Evaluation of the Performance in Dynamic Network Data Envelopment Analysis with Undesirable Outputs

Subject Areas : Data Envelopment Analysis

Mohammad Najari Alamuti ¹ , Reza Kazemi Matin ² , Mohsen Khounsiavash ³ , Zohreh Moghadas ⁴

1 - Department of Mathematics, Qazvin Branch, Islamic Azad University, Qazvin, Iran
2 - IAU Karaj Branch
3 - Department of Mathematics, Qazvin Branch, Islamic Azad University, Qazvin, Iran
4 - Department of Mathematics, Qazvin Branch, Islamic Azad University, Qazvin, Iran

Received: 2022-02-11 Accepted : 2022-04-16 Published : 2021-09-01

Keywords: Data Envelopment Analysis (DEA), Undesirable outputs, Dynamic network DEA, Evaluation of hospitals,

Abstract :

Data Envelopment Analysis (DEA) is a mathematical technique to assess the performance of Decision Making Units (DMUs) with similar inputs and outputs. The traditional DEA models disregard the internal structure of units and have a “black box” view. Thus, to evaluate the structures with more than one stage, the network DEA (NDEA) models expanded. On the other hand, the dynamic optimization models have been presented to eliminate the limitations of static models in optimization. In the article, for the first time, a systematic approach is used to present a dynamic NDEA with constant inputs and undesirable outputs. First, we used an axiomatic approach in DEA with undesirable output and presented an NDEA model with undesirable output. Then, we extended the proposed approach and presented a dynamic NDEA with undesirable output and a constant input. Afterward, we applied this model to evaluate hospitals’ performance in an experimental study to estimate the efficiency of their dynamic network.

References:

• Banker, R.D., Charnes, A., Cooper, W.W. (1984). “Some Models for estimating technical and scale inefficiencies in data envelopment analysis”, Management science, Vol. 32 No.7,pp. 18-70.


• Charnes A Cooper W.W and Rhodes, E . (1978). Measuring the efficiency of decision making units”, North-Holland Publishing Company. Eur. J. Oper. Res. 2(6): 429-444.


• Emrouznejad, A., Yang, G.: A survey and analysis of the first 40 years of scholarly literature in DEA: 1978–2016, Socio-Economic Planning Sciences, Vol. 51, 2017, pp. 152-164


• Fare, R., Grosskopf, S., (2003). Non-parametric Productivity Analysis with Undesirable Outputs: Comment. American Journal of Agricultural Economics, 85, 1070-74.


• Fare, R., Grosskopf, S., Lovell, C. A. K., Pasurka, C., (1984). Multilateral Productivity Comparisons When Some Outputs Are Undesirable: A Nonparametric Approach. Rev. Econ. Stat.75, 374-80.


• Fare, R., Grosskopf, S., Lovell, C.A.K., (1989). Multilateral productivity comparisons when some outputs are undesirable :a non-parametric approach. The Review of Economics and Statistics, 71, 90-98.


• Farrell, M. J. (1957), The measurement of productive efficiency, Journal of the Royal Statistical Society,Series A, General, 120(Part 3), 253–281.


• Fukuyama, H., & Weber, W.L. (2010). A slacks-based inefficiency measure for a two stage system with bad outputs. Omega, 38, 398-409.


• Hailu, A., Veeman, T., 2001. Non-parametric productivity analysis with undesirable outputs: an application to Canadian pulp and paper industry. American Journal of Agricultural Economics, 83, 605-616.


• Holod, D., & Lewis, H.F. (2011). Resolving the deposit dilemma: A new DEA bank efficiency model. Journal of Banking & Finance, 35, 2801–2810.


• Hosseinzadeh Lotfi, F., Ebrahimnejad, A., Vaez-Ghasemi, M., Moghaddas, Z. (2020). Data Envelopment Analysis with R, Springer International Publishing, Cham, Switzerland.


• Kaffash, S., Azizi, R., Huang, Y., Zhu, J. (2019).  A survey of data envelopment analysis applications in the insurance industry 1993-2018. European Journal of Operational Research. https://doi.org/10.1016/j.ejor.2019.07.034.


