ISSN 0253-2778

CN 34-1054/N

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Open AccessOpen Access JUSTC Original Paper

Efficiency evaluation and methods of resource allocation of parallel production system based on DEA

  • School of Management, University of Science and Technology of China, Hefei 230026, China

Cite this:
https://doi.org/10.3969/j.issn.0253-2778.2016.11.009
  • Received Date: 25 October 2015
  • Accepted Date: 10 April 2016
  • Rev Recd Date: 10 April 2016
  • Publish Date: 30 November 2016
    Abstract

  • Abstract

    To study the efficiency evaluation and resource allocation of parallel production system, the efficiency of service departments was calculated and the principle of allocation about shared resources in DEA parallel system, or the mechanism satisfying the maximization of overall efficiency, was explored. This is an indepth analysis and explanation of how to allocate shared resources in parallel production system with the methods of DEA. The results indicate that: firstly, when maximizing overall efficiency, the overall efficiency score is a convex combination of efficiency scores of two sub units under the optimal allocation coefficient; secondly, when maximizing overall efficiency, the sub unit whose efficiency score is equal to the overall efficiency reaches its own maximum efficiency. At this time, the efficient sub unit by DEA is allocated all of the shared resources, while the inefficient one gets nothing.

    Abstract

    To study the efficiency evaluation and resource allocation of parallel production system, the efficiency of service departments was calculated and the principle of allocation about shared resources in DEA parallel system, or the mechanism satisfying the maximization of overall efficiency, was explored. This is an indepth analysis and explanation of how to allocate shared resources in parallel production system with the methods of DEA. The results indicate that: firstly, when maximizing overall efficiency, the overall efficiency score is a convex combination of efficiency scores of two sub units under the optimal allocation coefficient; secondly, when maximizing overall efficiency, the sub unit whose efficiency score is equal to the overall efficiency reaches its own maximum efficiency. At this time, the efficient sub unit by DEA is allocated all of the shared resources, while the inefficient one gets nothing.
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    • References(22)
  • [1]
    FARRELL M J．The measurement of productive efficiency[J]. Journal of Royal Statistical Society, Series A (General), 1957, 120(3): 253-281.
    [2]
    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.
    [3]
    YANG Y, MA B, KOIKE M．Efficiency-measuring DEA model for production system with k independent subsystems[J]．Journal of the Operations Research Society of Japan, 2000, 43(3): 343-354.
    [4]
    杨锋,梁樑,凌六一,等.并联结构决策单元的DEA效率评价研究[J]．中国管理科学, 2009, 17(6): 157-162.
    YANG Feng, LIANG Liang, LING Liuyi, et a1. DEA efficiency evaluating models for DMUs with parallel structure[J]. Chinese Journal of Management Science, 2009, 17(6): 157-162.
    [5]
    KAO C．Efficiency measurement for parallel production systems[J]. European Journal of Operational Research, 2009, 196 (3):1 107-1 112.
    [6]
    段永瑞, 田澎, 张卫平. 具有独立子系统的DEA模型及其应用[J]．管理工程学报, 200620(1)：27-31.
    DUAN Yongrui, TIAN Peng, ZHANG Weiping. DEA models with independent subsystems and their application[J]. Journal of Industrial Engineering and Engineering Management, 2006, 20(1): 27-31.
    [7]
    CHEN Y，LIANG L，YANG F．A DEA game model approach to supply chain efficiency[J]. Annals of Operations Research, 2006, 145(1): 5-13.
    [8]
    LIANG L, YANG F, COOK W D, et a1. DEA models for supply chain efficiency evaluation[J]. Annals of Operations Research, 2006, 145(1): 35-49.
    [9]
    CHEN Y, LIANG L, ZHU J. Equivalence in two-stage DEA approaches[J]. European Journal of Operational Research, 2009, 193(2): 600-604.
    [10]
    CHEN Y, COOK W D, LI N, et a1. Additive efficiency decomposition in two-stage DEA[J]. European Journal of Operational Research, 2009, 196(3): 1 170-1 176.
    [11]
    GOLANY B. An interactive MOLP procedure for the extension of DEA to effectiveness analysis[J]. Journal of Operational Research Society, 1988, 39(8): 725-734.
    [12]
    ATHANASSOPOULOS A D. Goal programming ＆ data envelopment analysis (GoDEA) for target-based multi-level planning: Allocating central grants to the Greek local authorities[J]. European Journal of Operational Research, 1995, 87: 535-550.
    [13]
    ATHANASSOPOULOS A D．Decision support for target-based resource allocation of public services in multiunit and multilevel systems[J]. Management Science, 1998, 44 (2): 173-187.
    [14]
    GOLANY B, TAMIR E. Evaluating efficiency-effectiveness-equality trade-offs: A data envelopment analysis approach[J]. Management Science, 1995, 41(7): 1 172-1 184.
    [15]
    BEASLEY J E. Allocating fixed costs and resources via data envelopment analysis[J]. European Journal of Operational Research, 2003, 147: 198-216．
    [16]
    KORHONEN P, SYRJANEN M．Resource allocation based on efficiency analysis[J]. Management Science, 2004, 50(8): 1 134-1 144.
    [17]
