具有并行网络结构的生产系统是一类具有代表性的复杂生产系统. 由于一些重要的并行网络DEA 模型还没有处理好决策单元与其内部的子单元之间的关系, 因此, 可能导致DEA 投影点溢出生产可能集以及目标函数无法准确反映决策单元效率的问题. 为了解决这些问题, 本文首先通过实例分析了原有并行网络DEA 模型存在的问题. 然后, 提出一种基于全局视角的并行网络DEA 模型, 并讨论了该模型的相关性质. 最后, 将本文模型应用于中国台湾林地生产效率的实证分析. 结果表明, 本文模型不仅可以从全局的角度测算决策单元的效率、 给出无效决策单元及其子单元调整的信息, 而且还能解决子单元数量存在差异的效率分析问题.
Abstract
Production systems with parallel network structure are a representative class of complex production systems. Since some important parallel network DEA models have not well dealt with the relationship between the decision making unit (DMU) and its internal subunits, this leads to the problems that the DEA projection points may overflow the production possibility set and the objective function may not accurately reflect the efficiency of DMUs. In order to solve these problems, this paper first analyzes the problems of the original parallel network DEA model through some examples. Then, a parallel network DEA model based on a global perspective is proposed, and the relevant properties of the model are discussed. Finally, the model of this paper is applied to the empirical analysis of forest production efficiency in Taiwan, China. The results show that the model of this paper can not only measure the efficiency of DMUs from a global perspective, give information on the adjustment of inefficient DMUs and their subunits, but also solve the problem of efficiency analysis with differences in the numbers of subunits.
关键词
综合评价 /
多目标决策 /
数据包络分析 /
并行网络 /
DEA 有效
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Key words
comprehensive evaluation /
multi-objective decision making /
data envelopment analysis /
parallel network /
DEA efficiency
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中图分类号：
N94
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参考文献
[1] Charnes A, Cooper W W, Rhodes E. Measuring the efficiency of decision making units[J]. European Journal of Operational Research, 1978, 2(6): 429-444.
[2] Farrell M J. The measurement of productive efficiency[J]. Journal of the Royal Statistical Society, 1957, 120(3): 253-290.
[3] Kuan Y W, Chuen T K, Behrouzi F. A review on data envelopment analysis (DEA)[M]. Cambridge: Cambridge University Press, 2010.
[4] Zhou H B, Yang Y, Chen Y, et al. Data envelopment analysis application in sustainability: The origins, development and future directions[J]. European Journal of Operational Research, 2018, 264(1): 1-16.
[5] Färe R, Grosskopf S. Network DEA[J]. Socio-Economic Planning Sciences, 2000, 34(1): 35-49.
[6] Kao C, Hwang S N. Efficiency decomposition in two-stage data envelopment analysis: An application to non-life insurance companies in Taiwan[J]. European Journal of Operational Research, 2008, 185(1): 418-429.
[7] Liang L, Cook W D, Zhu J. DEA models for two-stage processes: Game approach and efficiency decomposition[J]. Naval Research Logistics, 2008, 55(7): 643-653.
[8] Kao C. Efficiency decomposition for general multi-stage systems in data envelopment analysis[J]. European Journal of Operational Research, 2014, 232(1): 117-124.
[9] Kao C. Efficiency decomposition for parallel production systems[J]. Journal of the Operational Research Society, 2012, 63(1): 64-71.
[10] An Q X, Wang Z R, Emrouznejad A, et al. Efficiency evaluation of parallel interdependent processes systems: An application to Chinese 985 Project universities[J]. International Journal of Production Research, 2019, 57(17): 5387-5399.
[11] Tone K, Tsutsui M. Dynamic DEA with network structure: A slacks-based measure approach[J]. Omega, 2014, 42(1): 124-131.
[12] Zarei M, Azar A, Emrouznejad A. A novel multilevel network slacks-based measure with an application in electric utility companies[J]. Energy, 2018, 158: 1120-1129.
[13] Podinovski V V. Variable and constant returns-to-scale production technologies with component processes[J]. Operations Research, 2022, 70(2): 1238-1258.
[14] Cook W D, Hababou M, Tuenter H J H. Multicomponent efficiency measurement and shared inputs in DEA: An application to sales and service performance in bank branches[J]. Journal of Productivity Analysis, 2000, 14: 209-224.
[15] Xiong X, Yang G L, Guan Z C. A parallel DEA-based method for evaluating parallel independent subunits with heterogeneous outputs[J]. Journal of Informetrics, 2020, 14(3): 101049.
[16] 王有森, 许皓. 基于数据包络分析的并行生产系统效率评价方法[J]. 运筹学学报, 2015, 19(4): 29-40.Wang Y S, Xu H. Parallel production systems efficiency evaluation based on DEA[J]. Operations Research Transactions, 2015, 19(4): 29-40.
[17] Kao C. Efficiency measurement for parallel production systems[J]. European Journal of Operational Research, 2009, 196(3): 1107-1112.
[18] Kashim R, Kasim M M, Rahman R A. Measuring effectiveness of a university by a parallel network DEA model[J]. AIP Conference Proceedings, 2017, 1905(1): 1-6.
[19] Gong Y, Zhu J, Chen Y, et al. DEA as a tool for auditing: Application to Chinese manufacturing industry with parallel network structures[J]. Annals of Operations Research, 2018, 263(1-2): 1-23.
[20] Färe R, Primont D. Efficiency measures for multiplant firms[J]. Operations Research Letters, 1988, 3(5): 257-260.
[21] Kao C. Measuring the efficiency of forest districts with multiple working circles[J]. Journal of Operational Research Society, 1998, 49(6): 583-590.
[22] Ashrafi A, Jaafar A B, Bakar M, et al. The efficiency measurement of parallel production systems: A non-radial data envelopment analysis model[J]. Journal of Computer Science, 2011, 7(5): 749-756.
[23] Lozano S. A joint-inputs network DEA approach to production and pollution-generating technologies[J]. Expert Systems with Applications, 2015, 42(21): 7960-7968.
[24] Bian Y W, Hu M, Wang Y S, et al. Energy efficiency analysis of the economic system in China during 1986-2012: A parallel slacks-based measure approach[J]. Renewable and Sustainable Energy Reviews, 2016, 55: 990-998.
[25] Tang T B, You J X, Sun H, et al. Transportation efficiency evaluation considering the environmental impact for China's freight sector: A parallel data envelopment analysis[J]. Multidisciplinary Digital Publishing Institute, 2019, 11(18): 5108.
[26] 马占新, 马生昀. 基于样本评价的广义数据包络分析方法[J]. 数学的实践与认识, 2011, 41(21): 155-171.Ma Z X, Ma S Y. Generalized data envelopment analysis method by using sample units[J]. Journal of Mathematics in Practice and Theory, 2011, 41(21): 155-171.
[27] 马占新. 广义参考集DEA 模型及其相关性质[J]. 系统工程与电子技术, 2012, 34(4): 709-714.Ma Z X. DEA model with generalized reference set and its properties[J]. Systems Engineering and Electronics, 2012, 34(4): 709-714.
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基金
国家自然科学基金(72161031); 国家自然科学基金(71661025); 内蒙古自然科学基金(2021MS07025); 内蒙古草原英才项目(12000-12102012)
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