• Kao, C. (2009a). Efficiency decomposition in network data envelopment analysis: A relational model. European Journal of Operational Research, 192, 949-962.


• Kao, C. (2014a). Efficiency decomposition for general multi-stage systems in data envelopment analysis. European Journal of Operational Research, 232, 117-124.


• Kao, C. (2014b). Network data envelopment analysis: A review. European Journal of Operational Research, 239, 1-16.


• Kao, C. )2019). Inefficiency identification for closed series production systems. Eur. J. Oper. Res., 275, 599–607.


• Kao, C., & Hwang, S. N. (2010). Efficiency measurement for network systems: IT impact on firm performance. Decision Support Systems, 48, 437-446.


• Kao, C., (2009). Efficiency decomposition in network data envelopment analysis: A relational model. European Journal of Operational Research, 192 (3), 949-962


• Kao, C., (2009b). Efficiency decomposition in network data envelopment analysis: A relational model. European Journal of Operational Research, 192 (3), 949-962.


• Khoveyni, M.; Fukuyama, H.; Eslami, R.; Yang, G.L. Variations effect of intermediate products on the second stage in two-stage processes. Omega-Int. J. Manag. Sci. 2019, 85, 35–48.


• Kuosmanen, T., (2005).Weak Disposability in Non-parametric Productivity Analysis with Undesirable Outputs. American Journal of Agricultural Economics, 87, 1077-1082.


• Kuosmanen, T., Poidinovski, V., (2009). Weak Disposability in Nonparametric Productivity Analysis with Undesirable Outputs: Reply to Fare and Grosskopf. American Journal of Agricultural Economics.


• Lim, S., Zhu, J. (2019). Primal-dual correspondence and frontier projections in two-stage network DEA models. Omega, Elsevier, vol. 83(C), pages 236-248.


• Liu, J. S., Lu, L. Y. & Lu, W. M. (2016)." Research fronts in data envelopment analysis. Omega, 58, 33-45.


• Nemoto, J., & Goto, M. (1999). Dynamic data envelopment analysis: Modeling inter temporal behavior of a firm in the presence of productive inefficiencies. Economics Letters, 64, 51-56.


• Nemoto, J., & Goto, M. (2003). Measurement of dynamic efficiency in production: An application of data envelopment analysis to Japanese electric utilities. Journal of Productivity Analysis, 19, 191-210.


• Moghaddas, Z., Vaez-Ghasemi, M., Hosseinzadeh Lotfi, F., Farzipoor Saen, R. (2020). Stepwise pricing in evaluating revenue efficiency in Data Envelopment Analysis: A case study in power plants. Scientia Iranica,


• Seiford, L.M., Zhu, J., (2002). Modeling undesirable factors in efficiency evaluation. European Journal of Operational Research, 142, 16-20.


• Shephard, R.W., (1970). Theory of Cost and Production Functions. Princeton: Princeton University Press.


• Tajik Yabr, A. H., Najafi, S. E., Moghaddas, Z., & Shahnazari Shahrezaei, P. (2022). Interval Cross Efficiency Measurement for General Two-Stage Systems. Mathematical Problems in Engineering, 2022.


• Tavana, M., Shabanpour, H., Yousefi, S., & Saen, R. F. (2017). A hybrid goal programming and dynamic data envelopment analysis framework for sustainable supplier evaluation. Neural computing and applications, 28(12), 3683-3696.


• Tone, K., & Tsutsui, M. (2009). Network DEA: A slacks-based measure approach. European Journal of Operational Research, 197, 243-252.


• Tone, k., & Tsutsui, M. (2010). Dynamic DEA: A slacks-based measure approach. Omega, 38, 3-4.


• Tone, K., (2001), A slacks-based measure of efficiency in data envelopment analysis, European Journal of Operational Research;130(3):498–509.


• Tone, T., & Tsutsui, M. (2014). Dynamic DEA with network structure: A slacks-based measure approach. Omega, 42, 124-131.


• Vaez-Ghasemi, M.; Moghaddas, Z.; Saen, R.F. Cost efficiency evaluation in sustainable supply chains with marginal surcharge values for harmful environmental factors: A case study in a food industry. Oper. Res. 2021, 1–16.