Efficiency Benchmarking Based on Data Envelopment Analysis:
A Case Study for Hospitals in Selangor, Malaysia
Salim, K.F.A.1, Alwadood, Z.1*, Noor, N.M.1
1 Faculty of Computer and Mathematical Sciences, Shah Alam, Malaysia
*Corresponding Author: [email protected]
Accepted: 15 February 2021 | Published: 1 March 2021
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Abstract: The rapid increase in the number of populations necessitates the healthcare system in Malaysia to withstand the growing demands for healthcare services. In mission to improve the quality and health status of populations, Malaysia health system should achieve remarkable outcome from its management. Even though the study of performance in healthcare sector is crucial, to date there is no study has been conducted to measure the technical efficiency of public hospitals, specifically in the state of Selangor. The goals of this study are to evaluate the efficiency among ten public hospitals in the state of Selangor by using Data Envelopment Analysis (DEA) technique and determine the improvement strategies that could maximize the utilisation of resources in order to achieve full efficiency in their services. Data of these hospitals was obtained from 2015 Selangor Annual Report of Health. The set of inputs and outputs from ten hospitals in Selangor for a one-year period were selected for this study. The hospitals input measures include the number of beds, number of doctors, public health expenditures and number of admission reports. The output measures include the number of inpatients, outpatients, discharged patients, bed occupancy rate and number of surgeries. The findings of this study have shown that eight DMUs are operating at efficiency level of more than 90%, while two DMUs below 90%. The study also recommended the improvement strategy for the inefficient DMU. This strategy could be the indicator for policy makers in improving the efficiency of healthcare facilities in Malaysia.
Keywords: data envelopment analysis, efficiency, healthcare
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1. Introduction
Measuring technical efficiency is crucial as it is a platform or a benchmark for the industrial, sector or organization in achieving and accomplishing it. According to Drebee and Razak (2018), technical efficiency refers to the ability of Decision-Making Units (DMUs) to produce a maximum level of output by using its available resources. It is also defined as the ratio of output to input, which deals with a combination of data that produces certain outputs (Fereshteh et al., 2016). Units in healthcare field will strengthen the management of the hospitals and clinical services and improve its performance through better use of resources. The economic growth and productivity of citizen can be influenced by their health level and this is strongly related to the efficiency of national healthcare system. By identifying area of improvement in the healthcare system, the efficiency of the existing system can be evaluated by using correct and suitable methods. The contextual analysis of the Malaysia Health System Volume I (2016) have stated that Malaysia government aims to build a strong health system and to develop a sustainable system that is equitable, efficient, effective and responsive to citizen needs. This can be achieved by strengthening the financing, deliveries and government mechanism to adapt with rapidly changing in the trend of the system. The key finding of this goal should be
accomplished so that any successfully changes can be adapted for national healthcare system in the future.
Since 1970s, Malaysia has been reported to achieve impressive health gain for its population with low health expenditure. The hospitals are giving a high level of universal access, comprehensive services and strong equitable financial protection from high care cost. As Malaysian live longer and the nation grows rapidly, the government must spend more to cope with the rising in the health system expenditure due to economies growth, increasing per capita GDP and medical technology advancement. Demographic changes, diseases pattern and lifestyle have influenced the healthcare cost. Demand for expensive medication and new type of high cost services such as transplant and implant have given significant impact on the limited health resources. This high health expenditure exposes families to the unexpected financial problem. The escalation in healthcare cost and limited financial resources causes public to demand low cost of health services. The poor urban is vulnerable to chronic and seasonal illnesses. It may lead to limited and unequal distribution of health status among the urban and rural population. Malaysia health sector should have an indicator in spending more on this sector.
Therefore, the objectives of the study are to determine the technical efficiency of the selected hospitals and to evaluate the efficiency improvement option that can maximize the hospitals’
efficiency. It will help healthcare sector in providing a rank of its performance accordingly.
