This paper intends to obtain the short-run average cost minimization and capacity utilization over 34 regional public hospitals in South Korea from 2007 to 2010 using Data Envelopment Analysis (DEA). Also, it explores the average cost for each hospital in order to determine whether the cost is increasing or decreasing. The annual capacity utilization rate, using an adjusted number of patients as an output, was 0.49, and by using value added as an output was 0.56, on average. Only Jeju showed the highest level of capacity utilization regardless of output type. It indicates that almost all regional public hospitals, except for Jeju, have not run with full capacity, and have been in the decreasing area in the short-run average cost curve during the same period.
According to an OECD (Organization for Economic Cooperation and Development) report (2013) [
Recently, the hottest issue in the public health sector has been the closure of Jinju Medical Center in South Korea. South Gyeongsang provincial government shut down Jinju Medical Center (JMC), a provincial public general hospital, despite strong opposition from its unionized workers. Similarly, many regional public hospitals have been facing difficulties such as accumulated debts, unpaid wages, outdated facilities, and a labor shortage.
When it comes to a result-oriented economic performance for hospitals, the issue of efficiency is considered as an important matter. However, in the short-run, the hospitals are also required to produce the maximum amount of outputs such as treatment of patients or value added under fixed factors as an example capital stock, land, and other fixed costs. Thus, it is meaningful to check whether or not these hospitals operate with an acceptable level of capacity utilization based on the cost minimization. Moreover, it would be also useful to learn the scale efficiency of each hospital to examine if the hospital runs at an optimal scale.
Many economists have recently tried to define capacity utilization; which is divided into physical and economic definitions of capacity. In general, capacity is referred to the most efficient level of output, and it indicates economic capacity, which is different from an engineering or technical maximum output. Technical maximum is not based on cost concerns however the economic capacity concept takes into account economic cost.
The capacity utilization usually refers to capacity utilization rates, and is called an operating rate. It represents the relationship between actual output and potential output that could be achieved with labor force and capital stock. This is shown in a percentage rate; one hundred (100) percent implies full capacity. If a hospital operates at a 70% capacity utilization rate, it illustrates that there is a possibility to improve its production by 30 percent without additional fixed costs, such as the cost of building a new facility. In this sense, as stated previously, it is meaningful to check the capacity utilization rate for each regional public hospital in order to increase its feasible improvement as a production unit.
While the economic concept of maximum output is based on Klein’s or Johansen’s definition employing a production function, from an engineering perspective, the capacity is simply rated one.
One of the earliest discussions of capacity measurement is provided by Cassels (1937) [
In South Korea, previous studies have mainly focused on the efficiency of hospitals. Yang et al. (1997) [
As described earlier, most domestic studies of hospitals have mainly focused on the analysis of the efficiency. The purpose of this paper is to measure cost minimization, capacity utilization rates and scale efficiencies of regional public hospitals from 2007 to 2010 in South Korea, while also considering the public good achieved for the disadvantaged, by adopting the number of patients as one of outputs using DEA. In this context, this paper is significant for being the first to explore the short-run average cost minimization and capacity utilization rate of all regional public hospitals in South Korea. The remainder of this paper is organized as follows: Section 2 explains a theoretical model of cost minimization and capacity utilization of the hospitals based on DEA. Section 3 presents data and the empirical results, and Section 4 provides the conclusions and discussions.
Let us assume that a hospital produce a vector of outputs,
Assuming strong disposal of inputs and outputs and variable returns to scale, the true technology can be represented by the following set of production possibility:
where
Whereas in the long-run, all factors of production in the hospital are variable, in the short-run, one or more inputs are fixed while others are variable. Therefore, the hospital chooses the variable inputs to minimize the cost of producing a given amount of output in the short-run. The inputs are composed of variable and fixed factors.
