A Glimpse of Input Congestion Methods in Data Envelopment Analysis

Authors

https://doi.org/10.48314/jidcm.v1i2.68

Abstract

This comprehensive review explores recent advances in measuring and analyzing congestion within Data Envelopment Analysis (DEA), a pivotal tool in efficiency assessment of Decision-Making Units (DMUs). The study categorizes multiple methodologies developed over the years, focusing on both classical and novel models to detect, quantify, and interpret congestion situations where input increases lead to output reductions or vice versa, indicating inefficiencies or overutilization. These approaches include input-oriented, output-oriented, multi-stage, weight-restriction, and models addressing undesirable outputs, as well as those accommodating integer data and production trade-offs. Several models utilize concepts such as Pareto efficiency, slack variables, and weight restrictions to formalize congestion detection, with specific attention to strong, weak, and wide congestion phenomena. The synthesis includes algorithms for projecting DMUs onto efficiency or congestion boundaries, alongside measures for the extent of congestion. Furthermore, innovative techniques addressing multiple stages, undesirable outputs, and integer data expand the applicability of DEA in complex, real-world scenarios. The findings offer researchers a robust, categorically organized toolkit for congestion analysis, advancing the understanding of resource overuse and production bottlenecks, thereby contributing to more accurate efficiency measurement and resource management strategies in diverse sectors. 

Keywords:

Data envelopment analysis, Decision-making units, Input-oriented, Output-oriented, Multi-stage

References

  1. [1] Charnes, A., Cooper, W. W., & Rhodes, E. (1978). Measuring the efficiency of decision making units. European journal of operational research, 2(6), 429–444. https://doi.org/10.1016/0377-2217(78)90138-8

  2. [2] Koopmans, T. C. (1951). Analysis of production as an efficient combination of activities. Analysis of production and allocation, 158(1), 33. https://www.sciepub.com/reference/39504

  3. [3] Färe, R., Grosskopf, S., Lovell, C. A. K., & Pasurka, C. (1989). “Multilateral productivity comparisons when some outputs are undesirable: A nonparametric approach.” Review of economics and statistics, 71(1), 90–98. https://doi.org/10.2307/1928055

  4. [4] 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

  5. [5] Stigler, G. J. (1976). The xistence of x-efficiency. The American economic review, 66(1), 213–216. https://www.jstor.org/stable/1804963

  6. [6] Leibenstein, H. (1966). Allocative efficiency vs." x-efficiency". The American economic review, 56(3), 392–415. https://www.jstor.org/stable/1823775%0A

  7. [7] Färe, R., & Svensson, L. (1980). Congestion of production factors. Econometrica: Journal of the econometric society, 48(7), 1745–1753. https://doi.org/10.2307/1911932

  8. [8] Färe, R., & Grosskopf, S. (1983). Measuring congestion in production. Zeitschrift für nationalökonomie journal of economics, 43(3), 257–271. https://www.jstor.org/stable/41796223

  9. [9] Färe, R., Grosskopf, S., & Lovell, C. A. K. (1985). The measurement of efficiencies of production. Boston: Kluwer-Nihoff Publishing. https://doi.org/10.1007/978-94-015-7721-2

  10. [10] Cooper, W. W., Thompson, R. G., & Thrall, R. M. (1996). Introduction: Extensions and new developments in DEA. Annals of operations research, 66, 3–45. https://doi.org/10.1007/bf02125451

  11. [11] Brockett, P. L., Cooper, W. W., Wang, Y., & Shin, H. C. (1998). Inefficiency and congestion in Chinese production before and after the 1978 economic reforms. Socio-economic planning sciences, 32(1), 1–20. https://B2n.ir/rh2344

  12. [12] Cooper, W. W., Seiford, L. M., & Zhu, J. (2000). A unified additive model approach for evaluating inefficiency and congestion with associated measures in DEA. Socio-economic planning sciences, 34(1), 1–25. https://www.deafrontier.net/papers/SEPScongestion.pdf

  13. [13] Cooper, W. W., Seiford, L. M., & Zhu, J. (2001). Slacks and congestion: Response to a comment by R. Färe and S. Grosskopf. Socio-economic planning sciences, 35(3), 205–215. https://doi.org/10.17485/ijst/2015/v8i6/61948

  14. [14] Färe, R., Grosskopf, S., & Lovell, C. A. K. (1994). Production frontiers. Cambridge University Press. https://B2n.ir/nf7981

  15. [15] Cooper, W. W., Gu, B., & Li, S. (2001). Note: Alternative treatments of congestion in DEA-a response to the Cherchye, Kuosmanen and post critique. European journal of operational research, 132(1), 81–87. https://www.sciencedirect.com/science/article/pii/S0377221700001764

  16. [16] Cherchye, L., Kuosmanen, T., & Post, T. (2001). Alternative treatments of congestion in DEA: A rejoinder to Cooper, Gu, and Li. European journal of operational research, 132(1), 75–80. https://B2n.ir/qt7156

  17. [17] Sueyoshi, T., & Sekitani, K. (2009). DEA congestion and returns to scale under an occurrence of multiple optimal projections. European journal of operational research, 194(2), 592–607. https://doi.org/10.1016/j.ejor.2007.12.022

