Shortest path Ranking Model With the Ability to Change the Importance of Inputs and Outputs: Case Studies from Education

Document Type : Research Paper

Authors

Department of Mathematics, Islamic Azad University, Central Branch, Tehran, Iran

Abstract

This paper presents a novel super efficiency model based on the Andersen-Petersen model, which serves as a bridge between input-oriented and output-oriented models. The proposed model defines a path from the deleted decision-making unit to the efficiency frontier with the shortest step length. Initially formulated as a nonlinear programming model, the developed model is transformed into a multi-objective linear programming model and then further simplified into a linear programming model through variable changes and the application of nonlinear programming solving methods. The feasibility of the proposed path is discussed, and a weighted version of the shortest path model is introduced to incorporate preferences regarding the relative importance of inputs or outputs. Addressing a weakness of the AP methods, the inability to prioritize weights is resolved in the developed model. Real case studies in the context of Iranian education are conducted, and the results of the AP and shortest path analyses are analyzed to validate the proposed method.

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References

Amirteimoori, A., Kordrostami, S., Nasrollahian, P. (2017). A Method for Solving Super-Efficiency Infeasibility by Adding virtual DMUs with Mean Values. Iranian Journal of Management Studies, 10(4), 905-916. doi: 10.22059/ijms.2017.235592.672706
Andersen, P. & Petersen, N. (1993). A procedure for ranking efficient units in data envelopment analysis. Management Science, 39, 1261-1264.
Banker, R.D. & Gifford, J.L. (1988). A relative efficiency Model for the evaluation of public health nurse productivity. Carnegie Mellon University, Pittsburgh.
Banker, R.D & Chang. H. (2006). the super efficiency procedure for outlier identify caution not for ranking efficient units. European Journal of Operational Research, 175, 1311-1320.
Banker, R.D., Charnes, A., Cooper W.W. (1984). Some models for estimating technical and scale inefficiency in data envelopment analysis. Management Science, 31, 1078-1092.
Banker, R.D., Chang, H. & Zheng, Z. (2017). On the use of super-efficiency procedures for ranking efficient units and identifying outliers. Annals of Operations Research, 250, 21–35.
Chiang, K. & Liu, S.T. (2020). A slacks-based measure model for calculating cross efficiency in data envelopment analysis. Omega, 95, 102-192.
Ersoy, Y. (2021). Performance Evaluation in Distance Education by Using Data Envelopment Analysis (DEA) and TOPSIS Methods. Arabian Journal for Science and Engineering, 46,1803-1817.
Gerami, J., Mozaffari, M.R., Wanke, P.F. & Correa, H. (2021). A novel slacks-based model for efficiency and super-efficiency in DEA-R. Operational Research. doi.org/10.1007/s12351-021-00679-6.
Gkouvitsos, I. & Giannikos, I. (2021). Using a MACBETH based multi criteria approach for virtual weight restrictions in each stage of a DEA multi‑stage ranking process. Operational Research, 24, 1787-1811.
Jahanshahloo, G.R., Hosseinzadeh Lotfi, F., Shoja, N., Tohidi, G. & Razavian, S. (2004). Ranking using -norm in data envelopment analysis. Applied mathematics and computation, 153(1), 215-224.
Kocisova, K. & Paleckova, I. (2017). The Super-efficiency Model and its Use for Ranking and Identification of Outliers. Acta Universitatis Agriculturae et Silviculturae Mendelianae Brunensis, Mendel University Press, 65(4), 1371-1382.
Khodabakhshi, M., Rashidi, S., Asgharian, M., & Neralic, L., (2014). Sensitivity analysis of input relaxation supper efficiency measure in data envelopment analysis. Data Envelopment Analysis Journal, 1(1), 113-134.
Kuosmanen, T., (2005). Weak disposability in nonparametric production analysis with undesirable outputs. Agricultural Economics Association, 87(4), 1077-1082.
Lin, R. & Li, Z. (2020). Directional distance based diversification super-efficiency DEA models for mutual funds. Omega, 97(C).
Mehrabian, S., Alirezaee, M. R. & Jahanshahloo, G.R. (1999). A complete efficiency ranking of decision making units in data envelopment analysis. Computational optimization and applications, 4, 261-266.
Torabi, M., & Mahlooji, H. (2016). An integrated simulation-DEA approach to multi-criteria ranking of scenarios for execution of operations in a construction project. Iranian Journal of Management Studies, 9(4), 801-827. doi: 10.22059/ijms.2017.60097
Interdisciplinary Journal of Management Studies (Formerly known as Iranian Journal of Management Studies)
Volume 16, Issue 3
July 2023
Pages 697-709

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