Equation (4) represents the minimization of the short-run total cost (SRTC), which produces a certain type of output,
where
The minimization of the short-run total cost (SRTC) using linear programming can be expressed as follows:
Whereas short-run average cost (SRAC) is defined as adding average variable cost (total variable cost divided by output) to the average fixed cost (total fixed cost divided by output) in the short-run.
The minimization of short-run average cost (SRAC) can be derived by setting to keep the fixed element constant, and the variable factors vary. This can be expressed as follows using linear programming:
Here, variable factors are labor
The maximum output which minimizes the short-run average cost can be obtained from the minimization point in Equation (6). The capacity utilization rate is the ratio between the maximum output minimizing the average cost and the actual output. Thus, the short-run capacity utilization (SCU) ratio can be derived by comparing the maximum output
If y0 is equal to
In
Short-run scale efficiency (SSE) can be defined as the ratio between the minimum average cost
The short-run scale efficiency (SSE) is less than or equal to 1 (one) since SRAC in Equation (8) is the actual average cost in the short-run.
The data are obtained from financial statements (Balance sheets & Income statements) and final accounts from the Korean Association of Regional Public Hospitals (KARPH) during the period from 2007 to 20102. The total cost of a hospital is measured as a sum of the recurrent cost of hospital in a given year. Both the adjusted number of patients and value added variables are outputs. While adjusted number of patients variable includes the total number of outpatients and the total number of inpatients in a given year, value added variable contains income and loss before income taxes, labor charges, net interest expenses, rental expenses, and taxes as well as public dues. The number of doctors, nurses, and beds are used as inputs. Capital stock (tangible fixed assets) is utilized as a fixed input, which excludes depreciation. Tangible fixed assets include land, buildings, land improvements, machinery, delivery equipment or vehicles, and medical equipment.
All price variables are expressed at constant prices based on 2010 using the Consumer Price Index (CPI). The method to estimate these variables are shown in
This study intends to seek for the cost minimization and capacity utilization rate over 34 regional public hospitals. When it comes to reduction of the cost, it is plausible to save the cost via enlargement or reduction of input factors for hospitals. It, then, can define the average cost for each hospital to determine whether a hospital runs at the minimum average cost.
The annual capacity utilization ratio of the regional public hospitals, across the nation, showed 0.49 on average using adjusted number of patients as an output in
Since the capacity utilization ratio of these hospitals, except for Jeju, ranged from 0.19 to 0.93, most of them were in the diminishing area of the short-run average cost curve, which means that their average cost decreases as their output (adjusted number of patients) increases. This maybe because the size of these hospitals is so small that they can relatively easily reduce their average cost in the short-run when increasing their output.
Excepting Jeju, all of these hospitals showed comparatively low levels of the short-run scale efficiency. Jeju represented one (1); Anseong (0.91), Icheon (0.88), Seoul (0.87), and Chungju (0.87) followed Jeju whereas Suncheon (0.39), Gongju (0.39), Yeongwol (0.38), and Uljin (0.36) showed low levels of the short-run scale ef-
Variables | Estimation method |
---|---|
AP | (Annual number of inpatients) + {(outpatient revenue) × (annual number of outpatients)}/(inpatient revenue)} |
VA | (Labor charge)+ (rental expense)+ (net interest expenses) + (income and loss before income taxes) + (tax and public dues) |
TC | (medical cost) +(non medical cost) |
ND | (Medical specialists) + (general practitioners) + (dentists) + (oriental doctors) + (interns) + (residents) |
NN | (nurses) + (nurses’ aides) |
Capital stock (TFA) | {(Land) + (buildings) + (land improvements) + (machinery) + (delivery equipment or vehicles) + (medical equipment) + (equipment) + (construction in progress)} − (accumulated amount of depreciation) |
a) AP, VA, TC, ND, NN, and TFA mean adjusted number of patients, value added, total cost, number of doctors, number of nurses, and tangible fixed assets, respectively; b) The estimation of method of VA is based on the addition method of the Bank of Korea (BOK).
