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A multiobjective programming method for ranking all units based on compensatory DEA model. (English) Zbl 1407.90199

Summary: In order to rank all decision making units (DMUs) on the same basis, this paper proposes a multiobjective programming (MOP) model based on a compensatory data envelopment analysis (DEA) model to derive a common set of weights that can be used for the full ranking of all DMUs. We first revisit a compensatory DEA model for ranking all units, point out the existing problem for solving the model, and present an improved algorithm for which an approximate global optimal solution of the model can be obtained by solving a sequence of linear programming. Then, we applied the key idea of the compensatory DEA model to develop the MOP model in which the objectives are to simultaneously maximize all common weights under constraints that the sum of efficiency values of all DMUs is equal to unity and the sum of all common weights is also equal to unity. In order to solve the MOP model, we transform it into a single objective programming (SOP) model using a fuzzy programming method and solve the SOP model using the proposed approximation algorithm. To illustrate the ranking method using the proposed method, two numerical examples are solved.

MSC:

90B50 Management decision making, including multiple objectives
90C08 Special problems of linear programming (transportation, multi-index, data envelopment analysis, etc.)
90C70 Fuzzy and other nonstochastic uncertainty mathematical programming
90C29 Multi-objective and goal programming
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[1] Charnes, A.; Cooper, W. W.; Rhodes, E., Measuring the efficiency of decision making units, European Journal of Operational Research, 2, 6, 429-444 (1978) · Zbl 0416.90080 · doi:10.1016/0377-2217(78)90138-8
[2] Jahanshahloo, G. R.; Lotfi, F. H.; Khanmohammadi, M.; Kazemimanesh, M.; Rezaie, V., Ranking of units by positive ideal DMU with common weights, Expert Systems with Applications, 37, 12, 7483-7488 (2010) · doi:10.1016/j.eswa.2010.04.011
[3] Wang, Y.-M.; Luo, Y.; Lan, Y.-X., Common weights for fully ranking decision making units by regression analysis, Expert Systems with Applications, 38, 8, 9122-9128 (2011) · doi:10.1016/j.eswa.2011.01.004
[4] Kao, C., Malmquist productivity index based on common-weights DEA: the case of Taiwan forests after reorganization, Omega, 38, 6, 484-491 (2010) · doi:10.1016/j.omega.2009.12.005
[5] Sun, J.; Wu, J.; Guo, D., Performance ranking of units considering ideal and anti-ideal DMU with common weights, Applied Mathematical Modelling, 37, 9, 6301-6310 (2013) · Zbl 1426.90163 · doi:10.1016/j.apm.2013.01.010
[6] Cook, W.; Roll, Y.; Kazakov, A., A DEA model for measuring the relative efficiencies of highway maintenance patrols, Information Systems and Operational Research, 28, 2, 113-124 (1990)
[7] Roll, Y.; Cook, W. D.; Golany, B., Controlling factor weights in data envelopment analysis, IIE Transactions, 23, 1, 2-9 (1991)
[8] Roll, Y.; Golany, B., Alternate methods of treating factor weights in DEA, Omega, 21, 1, 99-109 (1993) · doi:10.1016/0305-0483(93)90042-J
[9] Sinuany-Stern, Z.; Friedman, L., DEA and the discriminant analysis of ratios for ranking units, European Journal of Operational Research, 111, 3, 470-478 (1998) · Zbl 0939.91112 · doi:10.1016/S0377-2217(97)00313-5
[10] Jahanshahloo, G. R.; Memariani, A.; Lotfi, F. H.; Rezai, H. Z., A note on some of DEA models and finding efficiency and complete ranking using common set of weights, Applied Mathematics and Computation, 166, 2, 265-281 (2005) · Zbl 1074.90538 · doi:10.1016/j.amc.2004.04.088
[11] Kao, C.; Hung, H.-T., Data envelopment analysis with common weights: the compromise solution approach, Journal of the Operational Research Society, 56, 10, 1196-1203 (2005) · Zbl 1081.90033 · doi:10.1057/palgrave.jors.2601924
[12] Amin, G. R.; Toloo, M., Finding the most efficient DMUs in DEA: an improved integrated model, Computers and Industrial Engineering, 52, 1, 71-77 (2007) · doi:10.1016/j.cie.2006.10.003