    PACHKOVA E V. Restricted reallocation of resources[J]. European Journal of Operational Research, 2009, 196: 1 049-1 057.
    [18]
    李晓亚，崔晋川．基于DEA方法的额外资源分配算法[J].系统工程学报, 2007, 22( 1): 57 -61．
    LI Xiaoya, CUI Jinchuan. Arithmetic of extra resource allocation based on DEA method[J]. Journal of Systems Engineering, 2007, 22( 1): 57 -61.
    [19]
    YANG Y S, MA B J, MASAYUKI K. Efficiency-measuring DEA model for production system with k in-dependent subsystems[J]. Journal of the Operations Research Society of Japan, 2000, 43(3): 343-354.
    [20]
    段永瑞,田澎,张卫平.具有独立子系统的DEA模型及其应用[J].管理工程学报, 2006, 20(1): 27-31.
    DUAN Yongrui, TIAN Peng, ZHANG Weiping. DEA models with independent subsystems and their application[J]. Journal of Industrial Engineering and Engineering Management, 2006, 20(1): 27-31.
    [21]
    BEASLEY J E. Determining teaching and research efficiencies[J]. Journal of the Operational Research Society, 1995, 46(4): 441-452.
    [22]
    COOK W D, HABABOU M, TUENTER H J H. Multicomponent efficiency measurement and shared inputs in data envelopment analysis: An application to sales and service performance in bank branches[J]. Journal of Productivity Analysis, 2000, 14(3): 209-224.
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    [1]
    FARRELL M J．The measurement of productive efficiency[J]. Journal of Royal Statistical Society, Series A (General), 1957, 120(3): 253-281.
    [2]
    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.
    [3]
    YANG Y, MA B, KOIKE M．Efficiency-measuring DEA model for production system with k independent subsystems[J]．Journal of the Operations Research Society of Japan, 2000, 43(3): 343-354.
    [4]
    杨锋,梁樑,凌六一,等.并联结构决策单元的DEA效率评价研究[J]．中国管理科学, 2009, 17(6): 157-162.
    YANG Feng, LIANG Liang, LING Liuyi, et a1. DEA efficiency evaluating models for DMUs with parallel structure[J]. Chinese Journal of Management Science, 2009, 17(6): 157-162.
    [5]
    KAO C．Efficiency measurement for parallel production systems[J]. European Journal of Operational Research, 2009, 196 (3):1 107-1 112.
    [6]
    段永瑞, 田澎, 张卫平. 具有独立子系统的DEA模型及其应用[J]．管理工程学报, 200620(1)：27-31.
    DUAN Yongrui, TIAN Peng, ZHANG Weiping. DEA models with independent subsystems and their application[J]. Journal of Industrial Engineering and Engineering Management, 2006, 20(1): 27-31.
    [7]
    CHEN Y，LIANG L，YANG F．A DEA game model approach to supply chain efficiency[J]. Annals of Operations Research, 2006, 145(1): 5-13.
    [8]
    LIANG L, YANG F, COOK W D, et a1. DEA models for supply chain efficiency evaluation[J]. Annals of Operations Research, 2006, 145(1): 35-49.
    [9]
    CHEN Y, LIANG L, ZHU J. Equivalence in two-stage DEA approaches[J]. European Journal of Operational Research, 2009, 193(2): 600-604.
    [10]
    CHEN Y, COOK W D, LI N, et a1. Additive efficiency decomposition in two-stage DEA[J]. European Journal of Operational Research, 2009, 196(3): 1 170-1 176.
    [11]
    GOLANY B. An interactive MOLP procedure for the extension of DEA to effectiveness analysis[J]. Journal of Operational Research Society, 1988, 39(8): 725-734.
    [12]
    ATHANASSOPOULOS A D. Goal programming ＆ data envelopment analysis (GoDEA) for target-based multi-level planning: Allocating central grants to the Greek local authorities[J]. European Journal of Operational Research, 1995, 87: 535-550.
    [13]
    ATHANASSOPOULOS A D．Decision support for target-based resource allocation of public services in multiunit and multilevel systems[J]. Management Science, 1998, 44 (2): 173-187.
    [14]
    GOLANY B, TAMIR E. Evaluating efficiency-effectiveness-equality trade-offs: A data envelopment analysis approach[J]. Management Science, 1995, 41(7): 1 172-1 184.
    [15]
    BEASLEY J E. Allocating fixed costs and resources via data envelopment analysis[J]. European Journal of Operational Research, 2003, 147: 198-216．
    [16]
    KORHONEN P, SYRJANEN M．Resource allocation based on efficiency analysis[J]. Management Science, 2004, 50(8): 1 134-1 144.
    [17]
    PACHKOVA E V. Restricted reallocation of resources[J]. European Journal of Operational Research, 2009, 196: 1 049-1 057.
    [18]
    李晓亚，崔晋川．基于DEA方法的额外资源分配算法[J].系统工程学报, 2007, 22( 1): 57 -61．
    LI Xiaoya, CUI Jinchuan. Arithmetic of extra resource allocation based on DEA method[J]. Journal of Systems Engineering, 2007, 22( 1): 57 -61.
    [19]
    YANG Y S, MA B J, MASAYUKI K. Efficiency-measuring DEA model for production system with k in-dependent subsystems[J]. Journal of the Operations Research Society of Japan, 2000, 43(3): 343-354.
    [20]
    段永瑞,田澎,张卫平.具有独立子系统的DEA模型及其应用[J].管理工程学报, 2006, 20(1): 27-31.
    DUAN Yongrui, TIAN Peng, ZHANG Weiping. DEA models with independent subsystems and their application[J]. Journal of Industrial Engineering and Engineering Management, 2006, 20(1): 27-31.
    [21]
    BEASLEY J E. Determining teaching and research efficiencies[J]. Journal of the Operational Research Society, 1995, 46(4): 441-452.
    [22]
    COOK W D, HABABOU M, TUENTER H J H. Multicomponent efficiency measurement and shared inputs in data envelopment analysis: An application to sales and service performance in bank branches[J]. Journal of Productivity Analysis, 2000, 14(3): 209-224.
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