Goal programming approaches for data envelopment analysis cross efficiency evaluation. (English) Zbl 1226.90095

Summary: Cross efficiency evaluation has long been proposed as an alternative method for ranking the decision making units (DMUs) in data envelopment analysis (DEA). This study proposes goal programming models that could be used in the second stage of the cross evaluation. Proposed goal programming models have different efficiency concepts as classical DEA, minmax and minsum efficiency criteria. Numerical examples are provided to illustrate the applications of the proposed goal programming cross efficiency models.


90C29 Multi-objective and goal programming
90C08 Special problems of linear programming (transportation, multi-index, data envelopment analysis, etc.)
Full Text: DOI


[1] Adler, N.; Friedman, L.; Sinuany-Stern, Z., Review of ranking methods in the data envelopment analysis context, Eur. J. Oper. Res., 140, 249-265 (2002) · Zbl 1001.90048
[2] Alirezaee, M. R.; Afsharian, M. A., A complete ranking of DMUs using restrictions in DEA models, Appl. Math. Comput., 189, 1550-1559 (2007) · Zbl 1243.90075
[3] Anderson, T. R.; Hollingsworth, K. B.; Inman, L. B., The fixed weighting nature of a cross evaluation model, J. Prod. Anal., 18, 1, 249-255 (2002)
[4] Bal, H.; Örkcü, H. H., A goal programming approach to weight dispersion in data envelopment analysis, G.U.J.S., 20, 4, 117-125 (2007)
[5] Bal, H.; Örkcü, H. H.; Çelebioglu, S., A new method based on dispersion of weights in data envelopment analysis, Comput. Ind. Eng., 54, 3, 502-512 (2008)
[6] Bal, H.; Örkcü, H. H.; Çelebioglu, S., Improving the discrimination power and weights dispersion in the data envelopment analysis, Comput. Oper. Res., 37, 1, 99-107 (2010) · Zbl 1171.90418
[7] Bao, C. P.; Chen, T. H.; Chang, S. Y., Slack-based ranking method: an interpretation to the cross-efficiency method in DEA, J. Oper. Res. Soc., 59, 6, 860-862 (2008) · Zbl 1153.90451
[8] Bernroider, E.; Stix, V., A method using weight restrictions in data envelopment analysis for ranking and validity issues in decision making, Comput. Oper. Res., 34, 9, 2637-2647 (2007) · Zbl 1141.90439
[9] Charnes, A.; Cooper, W. W.; Rhodes, E., Measuring the efficiency of decision making units, Eur. J. Oper. Res., 2, 429-444 (1978) · Zbl 0416.90080
[10] Chen, T. Y., An assessment of technical efficiency and cross-efficiency in Taiwan’s electricity distribution sector, Eur. J. Oper. Res., 137, 2, 421-433 (2002) · Zbl 1008.90512
[11] Cooper, W. W.; Seiford, L. M.; Tone, K., Data Envelopment Analysis (2000), Kluwer Academic Publishers.: Kluwer Academic Publishers. Boston, USA
[12] Doyle, J. R.; Green, R., Efficiency and cross-efficiency in DEA: Derivations, meanings and uses, J. Oper. Res. Soc., 45, 5, 567-578 (1994) · Zbl 0807.90016
[13] Doyle, J. R.; Green, R., Self and peer appraisal in Higher Education, High. Edu., 28, 2, 241-264 (1994)
[14] Green, R.; Doyle, J. R.; Cook, W., Preference voting and project ranking using DEA and cross-evaluation, Eur. J. Oper. Res., 90, 3, 461-472 (1996) · Zbl 0911.90009
[15] Hosseinzadeh, L. F.; Jahanshahloo, G. R.; Esmaeili, M., An alternative approach in the estimation of returns to scale under weight restrictions, Appl. Math. Comput., 189, 719-724 (2007) · Zbl 1127.90367
[16] Lam, K. F., In the determination weight sets to compute cross-efficiency ratios in DEA, J. Oper. Res. Soc., 61, 134-143 (2010) · Zbl 1193.90129
[17] Liang, L.; Wu, J.; Cook, W. D.; Zhu, J., Alternative secondary goals in DEA crossefficiency evaluation, Int. J. Prod. Eco., 113:2, 1025-1030 (2008)
[18] Liang, L.; Wu, J.; Cook, W. D.; Zhu, J., The DEA game cross-efficiency model and its Nash equilibrium, Oper. Res., 56:5, 1278-1288 (2008) · Zbl 1167.91330
[19] Jahanshahloo, G. R.; Memariani, A.; Hosseinzadeh, L. F.; Shoja, N., A feasible interval for weights in data envelopment analysis, Appl. Math. Comput., 160, 155-168 (2005) · Zbl 1057.90028
