基于效率补偿机制的区间标杆面研究

doi:10.16381/j.cnki.issn1003-207x.2023.0311

摘要/Abstract

摘要：

在区间数据包络分析中，由于投入产出数据为区间数，作为评价参照的生产可能集与被评价的决策单元生产点会不一致，这导致区间效率评价存在正向以及负向溢出现象。本文考虑到评价统一性和全面性，提出效率补偿机制，通过设定相容约束条件构建基于最佳及最差生产可能集的交互式效率评价模型，一定程度减少了正向以及负向溢出。随后，本文通过一般区间效率和基准区间之间的可能度定义来表示评价结果的溢出度，并结合溢出度定义了决策单元效率的可达性。本研究从有效性和可达性定义标杆面，使得标杆面构建可适应于多种决策环境。最后，将本文方法应用于我国森林碳汇效率的评价，基于效率评价结果选取了8个省份作为标杆，结果表明这8个省份在森林碳汇发展中分别具有经济优势、资源优势或是管理优势，这为中国森林绩效管理提供了发展路径的指引，具有现实参考价值。

关键词: 数据包络分析, 区间数据, 效率补偿, 标杆面构建

Abstract:

Due to the input-output data are interval numbers in interval data envelopment analysis（DEA）， the production possibility set（PPS） used as the evaluation reference may not be consistent with the production point of the evaluated decision-making unit（DMU）， which leads to positive and negative spillovers in interval efficiency evaluation. Based on the existing interval efficiency DEA model considering the unity and comprehensiveness of the evaluation， an efficiency compensation mechanism is proposed， and an interactive efficiency evaluation model is constructed based on the best and worst PPS by setting compatible constraints， which reduces the positive and negative spillovers to a certain extent. Subsequently， the spillover of the evaluation results is expressed through the definition of the degree of likelihood between the general interval efficiency and the benchmarking interval， and the accessibility of the decision unit efficiency in conjunction with the spillover degree is defined. The benchmarking in terms of effectiveness and accessibility is defined， which makes the benchmarking construction adaptable to a variety of decision-making environments. Due to the fact that the input-output data of forest carbon sinks is not an accurate value， treating this input-output data as interval numbers is more in line with the actual situation. The method proposed in this article is very suitable forevaluating the efficiency of forest carbon sequestration in China. Choose the forest carbon sink data from remote sensing measurements in 2017 and forestry related data from the same year to evaluate the performance of forest carbon sinks in 30 provinces of China.Based on the efficiency evaluation results， 8 provinces were selected as benchmarking. The results show that these 8 provinces have economic， resource， or management advantages in the development of forest carbon sink， which provides guidance for the development path of forest performance management in China and has practical reference value.

Key words: data envelopment analysis, interval data, efficiency compensation, benchmarking

中图分类号:

C931

黄衍,陈丽烨,吴楠,王应明,戴永务. 基于效率补偿机制的区间标杆面研究[J]. 中国管理科学, 2023, 31(12): 317-328.

Yan HUANG,Li-ye CHEN,Nan WU,Ying-ming WANG,Yong-wu DAI. Study on Interval Benchmarking Based on Efficiency Compensation Mechanism——Taking Forest Carbon Sink Efficiency as An Example[J]. Chinese Journal of Management Science, 2023, 31(12): 317-328.

图/表 6

图1

图2

表1

效率补偿前后区间效率评价结果比较分析"

