Measuring the cost efficiency in NDEA
Subject Areas : StatisticsShahruz Fathi Ajirlu 1 , Alireza Amirteimoori 2 , Sohrab Kordrostami 3
1 - Department of Applied Mathematics, Guilan Science and Research Branch, Islamic Azad University, Rasht,, Iran.Department of mathematics, Rasht Branch, Islamic Azad University
2 - Department of mathematics, Rasht Branch, Islamic Azad University, Rasht , iran.
3 - Department of mathematics, lahijan Branch, Islamic Azad University, lahijan , iran
Keywords: سیستم شبکه, تحلیل پوششی دادهها, کارآیی هزینه,
Abstract :
Data Envelopment Analysis (DEA) is a relatively new data oriented approach for evaluating the performance of a set of peer entities called Decision-Making Units (DMUs) which convert multiple inputs into multiple outputs. In a relatively short period of time DEA has grown into a powerful quantitative, analytical tool for measuring and evaluating performance. DEA has been successfully applied to a host of different types of entities engaged in a wide variety of activities in many contexts worldwide. The issue of measuring the cost efficiency in manufacturing and economic systems is one of the most important issues in the world. In the real world, there are manufacturing and economic systems that are composed of independent units. One of the ways to measure the cost efficiency for economic and production systems is the DEA technique. This paper presents two network DEA models to measure the cost efficiency of a network model with identical processing components taking into account the individual processing functions in the network structure. In this paper, we examine the cost efficieny model of Färe et al., and through modifying the model of Färe et al., a model has been developed to measure the cost efficiency in economic and manufacturing networks.
[1] Charnes, A., Cooper, W. W., Rhodes, E. (1978). Measuring the efficiency of decision making units, European Journal of Operational Research, 2, 429–441.
[2] Kao, C. (2014). Network data envelopment analysis: A review, European Journal of Operational Research, 239,1–16
[3] Charnes, A., Cooper, W. W., Golany, B., Halek, R., Klopp, G., Schmitz, E., et al. (1986). Two-phase data envelopment analysis approaches to policy evaluation and management of army recruiting activities: Tradeoffs between joint services and army advertising, Research Report CCS #532, Center for Cybernetic Studies, University of Texas-Austin, Austin, TX.
[4] Wang, C. H., Gopal, R. D., Zionts, S. (1997). Use of data envelopment analysis in assessing information technology impact on firm performance, Annals of Operations Research, 73, 191–213.
[5] Färe, R., Grosskopf, S. (2000). Network DEA, Socio-Economic Planning Sciences, 34, 35-49.
[6] Kao, C., Hwang, S. N. (2008). Efficiency decomposition in two-stage data envelopment analysis: An application to non-life insurance companies in Taiwan Price of Robustness, European Journal of Operational Research, 185, 418–429.
[7] Chen, Y., Cook, W. D., Li, N., Zhu, J., (2009). Additive efficiency decomposition in two stage DEA, European Journal of Operational Research,196(3), 1170–1176.
[8] Wang, Y.-M., Chin, K.-S., (2010). Some alternative DEA models for two-stage process. Expert Systems with Applications, 37 (12), 8799-8808.
[9] Liang. L, Cook. W. D, Zhu.J. DEA models for two-stage processes: game approach and efficiency decomposition. Naval Research Logistics 2008; 55:643–53.
[10] Li, Y., Chen, Y., Liang, L., Xie, J., DEA models for extended two-stage network structures, Omega 40 (5) (2012) 611–618.
[11] Kao, C. Efficiency decomposition in network data envelopment analysis: a relational model. European Journal of Operational Research 2009;192: 949–62.
[12] Cook, W. D., Liang, L., Zhu, J. (2010). Measuring performance of two-stage network structures by DEA: A review and future perspective, Omega, 38, 423–430.
[13] Akther, S., Fukuyama, H., Weber, W. L. Estimating two-stage network Slacks-based inefficiency: an application to Bangladesh banking, Omega 41 (2013) 88–96.
[14] Barros, C. P., Managi, S., Matousek, R. The technical efficiency of the Japanese banks: non-radial directional performance measurement with undesirable output, Omega 40 (1) (2012) 1–8.
[15] Fujii, H., Managi, S., Matousek, R. Indian bank efficiency and productivity changes with undesirable outputs: a disaggregated approach, J. Bank. Finance 38 (2014) 41–50.
[16] Lozano, S., Gutierrez, E., Moreno, P. (2013). DEA approach to airports performance assessment considering undesirable outputs, Applied Mathematical Modelling, 37, 1665–1676.
[17] Lozano, S. (2017), Technical and environmental efficiency of a two-stage production and abatement system, Annals of Operations Research, 255, 199–219.
[18] Wu, J., Zhu, Q., Chu, J., Liang, L. (2015), Two-Stage Network Structures with Undesirable Intermediate Outputs Reused: A DEA Based Approach. Computational Economics, 46(3), 455-477.
