A Glimpse of Input Congestion Methods in Data Envelopment Analysis
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-stageReferences
- [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] 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] 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] 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] Stigler, G. J. (1976). The xistence of x-efficiency. The American economic review, 66(1), 213–216. https://www.jstor.org/stable/1804963
- [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] 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] 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] 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] 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] 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] 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] 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] Färe, R., Grosskopf, S., & Lovell, C. A. K. (1994). Production frontiers. Cambridge University Press. https://B2n.ir/nf7981
- [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] 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] 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] , 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] 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] 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] 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] 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] 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] 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] 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] 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] 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] 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] 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] 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] 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] 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] 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] 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] 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] 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] 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