ABSTRACT The perspective of internal structure of the decision making units (DMUs) was considered as the “black box” when employing data envelopment analysis (DEA) models. However, in the actual world there are always some DMUs that are composed of several sub-units or subsystems, each utilizes the same inputs to generate same outputs. Numerous instances can be listed, such as a firm with a few of plants. In this paper we present models that evaluated the efficiency of DMU which is comprised of same several parallel subsystems, the foremost contribution of our work is that we take the different importance of the subsystems into account in the model, which can be obviously distinguished to the existing DEA model. Secondly, since the alternative optimal multipliers may emerge in the model, the efficiency of each subsystem may be non-unique and we simultaneously develop models of efficiency decomposition for each subsystem. At last a case of technological innovation activities of each province in China is used as an example to state the models.
Cite this paper
nullJ. Wang and Y. Li, "DEA Models for the Efficiency Evaluation of System Composed of Parallel Subsystems," American Journal of Operations Research, Vol. 1 No. 4, 2011, pp. 284-292. doi: 10.4236/ajor.2011.14033.
 Y. J. Li, F. Yang, L. Liang and Z. S. Hua, “Allocating the Fixed Cost as a Complement of Other Cost Inputs: A DEA Approach,” European Journal of Operational Research, Vol. 197, No. 1, 2009, pp. 389-401.
 A. Charnes, W. W. Cooper and E. Rhodes, “Measuring the Efficiency of Decision Making Units,” European Journal of Operational Research, Vol. 2, No. 6, 1978, pp. 429-444. doi:10.1016/0377-2217(78)90138-8
 R. D. Banker, A. Charnes and W. W. Cooper, “Some Models for Estimating Technical and Scale Inefficiencies in Data Envelopment Analysis,” Management Science, Vol. 30, No. 9, 1984, pp. 1078-1092.
 R. F?re and S. Grosskopf, “A Nonparametric Cost Approach to Scale Efficiency,” Journal of Economics, Vol. 87, No. 4, 1985, pp. 594-604.
 L. M. Seiford and R. M. Thrall, “Resent Development in DEA—The Mathematical Programming Approach to Frontier Analysis,” Journal of Economics, Vol. 46, No. 1-2, 1990, pp. 7-38.
 C. Kao and S. N. Hwang, “Efficiency Decomposition in Two-Stage Data Envelopment Analysis: An Application to Non-Life Insurance Companies in Taiwan,” European Journal of Operational Research, Vol. 185, No. 1, 2008, pp. 418-429. doi:10.1016/j.ejor.2006.11.041
 L. Liang, W. D. Cook and J. Zhu, “DEA Models for Two-Stage Processes: Game Approach and Efficiency Decomposition,” Naval Research Logistics, Vol. 55, No. 7, 2008, pp. 643-653. doi:10.1002/nav.20308
 Y. Chen, J. Du, H. D. Sherman and J. Zhu, “DEA Model with Shared Resources and Efficiency Decomposition,” European Journal of Operational Research, Vol. 207, No. 1, 2010, pp. 339-349.
 Y. Zha and L. Liang, “Two-Stage Cooperation Model with Input Freely Distributed among the Stages,” European Journal of Operational Research, Vol. 205, No. 2, 2010, pp. 332-338. doi:10.1016/j.ejor.2010.01.010
 R. F?re and S. Grosskopf, “Network DEA,” Socio-Economic Planning Science, Vol. 34, No. 1, 2000, pp. 35-49.
 H. F. Lewis and T. R. Sexton, “Network DEA: Efficiency Analysis of Organizations with Complex Internal Structure,” Computers and Operations Research, Vol. 31, No. 9, 2004, pp. 1365-1410.
 K. Tone and M. Tsutsui, “Network DEA: A Slacks-Based Measure Approach,” European Journal of Operational Research, Vol. 197, No. 1, 2009, pp. 243-252.
 R. F?re and D. Primont, “Efficiency Measures for Multiplant Firms,” Operations Research Letters, Vol. 3, No. 5, 1984, pp. 257-260. doi:10.1016/0167-6377(84)90057-9
 Y. S. Yang, B. J. Ma and M. Koike, “Efficiency-Mea- suring DEA Model for Production System with k Independent Subsystems,” Journal of the Operations Research Society of Japan, Vol. 43, No. 3, 2000, pp. 343- 353.
 L. Castelli, R. Pesenti and W. Ukovich, “DEA-Like Models for the Efficiency Evaluation of Hierarchically Structured Units,” European Journal of Operational Research, Vol. 154, No. 2, 2004, pp. 465-476.
 C. Kao, “Efficiency Measurement for Parallel Production Systems,” European Journal of Operational Research, Vol. 196, No. 3, 2009, pp. 1107-1112.
 W. Meng, D. Q. Zhang, L. Qi and W. B. Liu, “Two-Level DEA Approached in Research Evaluation,” Omega, Vol. 36, No. 6, 2008, pp. 950-957.
 W. Zhong, W. Yuan, S. X. Li and Z. M. Huang, “The Performance Evaluation of Regional R&D Investments in China: An Application of DEA Based on the First Official China Economic Census Data,” Omega, Vol. 39, No. 4, 2011, pp. 447-455.
 Z. Griliches, “Patents Statistics as Economic Indicators: A Survey,” Journal of Economic Literature, Vol. 28, No. 4, 1990, pp. 1661-1707.
 G. Ahuja and R. Karila, “Technological Acquisition and the Innovation Performance of Acquiring Firms: A Longitudinal Study,” Strategic Management Journal, Vol. 22, No. 3, 2001, pp. 197-220. doi:10.1002/smj.157