An enhanced Russell model to measure aggregate efficiency of multi-period production systems
Subject Areas : StatisticsMohammad Najari Alamouti 1 , Mohsen Khounsiavash 2 , Reza Kazimi Matin 3 , Zohreh Moghaddas 4
1 - PhD Student in Applied Mathematics, Department of Mathematics, Qazvin Branch, Islamic Azad University, Qazvin, Iran
2 - Assistant Professor, Department of Mathematics, Qazvin Branch, Islamic Azad University, Qazvin, Iran
3 - Associate Professor, Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran
4 - Assistant Professor, Department of Mathematics, Qazvin Branch, Islamic Azad University, Qazvin, Iran
Keywords: تحلیل پوششی دادهها, واحدهای تصمیم گیرنده, اندازه راسل, کارایی, تولید چند دورهای,
Abstract :
Performance evaluation of the production systems by considering data related to different time periods is one of the most important issues of production theory. In this paper, a new method for measuring the aggregative efficiency of multi-period production systems using the data envelopment analysis (DEA) technique is proposed. The provided approach could be considered as extension of the radial methods in the literature. An extended Russell based model is presented for the first time to measure aggregative efficiency with respect to the time intervals of the production stages. One of the useful features of the proposed model is that the inefficiency of the existing aggregative approach is detected in one step without need to account for the second stage of optimizing slack variables. Some properties and advantages of the new model is discussed. Finally, to illustrate the applicability of the new approach, two practical examples are investigated and analyzed. The results show the good performance of the proposed method.
[1] Charnes, A., Cooper, W., Rhodes, E. (1978). Measuring the efficiency of decision making units, European Journal of Operational Research, 2, 429–444.
[2] Banker, R., Charnes, A., Cooper, W. (1984). Some models for estimating technical and scale inefficiencies in data envelopment analysis, Management Science, 30, 1031-1142.
[3] Wang, K., Huang, W., Wu, J., Liu, Y.-N. (2014). Efficiency measures of the Chinese commercial banking system using an additive two-stage DEA. Omega, 44,5-20.
[4] Lee, B.L., Worthington, A.C. (2016). A network DEA quantity and quality-orientated production model: An application to Australian university research services, Omega, 60, 26-33.
[5] Chowdhury, H., Zelenyuk, V. (2016). Performance of hospital services in Ontario: DEA with truncated regression approach, Omega, 63, 111-122.
[6] Akbari, F., Arab, M., Keshavarz, K., Dadashi, A. (2012). Technical efficiency analyses in hospitals of Tabriz University of Medical Sciences. Hospital, 11(2), 65-76. [Article in Persian]
[7] Wang, K., Yu, S., Zhang, W. (2013). China’s regional energy and environmental efficiency: A DEA window analysis based dynamic evaluation, 58(5-6), 1117-1127.
[8] Witzel, M. (2002). A short history of efficiency, Business Strategy Review, 13, 38-47.
[9] Sueyoshi, T. (2000). Stochastic DEA for restructure strategy: an application to a Japanese petroleum company, Omega,
28(4), 385-398.
[10] Shaw, G., Williams, M.A. (2004). Tourism and Tourism Spaces, SAGE Publications, London.
[11] Kralj, A., Solnet, D. (2010). Service climate and customer satisfaction in a casino hotel: An exploratory case study, International Journal of Hospitality Management, 29, 711-719.
[12] Caves, D., Christensen, L., Diewert, W.E. (1982). The economic theory of index numbers and the measurement input, output, and productivity, Econometrica, 50(6), 1393-1414.
[13] Färe, R., Grosskopf, S. (1996). Intertemporal Production Frontiers: With Dynamic DEA, Kluwer Academic Publishers, and Boston.
[14] Nemoto, J., Goto, M. (1999). Dynamic data envelopment analysis: modeling intertemporal behavior of a firm in the presence of productive inefficiencies, Economic Letters, 64, 51-56.
[15] Park, K.S., Park, K. (2009). Measurement of multi-period aggregative efficiency, European Journal of operational Research, 193(2), 567-580.
[16] Amirteimoori, A., Kordrostami, S. (2010). Multi-period efficiency analysis in data envelopment analysis, International Journal of Mathematics in Operational Research, 2(1), 113-128.
[17] Kao, C., Liu, S.-T. (2014). Multi-period efficiency measurement in data envelopment analysis: The case of Taiwanese commercial banks. Omega, 47, 90-98.
[18] Kau, C., Hwang, S.-N. (2014). Multi-period efficiency and Malmquist productivity index in two-stage production systems, European Journal of Operational Research, 232(3), 512-521.
[19] Jablonsky, J. (2016). Efficiency analysis in multi-period systems: an application to performance evaluation in Czech higher education, Central European Journal of Operations Research, 24(2), 283-296.
[20] Razavi Hajiagha, S.H., Hashemi, S.S., Amoozed Mahdiraji, H., Azaddel, J. (2015). Multi-period data envelopment analysis based on Chebyshev inequality bounds, Expert Systems with Applications, 42(21), 7759-7767.
[21] Kordrostami, S., Jahani Sayyed Noveiri, M. (2017). Evaluating the efficiency of firns with negative data in multi-period systems: An application to bank data, International Journal of Industrial Mathematics, 9(1), 27-35.
[22] Esmaeilzadeh, A., Hadi-Vencheh, A. (2013). A super-efficiency model for measuring aggregative efficiency of multi-period production systems, Measurement, 46(10), 3988-3993.
[23] Jahani Sayyad Noveiri, M., Kordrostami, S., Amirteimoori, A. (2018). Detecting the multi-period performance and efficiency changes of systems with undesirable outputs, Discrete Mathematics, Algorithms and Applications, 10(3), 1850034.
[24] Esmaeilzadeh, A., Matin, R.K. (2019). Multi-period efficiency measurement of network production systems, Measurement, 134, 835-844.
[25] Tavana, M., Khalili-Damghani, K., Santos Arteaga, F.J., Hosseini, A. (2019). A fuzzy multi-objective multi-period network DEA model for efficiency measurement in oil refineries, Computers & Industrial Engineering, 135, 143-155.