Using Shannon Entropy to Improve the Identification of MP-SBM Models with Undesirable Output
Abstract
:1. Introduction
2. Methodology
2.1. SBM Model with Undesirable Outputs
2.2. P-SBM Model with Undesirable Output for Measuring Panel Data
2.3. Problems and Causes of the P-SBM Model
2.3.1. Quantitative Analysis of Disposal Efficiency in Tibet from 2012 to 2017
2.3.2. Qualitative Analysis Results
2.3.3. Analysis of the Causes of the Efficiency Paradox
2.4. MP-SBM Model
2.5. MP-SBM-Shannon Entropy Model
- Step 1: Normalize the efficiency Matrix [Ejk]n×K and set
- Step 2: Compute entropy fk as
- Step 3: Calculate the degree of the diversification of Mk as
- Step 4: Normalize the value of dk as such that
- Step 5: Calculate the CES as
3. Indicator System and Data Sources
3.1. Selection of Indicator System
3.2. Data Sources and Descriptive Statistical Analysis
4. Results and Discussion
4.1. Comparison of Disposal Efficiency Based on MP-SBM-Shannon Entropy Model, MP-SBM Model, and P-SBM Model
4.2. Spatial and Temporal Analyses of the Disposal Efficiency
4.3. Analysis of Inefficient Provinces
5. Conclusions
- (1)
- In the long run, the staffing efficiency of CDCs and health supervision offices should be prioritized, and the efficiency of outpatient treatment also needs to be improved. The analysis of the inefficient provinces found that the staffing problem of the CDC and the health supervision office are two stumbling blocks. We need to develop an emergency management system to reduce personnel redundancy during normal times while alleviating the shortage of medical resources in the face of public health emergencies.
- (2)
- Disposal efficiency varies widely among these regions, which can be attributed to the differentiating growth in disposal efficiency. Therefore, paying attention to the optimal allocation of resources and improving the overall distribution of resources is urgently required. Additionally, it should accelerate technological progress and focus on improving management capabilities rather than blind investment and low-level expansion.
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Author | Input Indicators | Output Indicators |
---|---|---|
Zheng et al. [26] | Number of township health centers, number of beds, number of health technicians, number of other personnel | Number of outpatient medical visits, number of hospital discharges, bed occupancy rate, average length of stay in township health centers |
Ozcan et al. [27] | Total number of hospital beds, number of people working in related medical departments, number of CT scanners | Number of inpatient discharges, number of outpatient consultations |
Rouyendegh et al. [59] | Number of physicians, total number of beds | Bed utilization, total number of procedures, number of patients |
Campos et al. [44] | Total healthcare costs, percentage of public investment transferred to labor costs | Number of nursing services for residents, number of specialized healthcare services, number of primary healthcare services |
Karahan et al. [45] | Number of beds, total number of doctors, total number of nurses | Number of patients treated, number of inpatients |
Vitezić et al. [60] | Employee wages, direct costs, total investment, number of public healthcare departments | Total revenue, number of analyses in various public healthcare sectors |
Kawaguchi et al. [61] | Number of hospital managers, maintenance staff, physicians, nurses, nurse assistants, and medical technicians | Medical revenues, inpatient visits, outpatient visits |
Input Indicators | Output Indicators | |
---|---|---|
Desirable Output | Undesirable Output | |
Health surveillance staff (WR), number of CDCs (JR), number of public health physicians (GY), total health expenditure (WF), number of beds in the infectious disease department (CC) | The number of outpatients in DID (CM), the number of discharged patients in DID (CY) | The number of patients in DID (CF), the number of deaths in DID (CB) |
Year | Indicator | WR | JR | GY | WF | CC | CM | CY | CF | CB |
---|---|---|---|---|---|---|---|---|---|---|
Variables | ||||||||||
2012–2018 | Max | 7780 | 17,931 | 11,175 | 4622 | 10,714 | 561 | 230,498 | 387,240 | 3441 |
Min | 23 | 928 | 342 | 65 | 231 | 2 | 2223 | 7113 | 15 | |
