考虑决策单元间相对竞争力的成本DEA博弈及成本分配方法

doi:10.16381/j.cnki.issn1003-207x.2022.2113

Abstract

Abstract:

Cooperation is one of the effective strategies for companies to reduce costs； and reasonable measurement and allocation of potential benefits are the key to successful cooperation. For partners with a competitive relationship， their relative competitiveness should not change due to cooperation. A cost DEA game is first built based on data envelopment analysis （DEA） and cooperative game theory， with the aim of quantitatively describing the cooperation between decision making units （DMUs）； then， for the cost allocation， an equal competitiveness method （ECM） is proposed to minimize the relative competitiveness changes of any two DMUs （i.e.， cooperative players） before and after cost allocation， which makes it possible to maintain relative competitiveness as much as possible. By using the row generation algorithm and lexicographic min-max approach， the cost allocation provided by ECM satisfies uniqueness， effectiveness， stability， symmetry， virtual players， and so on. Finally， taking 3 DMUs and 25 supermarkets as examples， comparing ECM with the core， Shapley value， and nucleolus， it is found that after cost allocation， ECM can best maintain the relative competitiveness of DMUs. It provides a reference for enterprises' managers to make the cooperation decisions， and cost allocation after cooperation in this research.

Key words: data envelopment analysis, cost allocation, equal competitiveness method, row generation algorithm, lexicographic min-max approach

CLC Number:

C934

Yao Wen, Qingxian An, Yongli Li. Cost DEA Game and Cost Allocation Method Considering the Relative Competitiveness of Decision-making Units[J]. Chinese Journal of Management Science, 2025, 33(2): 71-83.

Figures/Tables 7

评价指标		DMU₁	DMU₂	DMU₃	价格
投入	$x 1 k$	1	4	5	5
投入	$x 2 k$	9	5	4	6
产出	$y 1 k$	1	7	6	-
产出	$y 2 k$	8	2	9	-

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分配方法	比较内容	DMU₁	DMU₂	DMU₃	f	计算时间
对偶理论	成本分配结果	13.65	50.00	49.00	不唯一	0.013秒
对偶理论	相对竞争力变化	0.313	1.000	1.000	0.69
核仁	成本分配结果	43.56	35.05	34.05	-	0.19秒
核仁	相对竞争力变化	1.000	0.701	0.695	0.43	0.19秒
ECM	成本分配结果	34.42	39.51	38.72	-	0.14秒
ECM	相对竞争力变化	0.790	0.790	0.790	0.00	0.14秒
Shapley 值	成本分配结果	41.31	40.03	31.31	-	0.09秒
Shapley 值	相对竞争力变化	0.948	0.801	0.639	0.31	0.09秒

DMUs	规模	工时	销售	利润	DMUs	规模	工时	销售	利润
DMU1	4.99	79.1	115.3	1.71	DMU14	3.14	54.9	62.4	1.42
DMU2	3.3	60.1	75.2	1.81	DMU15	4.43	48.8	55.2	1.38
DMU3	8.12	126.7	225.5	10.39	DMU16	3.98	59.2	95.9	0.74
DMU4	6.7	153.9	185.6	10.42	DMU17	5.32	74.5	121.6	3.06
DMU5	4.47	65.7	84.5	2.36	DMU18	3.69	94.6	107	2.98
DMU6	4.08	76.8	103.3	4.35	DMU19	3	47	65.4	0.62
DMU7	2.53	50.2	78.8	0.16	DMU20	3.87	54.6	71	0.01
DMU8	2.47	44.8	59.3	1.3	DMU21	3.31	90.1	81.2	5.12
DMU9	2.32	48.1	65.7	1.49	DMU22	4.25	95.2	128.3	3.89
DMU10	4.91	89.7	163.2	6.26	DMU23	3.79	80.1	135	4.73
DMU11	2.24	56.9	70.7	2.8	DMU24	2.99	68.7	98.9	1.86
DMU12	5.42	112.6	142.6	2.75	DMU25	3.1	62.3	66.7	7.41
DMU13	6.28	106.9	127.8	2.7

DMUs	对偶理论		核仁		ECM
DMUs	成本分配	相对竞争力变化	成本分配	相对竞争力变化	成本分配	相对竞争力变化
DMU1	197.06	1.00	202.65	1.03	197.06	1.00
DMU2	128.52	1.00	132.12	1.03	128.52	1.00
DMU3	385.39	0.97	389.00	0.98	385.39	0.97
DMU4	317.20	0.88	326.21	0.91	321.30	0.90
DMU5	144.42	1.00	148.02	1.02	144.42	1.00
DMU6	176.55	0.99	181.56	1.01	176.55	0.99
DMU7	134.67	1.00	138.28	1.03	134.67	1.00
DMU8	101.35	1.00	104.95	1.04	101.35	1.00
DMU9	112.29	1.00	115.89	1.03	112.29	1.00
DMU10	278.92	1.00	182.48	0.66	249.70	0.90
DMU11	120.83	1.00	124.43	1.03	120.83	1.00
DMU12	243.71	1.00	247.31	1.01	243.71	1.00
DMU13	218.42	1.00	222.02	1.02	218.42	1.00
DMU14	106.65	1.00	110.25	1.03	106.65	1.00
DMU15	94.34	1.00	97.94	1.04	94.34	1.00
DMU16	163.90	1.00	167.50	1.02	163.90	1.00
DMU17	207.82	1.00	211.42	1.02	207.82	1.00
DMU18	182.87	1.00	186.47	1.02	182.87	1.00
DMU19	111.77	1.00	115.37	1.03	111.77	1.00
DMU20	121.34	1.00	124.94	1.03	121.34	1.00
DMU21	138.78	0.83	142.38	0.85	143.59	0.86
DMU22	219.27	1.00	222.87	1.02	219.27	1.00
DMU23	230.72	1.00	234.33	1.02	230.72	1.00
DMU24	169.03	1.00	173.83	1.02	169.03	1.00
DMU25	113.99	0.59	117.60	0.61	134.30	0.70
f	-	0.4097	-	0.429	-	0.3045
计算时间	0.011 秒	1.006 秒	1.673 秒	DMU18	182.87	1.00

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Cost DEA Game and Cost Allocation Method Considering the Relative Competitiveness of Decision-making Units

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