Also, the efficiency score is helpful for hospital administrators in setting a benchmark and providing a systematic guideline for this sector to improvise its services to become representative at the population levels of satisfaction. The sample for this study covered ten hospitals located in the urbanization area of Selangor. This state is in the west coast of Peninsula Malaysia with an area of 8104 km2 and a population is approximately fifty-nine million. The information is based on the health statistical data from the Annual Health Report 2015, published by the Health Department of Selangor.
Data envelopment analysis (DEA) is a powerful mathematical method that utilizes linear programming (LP) model to determine the relative efficiencies of a set of functionally similar decision-making units (DMUs) by comparing it with other DMUs. This model is an analytical technique for measuring efficiency performance and has been broadly used by both academicians and practitioners in the industry in evaluating efficiency. The efficiency scores of DMU which are equal to one (1) are called efficient and the score close to zero (0) is called inefficient. DMUs refer to the collection of firms, departments, divisions or administrative units with the same goals and objectives, and which have common inputs and outputs. In healthcare system, DMUs can be hospitals, doctors, and sub-unit of department.
In this study, the DEA model assumes that all hospitals are having similar demand of services from patients since all selected hospitals are situated in large urban location and serve population of similar characteristics. All the input and output variables have been evaluated on detail analysis of the commonly used variables in some research studies. They have been restricted to the theoretical rule for the construction of DEA model and limitation for sample data used. This standard DEA models assume that all inputs and outputs are known precisely and can be modified at the discretion of management. The finding of this study provides a systematic approach to evaluate the technical efficiency of ten selected hospitals to maximize the utilization of resources while satisfying each technical constraint. An LP model used will analyse and interpret the relation of every common factor that will significantly affect the
efficiency of the hospitals. Therefore, the evaluation of efficiency is expected to be optimal since all the possible common factors are closely examined.
2. Related Studies
Decades back, efficiency models are very useful in optimizing the relationship between two or more complicated problems. Many researchers have suggested variety of models in solving efficiency and effectiveness of systems. The methods are applicable in estimating service productivity and efficiency, depending on the objectives or the suitability of the model used.
To name a few, some methods used includes Pabon Lasso (Mehtrak, Yusufzadeh &
Jaafaripooyan, 2014), Fuzzy-AHP Approach (Rouyendegh et al.,2019) and multilevel modelling (Min et al., 2019). These methods are applicable to specific problem, depending on the consistency and availability of data.
Applanaidu et al. (2014) examined the issue of efficiency of public hospitals in state of Kedah, Malaysia. The objectives of the study are to measure the technical efficiencies among the hospitals and identify the best allocation of resources to achieve optimal efficiency. It was found that 74% of the DMUs are best-practice frontier while the rest are technically inefficient with the score between 0.780 and 0.991. Each inefficient DMU able to achieve efficiency by reducing their resources by 6.25 % while maintaining the same number of outputs.
Wang et al. (2016) studied the efficiency of the 32 Maternal and Child Health Hospitals in China. DEA model is used to estimate the score efficiency while Tobit model is used to regress the hospital external and internal environmental factors toward the estimated score of efficiency. The result of the study has proven that the total expenditure and actual number of beds does not gives a significant effect on the inefficiency but it is contributed by the output variables, total annual income, the number of discharged patient and emergency visit.
Ali et al. (2017) studied the relation of the economic performance, rapid population growth and decline a public expenditure by the government on the efficiency of the hospitals in Sub- Saharan Africa. The aim is to examine the relative efficiency of 12 hospitals in Eastern Ethiopia for 6-year-round panel data that will lead to the improvement in productivity of the traditional healthcare system. It was found that the teaching status of the hospital is positively affecting the inefficiency score of the hospital. It implies that being a teaching hospital reduces the expected efficiency because the hospital mainly focuses on both academics and health services provision. In addition, the proportion of medical doctors to the total staff is negatively related to the inefficiency.
In Slovak Republic, the issue of healthcare and the application of window DEA were dealt by Stefko et al. (2018). The objectives of the research are to quantify the impact of output-oriented 4-year window DEA model on the result of assessment toward the efficiency of 8 regional healthcare facilities. They highlighted that there is an indirect dependence between the values of the variable over time with the result of regional efficiency obtained. Region with low values of variables achieved a high degree of efficiency and vice versa.
