基于动态非合作博弈超效率DEA的成本补偿激励方法研究

doi:10.16381/j.cnki.issn1003-207x.2022.1859

Abstract

Abstract:

In practice， a common problem faced by managers is how to motivate decision-making units （DMU） to improve their performance by means of cost compensation. It is especially common in the problems of cost supervision and price mechanism in the monopoly industry and public welfare service industry. The existing cost compensation studies do not provide sufficient positive incentives for effect DMUs， and also do not consider the non-cooperative game relationship that often occurs among DMUs in the face of interests. Therefore， dynamic non-cooperative game is combined with super-efficiency data envelopment analysis （DEA） and a dynamic game super-efficiency DEA algorithm with bidirectional incentive effect is proposed. The convergence of the algorithm is proved and the optimal solution is a unique Nash equilibrium point. The proposed method is applied to 25 provincial-level power grid enterprises of a power grid group in China from 2016 to 2019， and the effectiveness of the method is verified. The results of the case study show that： 1） The operating efficiency of power grid enterprises in different regions is significantly different， and the motivation of performance improvement is not strong； 2） The proposed cost compensation scheme can generate positive or negative incentives for DMU with different performance， and the proposed method is helpful to strengthen the motivation of DMUs to actively improve their performance.It further enriches the DEA theoretical research of cost compensation for incentives and provides an effective management tool for relevant managers in this study.

Key words: cost compensation, non-cooperative game, data envelopment analysis, incentive, performance improvement

CLC Number:

C934

Qian-zhi DAI,Xiao-chi XU,Xi-yang LEI, et al. Cost Compensation Method for Incentives Based on Dynamic Non-cooperative Game and Super-efficiency DEA[J]. Chinese Journal of Management Science, 2023, 31(12): 185-192.

Figures/Tables 5

DMU	$c j$	$b p C C R$	$b p B C C$	$b p s$	$b ? p C M$	$b ? p C S G$	$b p g a m e$
1	179.45	125.26	143.89	125.26	87.71	136.08	107.38
2	173.26	163.22	173.26	163.22	114.19	176.21	142.64
3	337.64	327.79	328.59	327.79	328.57	319.10	319.44
4	277.11	256.76	277.11	256.76	129.38	128.83	176.35
5	341.14	312.71	312.72	312.71	308.86	308.87	300.48
6	228.34	178.08	178.82	178.08	174.04	174.05	175.05
7	719.58	719.58	719.58	805.58	715.86	715.94	711.45
8	275.71	256.08	275.71	256.08	275.96	277.01	252.08
9	163.59	119.15	163.59	119.15	74.97	74.24	105.56
10	360.94	360.94	360.94	453.85	378.34	366.72	425.69
11	327.79	327.79	327.79	341.00	330.65	332.22	323.86
12	1068.76	1068.76	1068.76	1785.27	904.61	1196.68	1107.24
13	338.97	266.29	338.97	266.29	191.13	343.04	231.35
14	796.45	747.88	751.77	747.88	629.80	751.77	642.50
15	511.49	511.49	511.49	558.07	516.04	511.49	509.90
16	416.70	330.00	330.60	330.00	326.95	330.60	325.23
17	329.94	329.94	329.94	331.50	292.67	329.94	305.89
18	266.57	248.43	258.16	248.43	220.14	258.16	234.00
19	180.37	157.07	159.78	157.07	137.05	159.78	142.24
20	124.24	124.24	124.24	176.57	128.81	148.19	158.80
21	105.24	78.07	105.24	78.07	52.42	105.24	72.46
22	208.34	159.03	161.62	159.03	146.79	161.62	150.46
23	217.04	187.74	194.74	187.74	185.27	194.74	175.19
24	204.11	190.10	204.11	190.10	150.29	206.12	178.13
25	508.15	435.29	444.33	435.29	442.78	444.33	426.13
26	8660.92	7981.69	8245.74	8990.80	7243.28	8150.97	7699.51

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DMU	2016	2017	2018	2019	均值	方差
1	0.7987	0.7821	0.5857	0.5984	0.6912	0.0099
2	0.8237	0.8040	0.8274	0.8233	0.8196	0.0001
3	0.9209	0.8957	0.9414	0.9461	0.9260	0.0004
4	0.9712	0.9133	0.9410	0.6364	0.8655	0.0179
5	0.8700	0.8662	0.8496	0.8808	0.8666	0.0001
6	0.7516	0.7211	0.7118	0.7666	0.7378	0.0005
7	0.9326	1.0045	0.9656	0.9887	0.9729	0.0007
8	0.9522	0.9285	0.9381	0.9143	0.9333	0.0002
9	0.6417	0.6661	0.6866	0.6453	0.6599	0.0003
10	1.2105	1.2429	1.1879	1.1794	1.2052	0.0006
11	0.9607	0.8995	0.9827	0.9880	0.9577	0.0012
12	1.1702	1.0924	1.0794	1.0360	1.0945	0.0023
13	0.7053	0.7132	0.6637	0.6825	0.6912	0.0004
14	0.8657	0.8791	0.8730	0.8067	0.8561	0.0008
15	1.3423	1.1377	1.2510	0.9969	1.1820	0.0167
16	0.8887	0.8984	0.9154	0.7805	0.8707	0.0028
17	0.6612	0.6274	0.6773	0.9271	0.7232	0.0142
18	0.8369	0.8482	0.8614	0.8778	0.8561	0.0002
19	0.5965	0.6937	0.6560	0.7886	0.6837	0.0049
20	1.1473	1.2355	1.2041	1.2782	1.2163	0.0023
21	0.6395	0.6482	0.7046	0.6885	0.6702	0.0007
22	0.6266	0.6497	0.6236	0.7222	0.6555	0.0016
23	0.6220	0.6754	0.6760	0.8072	0.6951	0.0047
24	0.8049	0.7711	0.8792	0.8727	0.8320	0.0021
25	0.8836	0.8724	0.8155	0.8386	0.8526	0.0007

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Cost Compensation Method for Incentives Based on Dynamic Non-cooperative Game and Super-efficiency DEA

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