DMU	$W I E d ˉ$ （1）	$U I E d ˉ$ （2）	$C I E d (0.3) ˉ$ （3）	$C I E d (0.5) ˉ$ （4）	$C I E d (0.7) ˉ$ （5）	$N I E d ˉ$ （6）
北京市	[0.124, 0.317]	[0.157,0.257]	[0.238,0.243]	[0.158,0.233]	[0.143,0.241]	[0.198,0.209]
天津市	[0.512, 1.338]	[0.650, 1.061]	[0.636,1.036]	[0.607,0.989]	[0.574,0.934]	[0.820,0.831]
河北省	[0.451, 1.223]	[0.533, 1.016]	[0.498,0.943]	[0.485,0.905]	[0.4720,881]	[0.633,0.844]
山西省	[0.347, 1.564]	[0.420, 1.257]	[0.386,1.164]	[0.372,1.105]	[0.361,1.058]	[0.508,1.000]
内蒙古自治区	[0.343, 0.961]	[0.404, 0.788]	[0.388,0.727]	[0.378,0.701]	[0.367,0.678]	[0.496,0.654]
辽宁省	[0.399, 0.882]	[0.491, 0.721]	[0.453,0.666]	[0.434,0.638]	[0.418,0.615]	[0.589,0.600]
吉林省	[0.471, 0.999]	[0.587, 0.802]	[0.543,0.743]	[0.516,0.705]	[0.494,0.675]	[0.643,0.700]
黑龙江省	[0.295, 0.609]	[0.363, 0.497]	[0.344,0.471]	[0.330,0.452]	[0.316,0.433]	[0.405,0.445]
上海市	[0.733, 1.470]	[0.853, 1.209]	[0.806,1.188]	[0.794,1.141]	[0.777,1.089]	[1.000,1.000]
江苏省	[0.705, 1.375]	[0.838, 1.137]	[0.801,1.092]	[0.784,1.066]	[0.762,1.033]	[0.950,1.000]
浙江省	[0.700, 1.434]	[0.831, 1.196 ]	[0.795,1.146]	[0.776,1.098]	[0.751,1.130]	[0.994,1.000]
安徽省	[0.393, 0.877]	[0.499, 0.700]	[0.485,0.682]	[0.464,0.653]]	[0.437,0.617]	[0.552,0.627]
福建省	[0.503, 1.065]	[0.628, 0.873]	[0.595,0.817]	[0.571, 0.785]	[0.549,0.757]	[0.704,0.774]
江西省	[0.424, 0.815]	[0.513, 0.670]	[0.471,0.616]	[0.454, 0.593]	[0.440,0.575]	[0.554,0.623]
山东省	[0.663, 1.563]	[0.814, 1.254]	[0.769,1.193]	[0.734, 1.139]	[0.697,1.085]	[1.000,1.000]
河南省	[0.558, 1.429]	[0.682, 1.148]	[0.635,1.063]	[0.606, 1.009]	[0.584,0.969]	[0.851,0.924]
湖北省	[0.419, 0.926]	[0.525, 0.743]	[0.487,0.691]	[0.463, 0.657]	[0.443,0.628]	[0.594,0.653]
湖南省	[0.333, 0.756]	[0.419, 0.603]	[0.392,0.570]	[0.370, 0.537]	[0.353,0.509]	[0.480,0.524]
广东省	[0.730, 1.450]	[0.851, 1.202]	[0.805,1.135]	[0.793,1.108]]	[0.775,1.078]	[1.000,1.000]
广西壮族自治区	[0.316, 0.773]	[0.429, 0.588]	[0.802,0.542]	[0.481, 0.512]	[0.473,0.565]	[0.435,0.565]
海南省	[0.865, 1.383]	[0.865, 1.172]	[0.818,1.110]	[0.818, 1.091]	[0.818,1.064]	[1.000,1.000]
重庆市	[0.581, 1.090]	[0.580, 0.874]	[0.558,0.835]	[0.536, 0.802]	[0.510,0.768]	[0.688,0.726]
四川省	[0.891, 1.093]	[0.570, 0.891]	[0.547,0.833]	[0.524, 0.802]	[0.500,0.772]	[0.710,0.712]
贵州	[0.852,1.534]]	[0.853, 1.252]	[0.812,1.187]	[0.804, 1.140]	[0.791,1.101]	[1.000,1.000]
云南省	[0.859, 1.491]	[0.859, 1.198]	[0.807,1.152]	[0.796, 1.103]	[0.780,1.059]	[0.989,1.000]
陕西省	[0.347, 0.691]	[0.347, 0.552]	[0.321,0.517]	[0.306, 0.488]	[0.294,0.466]	[0.431,0.440]
甘肃省	[0.985, 1.217]	[0.486, 0.984]	[0.451,0.938]	[0.429, 0.897]	[0.411,0.854]	[0.603,0.786]
青海省	[0.971, 1.888]	[0.871, 1.449]	[0.818,1.438]	[0.818, 1.347]	[0.818,1.234]	[1.000,1.000]
宁夏回族自治区	[0.312, 1.185]	[0.312, 0.959]	[0.288,0.888]	[0.277, 0.846]	[0.268,0.812]	[0.384,0.770]
新疆维吾尔自治区	[0.882,1.811]]	[0.822, 1.376]	[0.790,1.372]	[0.764, 1.286]	[0.729,1.186]	[1.000,1.000]

表1

图3

表2

基于不同模型下的DMU溢出度和类型比较分析"

DMU	P(WIE)	P (UIE)	$P (C I E (0.7))$	$P (C I E (0.5))$	$P (C I E (0.3))$	DMU	P(WIE)	P (UIE)	$P (C I E (0.7))$	$P (C I E (0.5))$	$P (C I E (0.3))$
北京市	IEIA	EIA	IEA	IEA	IEA	河南省	EIA	EIA	IEA	EA	IEA
天津市	EIA	EIA	IEA	IEA	EIA	湖北省	IEIA	IEIA	IEA	IEA	IEA
河北省	EIA	EIA	IEA	IEA	IEA	湖南省	IEIA	IEIA	IEA	IEA	IEA
山西省	EIA	EIA	EA	EA	EIA	广东省	EIA	EIA	EA	EA	EA
内蒙古自治区	IEIA	IEIA	IEA	IEA	IEA	广西壮族自治区	IEIA	IEIA	IEIA	IEA	IEA
辽宁省	IEIA	IEIA	IEA	IEA	IEA	海南省	EIA	EIA	EA	EA	EA
吉林省	IEIA	IEIA	IEA	IEA	IEA	重庆市	EIA	IEIA	IEA	IEA	IEA
黑龙江省	IEIA	IEIA	IEA	IEA	IEA	四川省	EIA	IEIA	IEA	IEA	IEA
上海市	EIA	EIA	EA	EA	EA	贵州	EIA	EIA	EA	EA	EA
江苏省	EIA	EIA	EA	EA	EA	云南省	EIA	EIA	EA	EA	EA
浙江省	EIA	EIA	EA	EA	EA	陕西省	IEIA	IEIA	IEA	IEA	IEA
安徽省	IEIA	IEIA	IEA	IEA	IEA	甘肃省	EIA	IEIA	IEA	IEA	IEIA
福建省	EIA	IEIA	IEA	IEA	IEA	青海省	EIA	EIA	EIA	EIA	EIA
江西省	IEIA	IEIA	IEA	IEA	IEA	宁夏回族自治区	EIA	IEIA	IEA	IEA	EIA
山东省	EIA	EIA	EA	EA	EA	新疆维吾尔自治区	EIA	EIA	EA	EIA	EIA

表2

图4

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