[19] Amirteimoori, A. A DEA two-stage decision process with shared resources, Central European Journal of Operational Research 21 (2013) 141–151.
[20] Chu, J., Wu, J., Zhu, Q., An, Q., Xiong, B. Analysis of China’s Regional Eco-efficiency: A DEA, Two-stage Network Approach with Equitable Efficiency Decomposition. Comput Econ.23 Springer Science+Business Media NewYork 2016, Volume 54,1263–1285.
[21] Song, M., Wang, S., iLiu, W. A two-stage DEA approach for environmental efficiency Measurement. Environ Monit Assess (2014) 186:3041–3051.
[22] Despotis, D. K., Koronakos, G., Sotiros, D. (2016), Composition versus decomposition in two-stage network DEA: a reverse approach. Journal of Productivity Analysis, 45, 71–87.
[23] Halkos, G. E, Tzeremes, N. G., Kourtzidis, S. A. (2015), Regional sustainability efficiency index in Europe: an additive two-stage DEA approach. Operational Research 15, 1–23.
[24] Kao, C. Efficiency decomposition in network data envelopment analysis with slacks-based measures Omega 45 (2014) 1–6.
[25] Amirteimoori, A., Kordrostami, S. and Azizi, H. (2016), Additive models for network data envelopmentanalysis in the presence of shared resources, Transportation Research Part D: Transport and Environment, 48, 411-424.
[26] Farrell, M. J. (1957). The measurement productive of efficiency, Journal of the Royal Statistical Society. Series A (General), 120, (1957), 253-290.
[27] Fare, R., Grosskopf, S., Lovell, C.A.K. (1985). The measurement of efficiency of production, Kluwer Academic Publishers.
[28] Sueyoshi, T. (1997). Measuring efficiencies and returns to scale of Nippon telegraph telephone in production and cost analyses, Management Science, 43, 779–796.
[29] Puig-Junoy, J. (2000). Partitioning input cost efficiency into its allocative and technical components: An empirical DEA application to hospitals, Socio Economic Planning Sciences, 34, 199–218.
[30] Kuosmanen, T., Post, T. (2001). Measuring economic efficiency with incomplete price information: With an application to European commercial banks, European Journal of Operational Research, 134, 43–58.
[31] Tone, K. (2002). A Strange case of the cost and allocative efficiencies in DEA, Journal of the Operational Research Society, 53, 1225–1231.
[32] Camanho, A. S., Dyson, R. G. (2005). Cost efficiency measurement with price uncertainty: A DEA application to bank branch assessments, European Journal of Operational Research, 161, 432–446.
[33] Tone, K., Sahoo, B. K. (2006). Re-examining scale elasticity in DEA, Annals of Operations Research, 145, 69–87.
[34] Maniadakis, N., Thanassoulis, E. (2004). A cost Malmquist productivity index, European Journal of Operational Research, 154, 396–409.
[35] Sengupta, J. K., Sahoo, B. K. (2006). Efficiency models in data envelopment analysis: Techniques of evaluation of productivity of firms in a growing economy, London: Palgrave Macmillan.
[36] Jahanshahloo, G. R., Soleimani-Damaneh, M., Mostafaee, A. (2008). A simplified versionof the DEA cost efficiency model, European Journal of Operational Research, 184, 814–815.
[37] Mostafaee, A., Saljooghi, F. H. (2010). Cost efficiency measures in data envelopment analysis with data uncertainty., European Journal of Operational Research, 202, 595–603.
[38] Sahoo, B. K., Kerstens, K., Tone, K. (2012). Returns to growth in a non parametric DEA approach, International Transactions in Operational Research, 19, 463–486.
[39] Jahanshahloo, G. R., Mirdehghan, S. M., Vakili.J. (2011). An Interpretation of the Cost model in Data Invelopment Analysis, Journal of applied sciences, 11(2), 389-392.
[40] Toloo, M. Aghayi, N. Rostamy-malkhalifeh, M. (2008). Measuring overall profit efficiency with interval data, Applied Mathematics and Computation, 201(1-2), 640-649.
[41] Jahanshahloo, G.R. Shahverdi, R. RostamyMalkhalifeh, M. (2007). Cost efficiency and cost malmquist productivity index with interval data, International Mathematical Forum, 2(9), 441-453.
[42] RostamyMalkhalifeh, M. Aghayi, N. (2011). Cost efficiency and cost malmquist productivity index with interval data, Journal of Mathematical Extension, 5(2), 73-90.
[43] RostamyMalkhalifeh, M. Aghayi, N. (2013). Two Ranking of Units on the Overall Profit Efficiency with Interval Data, Mathematics Scientific Journal, 8(2), 73-93.
[44] Emrouznejad, A. Rostamy-Malkhalifeh, M. Hatami-Marbini, A. Tavana, M. Aghayi, N. (2011). An overall profit Malmquist productivity index with fuzzy and interval data, Mathematical and Computer Modelling, 54(11-12), 2827-2838.
