A Study on the Performance of Medical Centers in Taiwan: An Application of Data Envelopment Analysis
Yi-Horng Lai1*
1 Department of Health Care Administration, Asia Eastern University of Science and Technology, New Taipei City, Taiwan
*Corresponding Author: [email protected]
Accepted: 15 August 2022 | Published: 1 September 2022 DOI:https://doi.org/10.55057/ijbtm.2022.4.3.2
__________________________________________________________________________________________
Abstract: Background: The hospital industry in Taiwan has become more competitive than ever before. Improving operational performance is thus an important issue for hospital managers or operators. Methods: The research data of this study is the 2019 National Health Insurance Statistics obtained from National Health Insurance Administration, Ministry of Health and Welfare (Taiwan). The efficiency and productivity of hospital performance were evaluated by input-oriented Data Envelopment Analysis (DEA). Two inputs variables (number of doctors, number of beds) and five outputs variables (number of outpatients, outpatient revenues, number of inpatients, inpatient revenues, number of admission days) were adopted in the DEA model. Results: According to the DEA analysis, 8 hospitals are considered efficient.
With super-efficiency, efficiency can be detected in more detail. Conclusion: This study combines DEA results efficiency scores and total medical income into a BCG matrix. There are 6 hospitals in the super star group, 7 hospitals in the cow group, 2 in the question marks group, and 4 in the dog group.
Keywords: hospitals, technical efficiency, slack analysis, data envelopment analysis (DEA) ___________________________________________________________________________
1. Introduction
Aging of population is a big problem in developed countries, and Taiwan is no exception.
Owing to this problem, Taiwan’s National Health Insurance Program financial deficit is getting more serious. It enforces us to confront our resource allocation, and make it more efficiency (Hsu, Yamada, 2017). But hospitals efficiency is hard account. Data envelopment analysis (DEA) model is a good methodology to solve this problem. This study concentrated on person efficiency. Through this kind of resource type, hospital managers can presume efficiency more precisely.
Taiwan’s National Health Insurance Program (NHIP) took effect in 1995. NHIP is a landmark of Taiwan’s medicine care system, it also a social welfare policy, and benefit a great many of people. But coming problem is a large number of NHIP financial deficits (Chen, 2019). How to make hospital more efficiency and allow limited resources to be allocated more correctly is an important topic for every hospital in Taiwan.
The DEA model is a non-parametric mathematical programming method for frontier estimation. The major function of the DEA model is assessing the management performance of a group of decision-making units (DMUs) particularly in terms of efficiency. The DEA
model constructs a relative efficiency score by transforming the multiple-input/multiple-output into a ration of a single virtual output into a single virtual input.
Charnes, Cooper, and Rhodes were the first to describe the DEA model (the CCR model), and used a mathematical programming model to identify the efficiency frontier based on the concept of the Pareto optimum when using multiple measures. Charnes assume the circumstance is the constant return to scale (CCR model) (Charnes, Cooper, and Rhodes, 1978).
The problem of calculating DEA scores can be formulated as a linear programming problem.
Banker, Charnes, and Cooper used the fore postulates of production possibility aggregation and Shephard’s distance function to produce a BCC model for measuring the technical efficiency (TE) and scale efficiency (SE) (Banker, Charnes, and Cooper, 1984). The BCC model assumes under a variable return to scale situation. The main component of these models is that Charnes et al. included the Pareto optimality in the model, where each DMU selects the optimum input and output multipliers for maximizing its own efficiency, and with the only constraint being that the value of the selected multipliers must not exceed unity satisfy the maximum efficiency value unity.
The CCR model assumes that the production process involves constant returns to scale.
However, the production process may involve increasing or decreasing returns to scale, particularly an inefficient decision-making unit, the inefficiencies of which may result from the operation of different returns scale, and thus a thorough understanding the state of returns to scale of specific decision-making units can offer the information required by an administrator to further improve efficiency.
This study conducts data envelopment analysis model, and this model to assess the efficiency of 19 medical centers in Taiwan. Then, this research employed the BCG matrix to develop the management implications. It can be concluded all hospitals into their quadrant.
2. Methods and Materials
Theoretical Foundations of DEA
This study applied data envelopment analysis to assess the technical efficiency of Taiwan’s hospital. The DEA method was first proposed by Charnes, Cooper and Rhodes who employ mathematical programming model (CCR model) to measure the technical efficiency of DMUs (decision-making units) based on the concept of Pareto optimum. The prob-lem of illustrate DEA scores can be formulated as a linear programming problem (Banker, Charnes, and Cooper, 1984).