Mean | 2376 | 6180 | 3610 | 1293 | 3910 | 125 | 94,914 | 99,644 | 571 | |
Range | 7757 | 17,003 | 10,833 | 4557 | 10,483 | 559 | 228,275 | 380,127 | 3426 | |
Growth rate | −13.5% | −2.8% | 5.4% | 108.4% | 22.8% | 64.0% | 27.0% | −4.7% | 18.4% |
Wk | ||||||||||
1 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 1 | 0 | 0.0035991 |
2 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 1 | 1 | 0.0035989 |
3 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 0.0035984 |
4 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 0.0035982 |
5 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 1 | 0.0035981 |
6 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0.0035971 |
7 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 1 | 0 | 0.0035969 |
8 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 1 | 1 | 0.0035969 |
9 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 0.0035967 |
10 | 1 | 0 | 0 | 0 | 1 | 1 | 0 | 1 | 1 | 0.0035965 |
11 | 0 | 1 | 0 | 0 | 1 | 1 | 0 | 1 | 0 | 0.0035965 |
12 | 0 | 1 | 0 | 0 | 1 | 1 | 0 | 1 | 1 | 0.0035965 |
13 | 1 | 0 | 0 | 0 | 1 | 1 | 0 | 1 | 0 | 0.0035965 |
14 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 0.0035962 |
15 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 1 | 1 | 0.0035961 |
Region | Province | P-SBM Model (2012) | MP-SBM Model | MP-SBM-Shannon Entropy Model | ||||||
---|---|---|---|---|---|---|---|---|---|---|
Efficiency | Average Efficiency | Rank | Efficiency | Average Efficiency | Rank | Efficiency | Average Efficiency | Rank | ||
Eastern | Beijing | 1.1653 | 0.9634 | 4 | 1.0000 | 0.7115 | 1 | 0.8256 | 0.5647 | 3 |
Fujian | 0.6002 | 23 | 0.4186 | 19 | 0.3511 | 22 | ||||
Guangdong | 1.1422 | 7 | 0.4946 | 13 | 0.4404 | 13 | ||||
Hainan | 0.4346 | 30 | 0.3212 | 23 | 0.2556 | 20 | ||||
Hebei | 0.5191 | 27 | 0.3991 | 20 | 0.3078 | 27 | ||||
Jiangsu | 1.2161 | 3 | 1.0000 | 1 | 0.8269 | 2 | ||||
Shandong | 1.0417 | 15 | 0.6443 | 3 | 0.4329 | 15 | ||||
Shanghai | 1.1484 | 6 | 0.8370 | 2 | 0.6147 | 7 | ||||
Tianjin | 1.0936 | 10 | 1.0000 | 1 | 0.6458 | 5 | ||||
Zhejiang | 1.2732 | 2 | 1.0000 | 1 | 0.9461 | 1 | ||||
Central | Anhui | 1.1653 | 0.7259 | 5 | 1.0000 | 0.5510 | 1 | 0.7196 | 0.4085 | 4 |
Henan | 0.5205 | 26 | 0.4270 | 18 | 0.3264 | 25 | ||||
Hubei | 1.0133 | 19 | 0.6329 | 4 | 0.4615 | 11 | ||||
Hunan | 0.7186 | 21 | 0.4934 | 14 | 0.3707 | 21 | ||||
Jiangxi | 0.6373 | 22 | 0.5041 | 12 | 0.3844 | 20 | ||||
Shanxi 1 | 0.3004 | 31 | 0.2485 | 24 | 0.1885 | 31 | ||||
Western | Gansu | 0.5683 | 1.0012 | 25 | 0.4337 | 0.6382 | 17 | 0.3372 | 0.4501 | 24 |
Guangxi | 1.0515 | 14 | 0.5594 | 6 | 0.4435 | 12 | ||||
Guizhou | 1.0636 | 12 | 1.0000 | 1 | 0.6096 | 8 | ||||
Inner Mongolia | 1.0186 | 16 | 0.4785 | 15 | 0.3255 | 26 | ||||
Ningxia | 0.7709 | 20 | 0.5421 | 8 | 0.4288 | 16 | ||||
Qinghai | 1.0524 | 13 | 0.6091 | 5 | 0.4744 | 10 | ||||
Shanxi 3 | 0.5731 | 24 | 0.4398 | 16 | 0.3385 | 23 | ||||
Sichuan | 1.0771 | 11 | 0.5132 | 11 | 0.4071 | 17 | ||||
Tibet | 1.6153 | 1 | 1.0000 | 1 | 0.5527 | 18 | ||||
Xinjiang | 1.0141 | 18 | 0.5318 | 9 | 0.3995 | 9 | ||||
Yunnan | 1.0944 | 9 | 1.0000 | 1 | 0.6438 | 6 | ||||
Chongqing | 1.1150 | 8 | 0.5507 | 7 | 0.4401 | 14 | ||||
Northeast | Heilongjiang | 0.4703 | 0.6503 | 28 | 0.3598 | 0.4072 | 21 | 0.2791 | 0.3124 | 28 |
Jilin | 0.4643 | 29 | 0.3338 | 22 | 0.2592 | 29 | ||||
Liaoning | 1.0163 | 17 | 0.5280 | 10 | 0.3988 | 19 |
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Ma, Z.; Yin, J.; Yang, L.; Li, Y.; Zhang, L.; Lv, H. Using Shannon Entropy to Improve the Identification of MP-SBM Models with Undesirable Output. Entropy 2022, 24, 1608. https://doi.org/10.3390/e24111608
Ma Z, Yin J, Yang L, Li Y, Zhang L, Lv H. Using Shannon Entropy to Improve the Identification of MP-SBM Models with Undesirable Output. Entropy. 2022; 24(11):1608. https://doi.org/10.3390/e24111608
Chicago/Turabian StyleMa, Zhanxin, Jie Yin, Lin Yang, Yiming Li, Lei Zhang, and Haodong Lv. 2022. "Using Shannon Entropy to Improve the Identification of MP-SBM Models with Undesirable Output" Entropy 24, no. 11: 1608. https://doi.org/10.3390/e24111608
APA StyleMa, Z., Yin, J., Yang, L., Li, Y., Zhang, L., & Lv, H. (2022). Using Shannon Entropy to Improve the Identification of MP-SBM Models with Undesirable Output. Entropy, 24(11), 1608. https://doi.org/10.3390/e24111608