Hospitals | Cap-U | SRTC* | SRAC* | SSE | |
---|---|---|---|---|---|
Gangjin Suncheon Seogiwipo Jeju Jinju Masan Uljin Gimcheon Andong Pohang Mokpo Namwon Gunsan Seosan Hongseong Gongju Cheonan Chungju Cheongju Seoul Busan Daegu Incheon Wonju Gangneung Sokcho Yeongwol Samcheok Suwon Uijeongbu Icheon Anseong Paju Pocheon | 0.44 0.19 0.70 1.00 0.33 0.42 0.21 0.43 0.40 0.30 0.49 0.38 0.57 0.39 0.48 0.26 0.49 0.84 0.50 0.93 0.69 0.48 0.50 0.37 0.48 0.40 0.19 0.31 0.27 0.62 0.66 0.76 0.56 0.67 | 11,332 28,461 26,002 10,722 37,119 37,595 17,438 28,075 34,701 29,379 16,507 16,196 57,054 42,679 65,093 62,139 15,339 16,905 45,913 71,070 58,101 43,720 46,391 26,767 14,274 18,025 21,087 18,450 35,194 27,012 20,453 18,421 40,761 21,412 | 0.94 0.53 1.05 1.36 0.66 0.81 0.49 0.75 0.72 0.60 0.78 0.76 0.94 0.80 1.08 1.08 0.86 0.72 0.82 1.16 0.95 0.71 0.81 0.70 0.91 0.72 0.50 0.64 0.64 0.98 1.16 1.25 0.99 1.05 | 0.67 0.39 0.75 1.00 0.51 0.61 0.36 0.57 0.58 0.47 0.58 0.52 0.63 0.61 0.61 0.39 0.66 0.87 0.64 0.87 0.72 0.56 0.62 0.50 0.68 0.57 0.38 0.46 0.48 0.73 0.88 0.91 0.79 0.79 | |
Average | 0.49 | 32,640 | 0.85 | 0.63 |
a) Cap-U, SRTC*, SRAC*, and SSE denote short-run capacity-utilization, the minimum total cost in the short-run, the minimum average cost in the short-run, and short-run scale efficiency, respectively.
ficiency below 0.40. It means that except for Jeju, almost all these public hospitals were far away from the minimum average cost in the short-run during the same period by showing under one (1).
The empirical result above indicates that only Jeju has operated at the highest level of the capacity utilization whereas almost all regional public hospitals have not operated at full capacity during the same period. Also, it indicates that only Jeju has achieved the cost minimization but others have fallen in the decreasing area in the short-run average cost curve.
The annual capacity utilization ratio, using value added as an output, of the regional public hospitals across the nation showed 0.56 on average in
Hospitals | Cap-U | SRTC* | SRAC* | SSE | |
---|---|---|---|---|---|
Gangjin Suncheon Seogiwipo Jeju Jinju Masan Uljin Gimcheon Andong Pohang Mokpo Namwon Gunsan Seosan Hongseong Gongju Cheonan Chungju Cheongju Seoul Busan Daegu Incheon Wonju Gangneung Sokcho Yeongwol Samcheok Suwon Uijeongbu Icheon Anseong Paju Pocheon | 0.48 0.33 0.71 1.00 0.52 0.66 0.23 0.47 0.45 0.37 0.48 0.64 0.65 0.48 0.59 0.29 0.63 0.84 0.67 1.00 0.72 0.58 0.60 0.58 0.50 0.41 0.27 0.34 0.40 0.62 0.74 0.85 0.39 0.59 | 10,382 19,447 27,897 10,722 27,445 31,032 16,907 28,994 33,990 27,190 17,470 45,869 55,990 40,510 62,105 62,572 14,351 16,831 44,316 78,782 57,220 45,916 44,698 25,837 12,760 17,853 17,436 18,481 27,645 24,851 18,188 16,308 39,671 21,599 | 1.66 0.98 2.02 2.60 1.27 1.65 0.96 1.50 1.48 1.21 1.47 1.54 1.92 1.63 2.21 2.26 1.47 1.31 1.77 2.47 1.89 1.47 1.73 1.39 1.60 1.32 1.02 1.22 1.30 1.83 2.05 2.21 2.32 1.95 | 0.69 0.41 0.81 1.00 0.55 0.74 0.36 0.60 0.61 0.51 0.58 0.77 0.66 0.70 0.68 0.43 0.75 0.85 0.76 1.00 0.70 0.67 0.68 0.73 0.63 0.56 0.39 0.51 0.51 0.67 0.86 0.90 0.51 0.69 | |
Average | 0.56 | 31,222 | 1.67 | 0.66 |
a) Cap-U, SRTC*, SRAC*, and SSE denote short-run capacity-utilization, the minimum total cost in the short-run, the minimum average cost in the short-run, and short-run scale efficiency, respectively.