A study by Ibrahim and Daneshvar (2018) focused on the continuous migration of refugees from Syria to Lebanon and initiated a measure on the efficiency of the healthcare system in Lebanon hospitals. It identified the available resources to fulfil the growing demands, improve the efficiency, reduce costs and introduce a new and effective technology that will contribute to the optimal healthcare services. The result reveals that only 4 years over the 16-year period
of their study that the healthcare system operated efficiently. It is identified that the inefficiency comes from the increasing on number of newly infected HIV and maternal mortality ratio.
Several studies have proven the powerful and superiority of DEA as compared to the other technique. DEA has been used universally for relative performance measurement in public sector services such as education (Soteriou et al., 1998; Avila et al., 2017) and bankruptcy predictions (Cielen et al., 2004). The advantages of applying DEA is also in providing the identification on inefficient DMUs while having abilities to give suggestion on the best scarce resource allocation (Alwadood et al., 2011).
3. Methodology
The data for this study is taken for January to December of 2015, based on the 2015 Annual Health Report. The DMUs used in this study are ten selected government hospitals in Selangor, Malaysia. These DMUs are selected due to their similarities in the context of the facilities and services.
Table 1 shows the data of input and output values used in the study. The outputs selected are number of inpatients, number of outpatients, number of discharged patients, bed occupancy rate and number of surgeries. The number of beds available, number of doctors, public health expenditure and number of admission reports are selected as input variables and it is controllable by any changes made by the management.
Table 1: List of Input and Output Used in DEA Model
Input Output
Number of beds available Number of inpatients
Number of doctors Number of outpatients
Public Health Expenditure Number of discharged patients Number of Admission Reports Bed Occupancy Rate (BOR)
Number of Surgeries
The number of beds refer to the number of official beds available in the hospital at time ready to receive patients who already receive treatment or otherwise. The number of doctors includes the number of specialists, non-specialists, dentists and medical officers who are in charged to provide services. Public health expenditure represents the budget from the government to cover full payment of patient treatment, salary of the employees and equipment and facilities of the hospital. The number of admission reports is a hospital admission records that contains most of the feedback on the services given to patients, outsiders or providers in the hospital. Since there is fluctuation in number of these reports between hospitals, therefore this study considers the number of admission reports as input variable to determine if it has a significant effect on the DMUs efficiency. Nonetheless, the most important approach to identify the hospital inputs and outputs remains the one which would allow better and more accurate measurement of technical efficiency, and this must be associated with health outcomes. Health outcomes, as outputs, could involve health status measures, quality-of-life measures and well-being measures.
The reference model used in this research is adopted from the DEA model formulation developed by Charnes, Cooper and Rhodes (1978) or commonly known as CCR model, under the assumption of input-oriented of the Constant Return to Scale. CCR model is used as the base in the formulation the constraints due to the similarities in elements in this case study. The input-oriented model is the most appropriate in this context because the input is assumed to be
at the discretion of the health industry in Malaysia. This study focused on measuring the efficiency with the purpose to evaluate the hospitals’ performance.
The model sets and parameters are stated as:
r: index for output variable (r =1, 2,…, R) where R=5 i: index for input variable (i :1,2,…,I) where I=4 p: index for DMUs (p :1,2,…, P) where P=10 𝑣𝑝𝑟: amount of output r produced by DMUp 𝑢𝑝𝑖: amount of input i utilized by DMUp
The model decision variables are given as:
𝑦𝑟: The weights given to output r 𝑥𝑖: The weights given to input i Ep: Efficiency score for DMUp The mathematical model is
Maximize 𝐸𝑝= ∑ 𝑣𝑝𝑟
𝑅
𝑟=1
𝑦𝑟
(1)
Subject to,
∑ 𝑢𝑝𝑖𝑥𝑖 = 1
𝐼
𝑖=1
(2)
∑ 𝑣𝑝𝑟𝑦𝑟−
𝑅
𝑟=1
∑ 𝑢𝑝𝑖𝑥𝑖 ≤ 0
𝐼
𝑖=1
(3)
𝑦𝑟, 𝑥𝑖 ≥ 0 (4)
The objective function (1) represents the maximum efficiency score obtained by DMUp.