This study employee input-oriented CCR and BCC model. In equation (1), Yjn as the n-th output of the j-th DMU and Xim as the m-th input of i-th DMU. If a DMU use M inputs to generate N outputs, the efficiency score of j-th DMU, EK is a solution to the following LP problem.
𝑀𝑎𝑥 ∑ 𝑈𝑛𝑌𝑗𝑛
𝑁
𝑛=1
𝑠. 𝑡. ∑ 𝑉𝑚𝑋𝑖𝑚 = 1
𝑛𝑀
𝑚=1
∑ 𝑈𝑛𝑌𝑟𝑛 𝑁
− ∑ 𝑉𝑚𝑋𝑟𝑚 𝑀
≤ 0 ∀r
𝑈𝑛, 𝑉𝑚≥ 0 ∀n and m
Where n=1, 2, … N; m=1, 2, … M; r=1, 2, … R, and Un and Vm are the given weights associate with each input and output.
Banker, Charnes, and Cooper used the fore postulates of production possibility aggregation and Shephard’s distance function to produce a BCC model for measuring the technical efficiency (TE) and scale efficiency (SE). BCC model considers that not every industry is on the conception of constant return to scale. This study uses R 4.2.1 with dear package (Vicente, Vicente, and Rafael, 2020) to proceed to the efficiency analysis of BCC model.
In equation (2) the BCC model assumes under a variable return to scale situation and a free variable, de-noted by u0. Therefore, in an input-oriented BCC model, the formulation minimizes the inputs, given the outputs. The following optimization is obtained
𝑀𝑎𝑥 𝐸𝐾= ∑ 𝑈𝑛𝑌𝑗𝑛− 𝑢0
𝑁
𝑛=1
𝑠. 𝑡. ∑ 𝑉𝑚𝑋𝑖𝑚− 𝑢0= 1
𝑛𝑀
𝑚=1
∑ 𝑈𝑛𝑌𝑟𝑛 𝑁
𝑛=1
− ∑ 𝑉𝑚𝑋𝑟𝑚− 𝑢0 𝑀
𝑚=1
≤ 0
𝑈𝑛, 𝑉𝑚≥ 0 n = 1,2, ⋯ N m = 1,2, ⋯ M r = 1,2, ⋯ R u0 can be either positive or negative.
The Input and Output Items
This study discussed the efficiency of hospitals by using an input-oriented DEA, and try to measure the cross efficiency of each DMU, through this way, finally this study can obtain the cross-efficiency matrix, so as to get more disinterest efficiency score, and this might be much creditable.
It can be identified the sets of output measures and input factors to be included in the analysis.
Based on the data that provided by National Health Insurance Administration, Ministry of Health and Welfare (Taiwan), five outputs in general is defined by the channel of following items: outpatient visits, outpatient revenues, admissions, inpatient revenues, inpatient days.
The above elements are the major performance of a hospital.
Generally, admission is a common measurement of hospital productivity and is widely accepted. Outpatient visits can regard as an indicator that if a clinic satisfied the service that the hospital provide. It implies the same concept of marketing, the more satisfying the customers feel might create higher repurchase rate. Eventually, inpatient days is also an important element of a hospital performance, patient days can be treated as an index which the clinics trust the doctors or paramedical persons’ skills (Hunt, Link, 2019).
The inputs measure the above outputs operating re-sources. This study selects the following two input factors: doctors and the number of beds which are represented as the measures for a hospital labor and capital resources. Because Taiwan is a highly populated island nation and most hospitals have sufficient health-care facilities, so this study chose more labor force as our inputs (Hunt, Link, 2019).
Doctors are the major employee in a hospital. Doc-tors’ medical skills implicate a hospital core capacity. It can be concluded a hospital’s doctors is the same as a firm’s products (Chitnis, Mishra, 2019). The number of beds is a simple variable to measure a capital size, the same concept of machines of an enterprise. It can be well implied floors of a hospital; be-cause a hospital must have enough commendation to accommodate beds.
Research Data
The research data in this study is 2019 National Health Insurance Statistics which got from National Health Insurance Administration, Ministry of Health and Welfare (Taiwan) (National Health Insurance Administration, 2022).
3. Results
Presentation of Efficiency Value
Efficiency units can display through reference set analysis (Table 1). Calculating the amounts of units appears in reference set. In other words, it means that how many times that every efficiency unit be consulted and cause this efficiency result. The much times an efficiency one be referenced the higher robustness it is (Charnes, Cooper, and Thrall, 1991). The Network of Peers in this study is as Figure 1. Efficient DMUs’ times appearing in reference sets is as Figure 2. The heat map of cross efficiency is as Figure 3.