[20] Jahanshahloo, G. R.; Hosseinzadeh, L. F.; Jafari, Y.; Maddahi, R., Selecting symmetric weights as a secondary goal in DEA cross-efficiency evaluation, Appl. Math. Model., 35, 544-549 (2011) · Zbl 1202.90249
[21] Li, X. B.; Reeves, G. R., A multiple criteria approach to data envelopment analysis, Eur. J. Oper. Res., 115, 507-517 (1999) · Zbl 0953.91022
[22] Lu, W. M.; Lo, S. F., A closer look at the economic-environmental disparities for regional development in China, Eur. J. Oper. Res., 183, 2, 882-894 (2007)
[23] Meza, L. A.; E Lins, M. P., Review of methods for increasing discrimination in data envelopment analysis, Ann. Oper. Res., 116, 225-242 (2002) · Zbl 1013.90133
[24] Oral, M.; Kettani, O.; Lang, P., A methodology for collective evaluation and selection of industrial R& D projects, Manage. Sci., 37, 7, 871-885 (1991) · Zbl 0729.90671
[25] Sexton, T. R.; Silkman, R. H.; Hogan, A. J., Data envelopment analysis: critique and extensions, (Silkman, R. H., Measuring Efficiency: An Assessment of Data Envelopment Analysis (1986), Jossey-Bass: Jossey-Bass San Francisco), 73-105
[26] Sun, S.; Lu, W. M., A cross-efficiency profiling for increasing discrimination in data envelopment analysis, INFOR, 43, 1, 51-60 (2005) · Zbl 07682433
[27] Tofallis, C., Improving discernmentin DEA using profiling, Omega, 24, 3, 361-364 (1996)
[28] Tofallis, C., Input efficiency profiling: an application to airlines, Comput. Oper. Res., 24, 3, 253-258 (1997) · Zbl 0900.90006
[29] Wang, Y. M.; Chin, K. S., A neutral DEA model for cross-efficiency evaluation and its extension, Expert Syst. Appl., 37, 5, 3666-3675 (2010)
[30] Wang, Y. M.; Chin, K. S., Some alternative models for DEA cross-efficiency evaluation, Int. J. Prod. Eco., 128, 332-338 (2010)
[31] Wang, Y. M.; Chin, K. S., The use of OWA operator weights for cross-efficiency aggregation, Omega, 39, 493-503 (2011)
[32] Wang, Y. M.; Chin, K. S.; Luo, Y., Cross-efficiency evaluation based on ideal and anti-ideal decision making units, Expert Syst. Appl., 38, 10312-10319 (2011)
[33] Y.M. Wang, K.S. Chin, J. Peng, Weight determination in the cross-efficiency evaluation Comput. Ind. Eng., in press.; Y.M. Wang, K.S. Chin, J. Peng, Weight determination in the cross-efficiency evaluation Comput. Ind. Eng., in press.
[34] Wong, Y. H.B.; Beasley, J. E., Restricting weight flexibility in data envelopment analysis, J. Oper. Res. Soc., 41, 9, 829-835 (1990) · Zbl 0711.90005
[35] Wu, J.; Liang, L.; Yang, F., Achievement and benchmarking of countries at the Summer Olympics using cross-efficiency evaluation method, Eur. J. Oper. Res., 197, 2, 722-730 (2009) · Zbl 1159.90453
[36] Wu, J.; Liang, L.; Yang, F., Determination of the weights for the ultimate crossefficiency using Shapley value in cooperative game, Expert Syst. Appl., 36, 1, 872-876 (2009)
[37] Wu, J.; Liang, L.; Zha, H.; Yang, F., Determination of cross-efficiency under the principle of rank priority in cross-evaluation, Expert Syst. Appl., 36, 4826-4829 (2009)
[38] Wu, J.; Liang, L.; Chen, Y., DEA game cross-efficiency approach to Olympic rankings, Omega, 37, 909-918 (2009)
[39] Wu, J.; Liang, L.; Yang, F., A modified complete ranking of DMUs using restrictions in DEA models, Appl. Math. Comput., 217, 745-751 (2010) · Zbl 1197.90266
[40] Ramón, N.; Ruiz, J. L.; Sirvent, I., On the choice of weights profiles in cross-efficiency evaluations, Eur. J. Oper. Res., 207, 3, 1564-1572 (2010)
[41] Romero, C.; Rehman, T., Multiple Criteria Analysis for Agricultural Decisions (1989), Elseiver Science Publishing Company: Elseiver Science Publishing Company New York, USA
[42] Romero, C., Handbook of Critical Issues in Goal Programming (1991), Pergamon press: Pergamon press Oxford · Zbl 0817.68034
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.