimating and Bootstrapping Malmquist Indices. European Journal of Operational Research, 115(3), 459–471. https://doi.org/10.1016/S0377-2217(97)00450-5">https://doi.org/10.1016/S0377-2217(97)00450-5
  103. Simar, L., & Wilson, P. W. (2015). Statistical Approaches for Non-parametric Frontier Models: A Guided Tour. International Statistical Review, 83(1), 77–110. https://doi.org/10.1111/insr.12056">https://doi.org/10.1111/insr.12056
  104. Sueyoshi, T., & Aoki, S. (2001). A Use of Nonparametric Statistic for DEA Frontier Shift: The Kruskal and Wallis Rank Test. Omega, 29(1), 1–18. https://doi.org/10.1016/S0305-0483(00)00024-4">https://doi.org/10.1016/S0305-0483(00)00024-4
  105. Tavana, M., Khalili-Damghani, K., Santos Arteaga, F. J., & Hashemi, A. (2020). A Malmquist Productivity Index for Network Production Systems in the Energy Sector. Annals of Operations Research, 284(1), 415–445. https://doi.org/10.1007/s10479-019-03173-7">https://doi.org/10.1007/s10479-019-03173-7
  106. Tohidi, G. H., Razavyan, S. H., & Tohidnia, S. (2010). A Profit Malmquist Productivity Index. Journal of Industrial Engineering International, 6(11), 23–30.
  107. Tohidi, G., Razavyan, S., & Tohidnia, S. (2012). A Global Cost Malmquist Productivity Index Using Data Envelopment Analysis. Journal of the Operational Research Society, 63, 72–78. https://doi.org/10.1057/jors.2011.23">https://doi.org/10.1057/jors.2011.23
  108. Tohidi, G., & Razavyan, S. (2013). A Circular Global Profit Malmquist Productivity Index in Data Envelopment Analysis. Applied Mathematical Modelling, 37(1), 216–227. https://doi.org/10.1016/j.apm.2012.02.026">https://doi.org/10.1016/j.apm.2012.02.026
  109. Tohidi, G., & Tohidnia, S. (2014). The Biennial Cost Malmquist Productivity Index. Mathematical Research on Industrial Engineering Journal, 1(1), 24–29.
  110. Tohidnia, S., & Tohidi, G. (2019). Estimating Multi-Period Global Cost Efficiency and Productivity Change of Systems With Network Structures. Journal of Industrial Engineering International, 15(1), 171–179. https://doi.org/10.1007/s40092-018-0254-x">https://doi.org/10.1007/s40092-018-0254-x
  111. Tone, K. (2001). A Slacks-Based Measure of Efficiency in Data Envelopment Analysis. European Journal of Operational Research, 130(3), 498–509. https://doi.org/10.1016/S0377-2217(99)00407-5">https://doi.org/10.1016/S0377-2217(99)00407-5
  112. Tone, K. (2004). Malmquist Productivity Index: Efficiency Change Over Time. In W. W. Cooper, L. M. Seiford, & J. Zhu (Eds.), Handbook on Data Envelopment Analysis (pp. 203–227). Boston: Springer. https://doi.org/10.1007/1-4020-7798-X_8">https://doi.org/10.1007/1-4020-7798-X_8
  113. Tone, K., & Tsutsui, M. (2014). Dynamic DEA With Network Structure: A Slacks-Based Measure Approach. Omega, 42(1), 124–131. https://doi.org/10.1016/j.omega.2013.04.002">https://doi.org/10.1016/j.omega.2013.04.002
  114. Tone, K., & Tsutsui, M. (2017a). The Dynamic DEA Model. In K. Tone (Ed.), Advances in DEA Theory and Applications: With Extensions to Forecasting Models (pp. 64–73). Hoboken: John Wiley & Sons. https://doi.org/10.1002/9781118946688.ch8">https://doi.org/10.1002/9781118946688.ch8
  115. Tone, K., & Tsutsui, M. (2017b). The Dynamic Network DEA Model. In: K. Tone (Ed.), Advances in DEA Theory and Applications: With Extensions to Forecasting Models (pp. 74–84). Hoboken: John Wiley & Sons. https://doi.org/10.1002/9781118946688.ch9">https://doi.org/10.1002/9781118946688.ch9
  116. Tone, K., & Tsutsui, M. (2017c). Malmquist Productivity Index Models. In: K. Tone (Ed.), Advances in DEA Theory and Applications: With Extensions to Forecasting Models (pp. 40–56). Hoboken: John Wiley & Sons. https://doi.org/10.1002/9781118946688.ch6">https://doi.org/10.1002/9781118946688.ch6
  117. Walheer, B. (2022). Global Malmquist and Cost Malmquist Indexes for Group Comparison. Journal of Productivity Analysis, 58(1), 75–93. https://doi.org/10.1007/s11123-022-00640-5">https://doi.org/10.1007/s11123-022-00640-5
  118. Wang, Y. -M., & Lan, Y. -X. (2011). Measuring Malmquist Productivity Index: A New Approach Based on Double Frontiers Data Envelopment Analysis. Mathematical and Computer Modelling, 54(11), 2760– 2771. https://doi.org/10.1016/j.mcm.2011.06.064">https://doi.org/10.1016/j.mcm.2011.06.064
  119. Wang, Z., & Zelenyuk, V. (2024). Data Envelopment Analysis: From Foundations to Modern Advancements. Foundations and Trends in Econometrics, 13(3), 170–282. https://doi.org/10.1561/0800000040">https://doi.org/10.1561/0800000040
  120. Zelenyuk, V. (2006). Aggregation of Malmquist Productivity Indexes. European Journal of Operational Research, 174(2), 1076–1086. https://doi.org/10.1016/j.ejor.2005.02.061">https://doi.org/10.1016/j.ejor.2005.02.061
  121. Zelenyuk, V. (2023). Productivity Analysis: Roots, Foundations, Trends and Perspectives. Journal of Productivity Analysis, 60(3), 229–247. https://doi.org/10.1007/s11123-023-00692-1">https://doi.org/10.1007/s11123-023-00692-1
  122. Zhu, N., Liu, Y., Emrouznejad, A., & Huang, Q. (2017). An Allocation Malmquist Index With an Application in the China Securities Industry. Operational Research, 17(2), 669–691. https://doi.org/10.1007/s12351-016-0249-6">https://doi.org/10.1007/s12351-016-0249-6
  123. Zofío, J. L., & Lovell, C. A. K. (2001). Graph Efficiency and Productivity Measures: An Application to US Agriculture. Applied Economics, 33(11), 1433– 1442. https://doi.org/10.1080/00036840010009865">https://doi.org/10.1080/00036840010009865
  124. Zofio, J. L. (2007). Malmquist Productivity Index Decompositions: A Unifying Framework. Applied Economics, 39(18), 2371–2387. https://doi.org/10.1080/00036840600606260">https://doi.org/10.1080/00036840600606260
DOI: https://doi.org/10.2478/ceej-2025-0007 | Journal eISSN: 2543-6821 | Journal ISSN: 2544-9001
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