period. This means Jeju and Seoul have reached the cost minimization but others have failed to achieve the same ratio of decreasing average cost, which means most of them were in the diminishing area in the short-run average cost curve as their output (value added) increases.
Most of these hospitals showed comparatively low levels of the short-run scale efficiency. Jeju and Seoul represented one (1); Anseong (0.90), Icheon (0.86), and Chungju (0.85) followed Jeju and Seoul whereas Uljin (0.36) and Yeongwol (0.39) showed low levels of the short-run scale efficiency below 0.40. It means that except for Jeju and Seoul, many of them were far away from the minimum average cost in the short-run during the same period by showing under one (1).
The empirical result above illustrates that only Jeju and Seoul have run at full capacity whereas most of the regional public hospitals have not during the same period. In addition, it illustrates that only Jeju and Seoul have reached the cost minimization but others have been in the decreasing area in the short-run average cost curve.
This paper estimated the cost minimization and capacity utilization of 34 regional public hospitals in South Korea from 2007 to 2010 utilizing DEA. During the same period, we found that the annual capacity utilization ratio, using adjusted number of patients as an output was 0.49, and the figure using value added as an output was 0.56, on average. Only Jeju showed the highest level of the capacity utilization regardless of output type. In other words, almost all these public hospitals, except for Jeju, have not operated at full capacity during the time period.
Also, we learned that the annual short-run scale efficiency using adjusted number of patients as an output was 0.63, and the figure using value added as an output was 0.66, on average. When it comes to the annual short-run scale efficiency using adjusted number of patients as an output, except for Jeju, almost all these public hospitals have been far away from the minimum average cost showing under one (1). When it comes to the annual short-run scale efficiency using value added, except for Jeju and Seoul, most of these public hospitals have failed to reach the minimum average cost showing under one (1). Thus, only Jeju showed the optimal short-run scale efficiency regardless of output type by representing one (1).
It is important whether an individual regional public hospital hires a proper amount of workers and medical equipment under the optimal size, since the capacity utilization rate allows each hospital to benefit from the information which indicates what kind of resource is a waste. Although this study has a limitation to offer in terms of a comprehensive analysis of these hospitals, future research may consider some other important data such as the quality of medical service or DRGs.
As the empirical results above showed, only Jeju has achieved not only the cost minimization but also the full capacity utilization and the optimal scale efficiency in the short-run during the time period, regardless of the output type. It illustrates that almost all regional public hospitals, except for Jeju, have not run at full capacity, and the short-run average cost of operation of the hospitals has been decreasing, during the same period. It also implies that there is the potential to possibly increase their capacity utilization ratio by utilizing unused facilities. However, taking circumstances into consideration, such as the fact that the regional public hospitals have to have invested in certain types of capital such as acute care facilities, even if these facilities remain unused as a necessary role to serve potential patients, we need to be careful when estimating the economic performance of public hospitals when considering its unique role in serving the public as a whole.