[13] Liu, F.-H. F.; Peng, H. H., Ranking of units on the DEA frontier with common weights, Computers & Operations Research, 35, 5, 1624-1637 (2008) · Zbl 1211.90101 · doi:10.1016/j.cor.2006.09.006
[14] Davoodi, A.; Rezai, H. Z., Common set of weights in data envelopment analysis: a linear programming problem, Central European Journal of Operations Research, 20, 2, 355-365 (2012) · Zbl 1339.90230 · doi:10.1007/s10100-011-0195-6
[15] Ramón, N.; Ruiz, J. L.; Sirvent, I., Common sets of weights as summaries of DEA profiles of weights: with an application to the ranking of professional tennis players, Expert Systems with Applications, 39, 5, 4882-4889 (2012) · doi:10.1016/j.eswa.2011.10.004
[16] Lotfi, F. H.; Hatami-Marbini, A.; Agrell, P. J.; Aghayi, N.; Gholami, K., Allocating fixed resources and setting targets using a common-weights DEA approach, Computers & Industrial Engineering, 64, 2, 631-640 (2013) · doi:10.1016/j.cie.2012.12.006
[17] Adler, N.; Friedman, L.; Sinuany-Stern, Z., Review of ranking methods in the data envelopment analysis context, European Journal of Operational Research, 140, 2, 249-265 (2002) · Zbl 1001.90048 · doi:10.1016/S0377-2217(02)00068-1
[18] Hosseinzadeh Lotfi, F.; Jahanshahloo, G. R.; Rostamy-Malkhlifeh, M.; Moghaddas, Z.; Vaez-Ghasemi, M., A review of ranking models in data envelopment analysis, Journal of Applied Mathematics, 2013 (2013) · Zbl 1271.62031 · doi:10.1155/2013/492421
[19] Khodabakhshi, M.; Aryavash, K., Ranking all units in data envelopment analysis, Applied Mathematics Letters, 25, 12, 2066-2070 (2012) · Zbl 1260.90113 · doi:10.1016/j.aml.2012.04.019
[20] Zhang, D.; Li, X.; Meng, W.; Liu, W., Measuring the performance of nations at the olympic games using DEA models with different preferences, Journal of the Operational Research Society, 60, 7, 983-990 (2009) · Zbl 1168.90552 · doi:10.1057/palgrave.jors.2602638
[21] Azizi, H.; Wang, Y.-M., Improved DEA models for measuring interval efficiencies of decision-making units, Measurement, 46, 3, 1325-1332 (2013) · doi:10.1016/j.measurement.2012.11.050
[22] Ramezani-Tarkhorani, S.; Khodabakhshi, M.; Mehrabian, S.; Nuri-Bahmani, F., Ranking decision-making units using common weights in DEA, Applied Mathematical Modelling, 38, 15-16, 3890-3896 (2014) · Zbl 1428.90083 · doi:10.1016/j.apm.2013.08.029
[23] Wang, Y. M.; Luo, Y.; Liang, L., Ranking decision making units by imposing a minimum weight restriction in the data envelopment analysis, Journal of Computational and Applied Mathematics, 223, 1, 469-484 (2009) · Zbl 1179.90201 · doi:10.1016/j.cam.2008.01.022
[24] Jiménez, M.; Bilbao, A., Pareto-optimal solutions in fuzzy multi-objective linear programming, Fuzzy Sets and Systems, 160, 18, 2714-2721 (2009) · Zbl 1181.90303 · doi:10.1016/j.fss.2008.12.005
[25] Vasant, P.; Bhattacharya, A.; Sarkar, B.; Mukherjee, S. K., Detection of level of satisfaction and fuzziness patterns for MCDM model with modified flexible S-curve MF, Applied Soft Computing Journal, 7, 3, 1044-1054 (2007) · doi:10.1016/j.asoc.2006.10.005
[26] Baykasoglu, A.; Gocken, T., Multi-objective aggregate production planning with fuzzy parameters, Advances in Engineering Software, 41, 9, 1124-1131 (2010) · Zbl 1231.90395 · doi:10.1016/j.advengsoft.2010.07.002
[27] Zimmermann, H., Fuzzy programming and linear programming with several objective functions, Fuzzy Sets and Systems, 1, 1, 45-55 (1978) · Zbl 0364.90065
[28] Jiménez, M., Ranking fuzzy numbers through the comparison of its expected intervals, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 4, 4, 379-388 (1996) · Zbl 1232.03040 · doi:10.1142/S0218488596000226
[29] Lai, Y.-J.; Hwang, C.-L., Possibilistic linear programming for managing interest rate risk, Fuzzy Sets and Systems, 54, 2, 135-146 (1993) · doi:10.1016/0165-0114(93)90271-I
[30] Guu, S. M.; Wu, Y. K., Two-phase approach for solving the fuzzy linear programming problems, Fuzzy Sets and Systems, 107, 2, 191-195 (1999) · Zbl 0949.90098 · doi:10.1016/S0165-0114(97)00304-7
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