 模型不考虑投入产出的规模报酬,只能计算出综合效率（即技术效率）,因此进一步引入考虑规模报酬可变的 模型,将技术效率分解为纯技术效率和规模效率.
 称为可变规模报酬的纯粹技术效率(Technical Efficiency from Variable Return to Scale) ,取值范围在 之间. 其经济意义为:
当 时,表示此时纯技术有效.当 时,表示此时纯技术无效.为了说明决策单元的规模报酬,引入规模效率(Scale Efficiency , ) ,表示在某一既定产出水平与生产前沿面的距离, .当规模效率 时,说明该决策单元的规报酬不变, 即为最优规模状态;当 时,说明该决策单元的规模报酬尚未处于最优,必须进行改进.
若 ,则DMU规模收益不变,此时DMU已达到最佳规模收益点；若 ,则DMU规模收益递减,表明对DMU投入量的增加,不会带来产出更高比例的增加,反而使投入比例的减少;若 ,则DMU规模收益递增,表明若对DMU在原有投入的基础上增加适当投入量会带来产出更高比例的增加.
4 DEA实证结果及分析
利用Deap2.1求解DEA模型,得到的结果如表6所示：
表6 DEA效率与规模收益计算结果
|
|
技术效率
|
纯技术效率
|
规模效率
|
规模收益
|
|
DMU 1
|
0.463
|
0.468
|
0.990
|
递增
|
|
DMU 2
|
0.780
|
0.820
|
0.952
|
递减
|
|
DMU 3
|
0.852
|
1.000
|
0.852
|
递减
|
|
DMU 4
|
0.525
|
0.529
|
0.992
|
递减
|
|
DMU 5
|
1.000
|
1.000
|
1.000
|
不变
|
|
DMU 6
|
0.610
|
0.613
|
0.995
|
递增
|
|
DMU 7
|
0.491
|
0.560
|
0.878
|
递减
|
|
DMU 8
|
0.717
|
0.857
|
0.837
|
递减
|
|
DMU 9
|
0.658
|
0.677
|
0.973
|
递增
|
|
DMU 10
|
1.000
|
1.000
|
1.000
|
不变
|
|
DMU 11
|
0.612
|
0.621
|
0.985
|
递减
|
|
DMU 12
|
0.808
|
1.000
|
0.808
|
递减
|
|
DMU 13
|
0.483
|
0.488
|
0.989
|
递增
|
|
DMU 14
|
0.806
|
0.828
|
0.973
|
递减
|
|
DMU 15
|
1.000
|
1.000
|
1.000
|
不变
|
|
DMU 16
|
0.684
|
0.694
|
0.985
|
递减
|
|
DMU 17
|
0.910
|
0.977
|
0.932
|
递减
|
|
DMU 18
|
1.000
|
1.000
|
1.000
|
不变
|
|
DMU 19
|
0.513
|
0.562
|
0.913
|
递减
|
|
DMU 20
|
0.604
|
0.638
|
0.947
|
递减
|
|
DMU 21
|
0.933
|
0.988
|
0.944
|
递减
|
|
DMU 22
|
0.894
|
1.000
|
0.894
|
递增
|
|
DMU 23
|
0.790
|
0.801
|
0.986
|
递增
|
|
DMU 24
|
0.820
|
0.975
|
0.840
|
递减
|
|
DMU 25
|
0.814
|
0.857
|
0.950
|
递减
|
|
DMU 26
|
0.656
|
0.670
|
0.979
|
递减
|
|
DMU 27
|
0.684
|
0.717
|
0.953
|
递减
|
|
DMU 28
|
0.817
|
0.850
|
0.961
|
递减
|
|
DMU 29
|
0.941
|
1.000
|
0.941
|
递减
|
|
DMU 30
|
0.608
|
0.631
|
0.963
|
递减
|
|
DMU 31
|
0.627
|
0.688
|
0.911
|
递减
|
|
DMU 32
|
0.588
|
0.625
|
0.941
|
递减
|
|
DMU 33
|
0.650
|
0.652
|
0.996
|
递增
|
|
DMU 34
|
0.778
|
0.840
|
0.927
|
递减
|
|
DMU 35
|
0.607
|
0.610
|
0.995
|
递增
|
由上表知35家医院之中D5, D10, D15, D18共4家医院的总体有效性为DEA有效,占总数的11.43%,说明这4家医院既是规模有效又是技术有效的.这4家医院样本数据组成的经济系统中,他们的生产要素己经达到最佳组合,并取得了最佳的产出效果,另有8家医院即D3,D5,D10,D12,D15,D18,D22及D29为纯技术效率有效,说明了这8家DMU是技术有效的,技术水平较高.在规模收益分析中,D5,D10,D15和D18的总体有效的DMU的规模收益不变,说明它们的医疗资源投入及产出比例很恰当,己经达到最佳规模点.D1,D6,D9,D13,D22, D23,
D33及D35规模收益为递增,说明这些DMU处在规模收益递增的阶段,这些DMU应当在合理的范围内加强资源的投入力度以提高各方面的产出.剩下DMU的收益为递减,说明这些DMU处在规模收益递减的阶段,这些DMU需要在合理的范围内调整资源的投入力度以提高各方面的产出.
参考文献
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