Table 1: The Result of Efficiency Analysis in This study
ID Hospital Name TE Summary of peers Peer count summary
H01 National Taiwan University Hospital 1.000 1
H02 Tri-Service General Hospital 0.987 H07, H13, H17
0
H03 Taipei Veterans General Hospital 1.000 5
H04 Cathay General Hospital 0.961 H06 0
H05 MacKay Memorial Hospital 0.972 H06,
H07 0
H06 Shin Kong Memorial Wu Ho-Su Hospital 1.000 3
H07 Far Eastern Memorial Hospital 1.000 9
H08 Taipei Municipal Wanfang Hospital 0.973 H06,
H07 0
H09 Linkou Chang Gung Memorial Hospital 0.908 H01, H03, H07, H10, H13
0
H10 Taichung Veterans General Hospital 1.000 5
H11 Changhua Christian Hospital 0.950 H03, H07, H10, H13
0
H12 Chung Shan Medical University Hospital 0.876 H13,
H17 0
H13 China Medical University Hospital 1.000 8
H14 National Cheng Kung University Hospital 1.000 0
H15 Chi Mei Medical Center 0.926
H03, H07, H10, H13
0
H16 Kaohsiung Veterans General Hospital 0.901 H07,
H10, 0
H13
H17 Kaoshiung Chang Gung Memorial Hospital 1.000 3
H18 Kaoshiung Medical University Hospital 0.898 H03, H07, H10, H13
0
H19 Buddhist Hualien Tzu Chi General Hospital 0.925 H03, H07, H13, H17
0
Figure 1: The network of peers in this study
Figure 2: Efficient DMUs’ times appearing in reference sets
Figure 3: The heat map of cross efficiency
Super-efficiency
Super-efficiency is obtained from the regular DEA model by excluding the fund under evaluation from the reference set. Super-efficiency (input-oriented) allows a highly efficient hospital to attain an efficiency score greater than 1.0. Through this method, it can be deeply distinguished which efficiency unit performance well in the group.
In the result of DEA analysis, 8 efficiency ones are obtained in this study. With super- efficiency, it can be detective efficiency ones more detail (Table 2). It can be found that Far Eastern Memorial Hospital got the highest score (1.142), Kaoshiung Chang Gung Memorial Hospital is second one (1.141), and China Medical University Hospital is third one (1.127).
Table 2: The result of super efficiency
ID Hospital Name TE Super efficiency Rank
H01 National Taiwan University Hospital 1.000 1.061 6
H02 Tri-Service General Hospital 0.987 0.987 9
H03 Taipei Veterans General Hospital 1.000 1.087 5
H04 Cathay General Hospital 0.961 0.961 12
H05 MacKay Memorial Hospital 0.972 0.972 11
H06 Shin Kong Memorial Wu Ho-Su Hospital 1.000 1.025 7
H07 Far Eastern Memorial Hospital 1.000 1.189 2
H08 Taipei Municipal Wanfang Hospital 0.973 0.973 10
H09 Linkou Chang Gung Memorial Hospital 0.908 0.908 16
H10 Taichung Veterans General Hospital 1.000 1.098 4
H11 Changhua Christian Hospital 0.950 0.950 13
H12 Chung Shan Medical University Hospital 0.876 0.876 19
H13 China Medical University Hospital 1.000 1.213 1
H14 National Cheng Kung University Hospital 1.000 1.008 8
H15 Chi Mei Medical Center 0.926 0.926 14
H16 Kaohsiung Veterans General Hospital 0.901 0.901 17 H17 Kaoshiung Chang Gung Memorial Hospital 1.000 1.123 3 H18 Kaoshiung Medical University Hospital 0.898 0.898 18 H19 Buddhist Hualien Tzu Chi General Hospital 0.925 0.925 15
Slack analysis
After efficiency analysis, the next step is of interest in estimating how much the outputs could be in-creased and/or the magnitude of inputs that could be conserved by inefficient hospitals.
This means additional decreases in specific inputs could be achieved for a hospital to operate
as well as the most efficient hospitals, and increases in output could be reached at lowered levels of resource inputs. illustrates the results of slack analysis for four inefficient hospitals.
The result of output slack analysis is as Table 3, and the result of input slack analysis is as Table 4. Sever-al non-zero slacks are selected for each output/input to cross-check the above results. Non-zero slack identifies the marginal contribution to efficiency score with additional specific input amounts. The outpatient visits, inpatient days and the number of doctors are the largest number of cases of non-zero slack. This implies that hospital managers can effectively promote resource utilization efficiency in inefficient hospitals by handling the hospital’s outpatient visits and inpatient days efficiently and enlarging the doctor’s number.