Constraint (2) restricts the weighted sum of input variables for DMUp, to be equal to one or unity. Constraint (3) restricts the weighted sum of all output variables is less than the weighted sum of all input variables for each DMUp. Constraint (4) restricts that each decision variable should be positive to avoid any input or output variable being neglected in determining efficiency.
To find the optimal solution, the DEA model is set up as a Simplex LP engine. The constraint precision for the value of the efficiency obtained in the model is set to be 0.000001 or 6 decimal places and the integer optimality in percentage equals 1. Automatic scaling is used where the Solver will produce a solution if all the constraints and the optimality conditions are satisfied.
Simplex LP allows the user to find the global optimum for the solution and it is assumed that the unconstrained variables are non-negative to avoid infeasibility.
4. Experimental Results
The efficiency score of 10 hospitals in Selangor, Malaysia is given by the objective function value of its DEA model. The DEA result of technical efficiency identifies the comparatively efficient best-practice hospitals (score = 1) and the relatively inefficient score (score < 1). An analysis has been carried out as input-oriented and the result is obtained under the assumption
of constant return to scale. Figure 1 shows the average efficiency score for each of the 10 hospitals under study. The result of the corresponding DEA frontier analysis provides an overview of the current performance of each DMU.
Figure 1: Average efficiency score for each DMU
The result shows that eight DMUs have efficiency score of more than 90% and the other two have efficiency score less than 90%. DMU9 has recorded the highest efficiency of 99.7%, followed by DMU6, DMU1, DMU7, DMU8, DMU5, DMU2, DMU4, DMU10 and finally DMU3. This indicates that almost all hospitals in Selangor are operating at near-efficient level of efficiency. DMU3 and DMU10 are identified as relatively inefficient with efficiency score of 89.8% and 89.9%, respectively. They are the most inefficient DMU as compared to other DMUs in the set. The low efficiency scores obtained by DMU3 and DMU10 indicates that these two DMUs are underutilizing their resource in their service operation. This implies that there are some factors that could be considered to increase the efficiency of these DMUs.
In providing the improvement value of input and output of inefficient DMUs, dual DEA model are used. The value of decision variables from the dual model can be used to identify efficient peers for those hospitals that are not efficient and help the inefficient hospitals to emulate the functional organization of their peers to improve their efficiency. In this case, a model introduced by El-Mahgary (1995) have been applied to identify the input or output amount that should be increased or decreased to make the inefficient unit become efficient. This method is useful in visualizing the criterion of inefficient units when an efficiency frontier cannot be drawn.
The dual version of the CCR model has fewer constraints, as they depend on the number of inputs and outputs. For every inefficient DMU, dual DEA model identifies a set of corresponding efficient units. The units involved in the construction of the composite DMU can be considered as the benchmarks for improving the inefficient DMU. By taking the dual from the DEA model, the weight of dual for the reference set can be found. The reference set and weight of dual values are produced by solving the reduced linear programming model for every DMUs. The reference set are basically consisting of hospitals that have greater efficiencies and hence, they are served as the basis for improving the efficiency of the inefficient hospitals. The weight of dual is used as an indicator or multiplier represented by each reference set to obtain the suggested value for improvement.
Upon arrival the final solution, the DEA model is set up as a Simplex LP engine since it is a linear programming problem. Automatic scaling is used where the Solver will find a solution if all the constraints and the optimality conditions are satisfied. Simplex LP allows the user to find the global optimum for the problem. In addition, it is assumed that the unconstrained variables are non-negative to avoid infeasible region. Based on the result obtained from the experiment, DMU3 and DMU10 are the inefficient DMU. However, only the method to improve the inputs and outputs for the inefficient unit of DMU3 is illustrated here. The same approach could be applied for the other inefficient unit, DMU10.