  18. [18] , A., Lotfi, F. H., & others. (2015). Congestion in DEA under weight restriction using common weights. Journal of mathematical extension, 10, 121–133. https://ijmex.com/index.php/ijmex/article/view/367

  19. [19] Färe, R., Grosskopf, S., & Lovell, C. K. (1985). The measurement of efficiency of production (Vol. 6). Springer Science & Business Media. https://B2n.ir/ff1558

  20. [20] Cooper, W. W., Deng, H., Huang, Z. M., & Li, S. X. (2002). A one-model approach to congestion in data envelopment analysis. Socio-economic planning sciences, 36(4), 231–238. https://B2n.ir/es2070

  21. [21] Tone, K., & Sahoo, B. K. (2004). Degree of scale economies and congestion: A unified DEA approach. European journal of operational research, 158(3), 755–772. https://doi.org/10.1016/S0377-2217(03)00370-9

  22. [22] Brockett, P., Cooper, W., Deng, H., Golden, L., & Ruefli, T. (2004). Using DEA to identify and manage congestion. Journal of productivity analysis, 22, 207–226. https://doi.org/10.1007/s11123-004-7574-0

  23. [23] Noura, A. A., Lotfi, F. H., Jahanshahloo, G. R., Rashidi, S. F., & Parker, B. R. (2010). A new method for measuring congestion in data envelopment analysis. Socio-economic planning sciences, 44(4), 240-246. https://doi.org/10.1016/j.seps.2010.06.003

  24. [24] Flegg, A. T., & Allen, D. O. (2009). Congestion in the Chinese automobile and textile industries revisited. Socio-economic planning sciences, 43(3), 177–191. https://doi.org/10.1016/j.seps.2008.10.003

  25. [25] Wang, Y. M., Greatbanks, R., & Yang, J. B. (2005). Interval efficiency assessment using data envelopment analysis. Fuzzy sets and systems, 153(3), 347–370. https://doi.org/10.1016/j.fss.2004.12.011

  26. [26] Javanmard, M., & Mishmast Nehi, H. (2019). A solving method for fuzzy linear programming problem with interval type-2 fuzzy numbers. International journal of fuzzy systems, 21, 882–891. https://doi.org/10.1007/s40815-018-0591-3

  27. [27] Davoudi, N., Hamidi, F., & Mishmast Nehi, H. (2023). A method for solving interval type-2 Triangular fuzzy Bilevel linear programming problem. Yugoslav journal of operations research, 33(1), 71–90. https://doi.org/10.2298/YJOR210715027H

  28. [28] Podinovski, V. V. (2007). Computation of efficient targets in DEA models with production trade-offs and weight restrictions. European journal of operational research, 181(2), 586–591. https://doi.org/10.1016/j.ejor.2006.06.041

  29. [29] Podinovski, V. V. (2004). Production trade-offs and weight restrictions in data envelopment analysis. Journal of the operational research society, 55(12), 1311–1322. https://doi.org/10.1057/palgrave.jors.2601794

  30. [30] Gattoufi, S., Oral, M., & Reisman, A. (2004). Data envelopment analysis literature: A bibliography update (1951--2001). Journal of socio-economic planning sciences, 38(2–3), 159–229. https://B2n.ir/nx5174

  31. [31] Seiford, L. M., & Zhu, J. (2005). A response to comments on modeling undesirable factors in efficiency evaluation. European journal of operational research, 161(2), 579–581.

  32. [32] Noura, A. A., & Hoseini, E. (2013). Measuring congestion in data envelopment analysis with common weights. International journal of data envelopment analysis, 3(1), 627–632. (In Persian). https://www.sid.ir/FileServer/JE/5072820130301

  33. [33] Karimi, B., Khorram, E., & Moeini, M. (2016). Identification of congestion by means of integer-valued data envelopment analysis. Computers & industrial engineering, 98, 513–521. https://doi.org/10.1016/j.cie.2016.06.017

  34. [34] Lozano, S., & Villa, G. (2006). Data envelopment analysis of integer-valued inputs and outputs. Computers & operations research, 33(10), 3004–3014. https://doi.org/10.1016/j.cor.2005.02.031

  35. [35] Lozano, S., & Villa, G. (2007). Integer DEA models: How DEA models can handle integer inputs and outputs. Modeling data irregularities and structural complexities in data envelopment analysis, 271–289. https://doi.org/10.1007/978-0-387-71607-7_15

  36. [36] Matin, R. K., & Kuosmanen, T. (2009). Theory of integer-valued data envelopment analysis under alternative returns to scale axioms. Omega, 37(5), 988–995. https://doi.org/10.1016/j.omega.2008.11.002

  37. [37] Kuosmanen, T., & Matin, R. K. (2009). Theory of integer-valued data envelopment analysis. European journal of operational research, 192(2), 658–667. https://doi.org/10.1016/j.ejor.2007.09.040

Published

2025-06-16

How to Cite

Jokar, F. ., & Hadi Vencheh, A. . (2025). A Glimpse of Input Congestion Methods in Data Envelopment Analysis. Journal of Intelligent Decision and Computational Modelling, 1(2), 107-137. https://doi.org/10.48314/jidcm.v1i2.68

Similar Articles

1-10 of 11

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