Table 3: The result of output slack analysis
ID Hospital Name TE Doctors (person) Beds (bed)
H01 National Taiwan University Hospital 1.000 0 0
H02 Tri-Service General Hospital 0.987 0 0
H03 Taipei Veterans General Hospital 1.000 0 0
H04 Cathay General Hospital 0.961 6.117 0
H05 MacKay Memorial Hospital 0.972 55.032 0
H06 Shin Kong Memorial Wu Ho-Su Hospital 1.000 0 0
H07 Far Eastern Memorial Hospital 1.000 0 0
H08 Taipei Municipal Wanfang Hospital 0.973 67.679 0
H09 Linkou Chang Gung Memorial Hospital 0.908 0 0
H10 Taichung Veterans General Hospital 1.000 0 0
H11 Changhua Christian Hospital 0.950 0 0
H12 Chung Shan Medical University Hospital 0.876 0 41.852
H13 China Medical University Hospital 1.000 0 0
H14 National Cheng Kung University Hospital 1.000 0 0
H15 Chi Mei Medical Center 0.926 0 0
H16 Kaohsiung Veterans General Hospital 0.901 0 0
H17 Kaoshiung Chang Gung Memorial Hospital 1.000 0 0
H18 Kaoshiung Medical University Hospital 0.898 28.589 0
H19 Buddhist Hualien Tzu Chi General Hospital 0.925 0 0
Table 4: The result of input slack analysis
ID TE
Outpatient visits (ten thousand)
Outpatient revenues
(100 million points)
Number of
inpatient (ten thousand)
Inpatient revenues
(100 million points)
Number of admission day (ten thousand days)
H01 1.000 0 0 0 0 0
H02 0.987 28.950 14.758 0 1.356 0
H03 1.000 0 0 0 0 0
H04 0.961 0 5.161 23.002 2.691 0
H05 0.972 0 3.810 11.005 1.194 0
H06 1.000 0 0 0 0 0
H07 1.000 0 0 0 0 0
H08 0.973 0 2.897 0 1.838 0
H09 0.908 0 8.005 0 0 0
H10 1.000 0 0 0 0 0
H11 0.950 44.840 8.283 0 0 0
H12 0.876 10.425 6.974 0 3.573 0
H13 1.000 0 0 0 0 0
H14 1.000 0 0 0 0 0
H15 0.926 7.106 9.930 0 0 0
H16 0.901 58.203 16.770 0 0 0
H17 1.000 0 0 0 0 0
H18 0.898 36.662 10.001 0 0 0
H19 0.925 20.520 4.991 0 0 0
Managerial implications
The results are applied into BCG Model in this study (Figure 4). It first been proposed by The Boston Consulting Group. Originally the matrix depends on growth rate and market share. And it can be divided into four types. The first one is both growth rate and market share are high which be called Superstar. It can be a company highly growth market. The second one is Cow.
This business can be a major cash afflux. And the third is Question Marks with towering growth rate but lower market share. Some of them will become a Dog, and others may change to Super- star. It all depends on the manager’s strategies. The last one is Dog. Its performance is badly in these two parts. The matrix be amended into different types in this study.
Efficiency
Question Marks H07
H13
Super Star H01
H03 H06 H10 H14 H17
Inefficiency
Dog H05 H08 H09 H19
Cow H02 H04 H11 H12 H15 H16 H18
Low-Income High-Income
Figure 4: The BCG matrix with satisfactions and efficiency scores without considering satisfactions
This matrix is conducted efficiency scores and total income as vertical and horizontal axis.
With the same concept in BCG matrix can take our SBU into four groups. Superstars are good at sides, high efficiency scores and excellent performance in satisfaction. This group may be an indicator to other ones. Cow can do well in total income but failure in DEA efficiency scores.
Hospitals managers must think about how to improve their efficiency scores. Question Marks clever at DEA performance but do not do well in total income. Dog is the bad ones which are unsuccessful in both ways. It has much space to mend or try to concentrate on other businesses.
They can seek for some help from other hospitals, for example to take strategic alliance with other ones.
4. Discussion and Conclusion
Though Taiwan NHI get much of advantages, but NHI still have a big trouble of financial deficient. So, how to make our resource allocation effectively is an important issue for us. The health system in Taiwan isn't perfect, but it shows what is possible: comparatively much lower costs and improving health outcomes.
This study reaches shown that the firm that best performance is Far Eastern Memorial Hospital in Tai-wan. Especially, this research also compares the data envelopment analysis results between efficiency scores and total medical income, and, there are 6 hospitals in the super star group, 7 hospitals in the cow group, 2 in the question marks group, and 4 in the dog group.
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