Table 2: The Weight of Dual of the Reference Set for DMU3 Scalar
Constant
DMU 1
DMU 2
DMU 3
DMU 4
DMU 5
DMU 6
DMU 7
DMU 8
DMU 9
DMU 10
0.9997 0.1259 0 0 0.0046 0.7899 0 0 0.5200 0 0
To find the value of improvement to the output and input variable for the DMU3, Table 2 represents the result for the dual weight for the reference set. Taking only the nonzero dual weight, the reference set of DMU1, DMU4, DMU5 and DMU8 will be used to determine the improvement strategy. The scalar constant 99.7 percent of DMU3 is the comparative efficiency which indicates the extent to which the efficiency of DMU3 is lacking in comparison to the efficiency of its reference subset DMUs (DMU1, DMU4, DMU5 and DMU8). These efficiency reference subsets DMUs represent the basis vectors of the LP solution for DMU3. In other words, a convex combination of the actual outputs and inputs of the reference subset of DMUs results in a composite DMU3 that produces more outputs as DMU3 but uses less inputs than DMU3. Table 3 shows the actual, target and percentage difference of outputs for inefficient DMU3.
Table 3: The Deficient/Surplus Outputs of DMU3 Number of
Inpatients
Number of Outpatients
Number of Discharged Patients
Bed Utilization
Rates
Number of Surgeries
Actual 50487 327568 50514 91 13812
Target 50487 327568 50514 112 13812
Percentage Difference 0% 0% 0% +23.1% 0%
Based on the result DMU3, the efficiency of this DMU can be improved if it allows the bed utilization rates to be increased to 112. All other outputs like the number of inpatients and outpatients, the number of discharged patients and the number of surgeries should be kept unchanged.
Table 4: The Excess/Slack Inputs of DMU3 Number of
Beds Available
Number of Doctors
Public Health Expenditure
(RM)
Number of Admission Reports
Actual 656 582 150,000,000 71
Target 635 582 134,805,397 43
Percentage Difference -3.2% 0% -10.1% -39.4%
On the contrary, Table 4 shows the corresponding results of the actual, target and percentage difference of inputs for inefficient DMU3. It is shown that there should be several reductions that should be made on the inputs to boost the efficiency level. In this context, the number of beds available must be reduced at least 635, the public health expenditure must be decreased to RM134,805,397, while the number of admission reports should be reduced to 43. The
number of doctors should be maintained. As a result of these recommendations, DMU3 will be able to maximize its efficiency level. The same approach could be also applied to any other DMUs in the set to determine the corresponding improvement strategies that should be taken.
Besides these improvement strategies, the inefficient DMUs must learn from the efficient peers’ practices and strive to reach the targets in relation to the benchmark inputs and outputs levels of the efficient DMUs. The result obtained from the DEA technique does not only help in measuring the performance and determine best practice of DMUs, but also provide the direction and magnitude for each inefficient DMU to be efficient. It is worth emphasizing on minimizing the values of input to produce maximum level of outputs as it is less cost consuming.
5. Conclusion
This study evaluates the efficiency among ten public hospitals in Selangor using DEA technique. It was found that eight DMUs are operating at efficiency level of more than 90%, while two DMUs have recorded the efficiency below 90%. The experimental result has shown that DMU3 is the most inefficient among the other hospitals in the study, with an efficiency score of 89.8%. An improvement strategy by using reference set was carried out to achieve full efficiency. Reference set utilizes the idea of using hospitals with greater efficiencies as the basis for improving the efficiency of the inefficient hospitals. The results have indicated the value of the inputs and outputs that should be changed, which would bring the inefficient DMU to achieve full score of efficiency. This improvement strategy could be the indicator for policy makers in improving the efficiency of healthcare facilities in Malaysia.
Future study may look at greater perspective of inputs and outputs factors, for example to extend the study on non-controllable input-output to represent more practical real-life problems. In addition, further study should be looking at larger number of hospitals so that the efficiency levels can be measured, and improvement strategies can be identified accordingly.
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