Efficiency Analysis of Health Care Organization using Data Envelopment Analysis Swati Tripathi, Sonali Katiyar, Saifali Jain and Pravin Kumar Indian Institute of Information Technology, Allahabad Abstract The main purpose of this paper is to examine the technical efficiency of hospitals located in Allahabad region using Data Envelopment Analysis (DEA). Data envelopment analysis is a non-parametric method for measuring and evaluating performance of set of entities called Decision Making Units (DMU). This technique is able to deal with multi-dimensional nature of input/output variables. Some of the local hospitals situated in Allahabad (Uttar Pradesh) region have been considered for efficiency analysis. Some of the important inputs and outputs of these hospitals have been incorporated to demonstrate the method. Finally, the frontiers have been identified and compared on the basis of which lagging hospitals have been given suggestion for improving their services. Keywords:Data envelopment analysis, Technical efficiency, Decision making unit, Scale efficiency, constant return to scale, variable return to scale. I. INTRODUCTION Health care is a sector that has to provide services related to the general public and take care of not just their needs to make them well but also to provide the same in a better manner. Health care organizations are the ones that take care of people in their illness and so they have to be hygienic, clean and provide better services. The services provided by Health Care Centersand the Quality of services provided are the main basis on which they have to be judged, even their name is spread through word of mouth if they provide with good services. The efficiency of a Health care unit depends on the quality of service provided and to measure the same we are using Data Envelopment Analysis (DEA) as a tool. Data envelopment analysis is a method that is based on analyzing the statistical data based on a set of inputs called Decision Making Units, and mostly used for measuring and evaluating performance of the data provided. Data Envelopment Analysis has been done by taking the following inputs – Number of Doctors, Number of Nurses, Number of beds, Number of Paramedical Staff and the Number of wards. The output of the provided input areAverage number of OPD patients per day and Average number of patients admitted per day. The first application of DEA was done in Health care to measurethe routine nursing service efficiency(Nunamaker and Lewin, 1984). Since then DEA is being used extensively in the performance evaluation of technical efficiency of hospitals. Sherman (1984) was first to use DEA in evaluating overall hospital efficiency. The Data Envelopment Model, used in this paper is CCR Model, which was initially proposed by Charnes, Cooper and Rhodes in 1978.The DMU has Inputs and Outputs which have some assigned weights: Input=

v1 x 1 + v 2 x 2 +….+v 0 x 0

Output= u 1 y 1 +u 2 y 2 +….+u 0 y 0 Trying to determine the weight to maximize the ratio using linear programming –

Input Output Health care system in Allahabad Health sector at Allahabad are run by both public and private sectors. The health care facilities can be distributed as First Tier, Second Tier, Private health service providers and Private not-for-profit health providers. The performance

of these services is very important because the patients come from different various groups and regions such as rural, semi urban, urban etc. Most of the patients belong to low or average income group. Therefore, small sized or lower capacity hospitals, nursing homes, or polyclinics are very important in this area. Table 1 shows the distribution of health facilities in the Allahabad region. Table 1: Distribution of Heath Facilities in Allahabad Types of Facilities Government Health Facilities First tier (Primary Healthcare Facilities) Urban Family Welfare Centre D type Urban Health Centre Medical Care Unit Dispensary AWC ESI Dispensary Second Tier Facilities District/ Joint Hospital District Women Hospital Post Partum Centre Hospital Medical College Tuberculosis Hospital Children Hospital ESI Railway Hospital Defense Hospital

Number

3 12 30 535 7 1 1 1 1 1 1 1 1 2 3

Types of Facilities Private Health Facilities Private for Profit Health Practitioners Maternity/ Nursing Homes Certified Abortion Providers Certified NSV/DMPA Providers NGO/ Not for Profit/ Charitable Clinics Blood Bank District Health Training Centres

Number

1421 272 6 10

3 2

Source: Office of Chief Medical Officer, 2009 II. LITERATURE REVIEW Cooper, Charnes and Rhodes (1978) introduced the technique DEA. It is a non-parametric technique to find the relative efficiencies of decision-making units (DMUs) incorporating multiple inputs and multiple outputs. After, the work of Cooper, Charnes and Rhodes (1978), this field has been greatly explored by the various researchers e.g. Banker, Charnes, Cooper (1984). In recent years, DEA has flourished in many areas such as banking, hospitals, energy and environment etc. Zhou et al. (2008) conducted a literature review on the importance of energy and environmental modeling techniques. In his research, various DEA techniques have been highlighted and a large number of publications have been classified in this field. They observed that the benchmarking of electricity utilities accounts was common for the most studies. This paper of DEA helped the researchers to to measure the efficiency in the field of energy and environmental studies. Shafieeet al. (2013) evaluated the efficiency of an Iranian Bank using dynamic Slack Based Model (SBM) of Data Envelopment Analysis. They measured the efficiency of bank branches for more than two periods considering net profit as a good link and loan losses as a bad link. This paper compared the dynamic SBM efficiency with the static efficiency. In this paper, evaluation of inefficient branch was identified. In addition to this, several studies was conducted on hospitals. Recently, a research was conducted in public district hospitals in Madhya Pradesh to measure the technical efficiency (Jat and Sebastian, 2013). Data from 40 district hospitals were collected and DEA was performed with return to scale assumptions. Out of all the hospitals in this study, 50% were technically efficient and the rest were inefficient according to the “best practice frontiers.” Benneyanet al. (2007) applied DEA to identify the countries with most efficient healthcare systems. Almost 65 countries were identified on following six key dimensions - clinical outcomes, health ad- justed life years, access,

equity, safety and resources. The results reported only few countries to be efficient and suggested improvement measures. The performance evaluation of Indian Private Hospitals was evaluated by Moghaet al. (2012). DEA based on CCR and BCR models were applied on 55 private sector hospitals for the year 2009-10. The findings indicated that ten hospitals set an example of best operating practice for the remaining 45 inefficient hospitals to follow. The study says that on an average each hospital has to increase its output by 23.7% by maintaining the existing level of output. The analysis reveals that performance of hospitals is affected due to poor utilization of resources. The sensitivity analysis shows that efficiency scores of hospitals are stable even after the exclusion of the top performer. The results of this study based on the choice of inputs and outputs. Banker et al. (2004) discussed Returns to Scale (RTS) in different DEA models like BCC, CCR and multiplicative model. Debataet al. (2013) developed a framework to benchmark medical tourism service providers in India and formulated strategies to understand deficiencies to improve their performance. In this study they collected the data for thirty-nine major medical tourism service providers in India for benchmarking purposes. They used both BCR and CCR models to check the differences the relative efficiencies of the medical tourism service providers. If DMUs are homogenous in nature, this method can be used to assess performance in any environment. Jong Jooet al. (2011) used DEA for benchmarking and illustrate variable selection using Return on Asset (ROA) for comparing efficiency of companies in the same industry. Moreover, a framework was suggested for selecting variables for performance measurement and benchmarking which includes general merchandisers. Weber (1996) published his work on performance measurement of vendors. It was recognized that vendor selection is a multiple criteria decision-making problem. This work demonstrated that how DEA could be used to measure the performance of vendors on mult-criteria. DEA was applied in the firms operating in a Just-in-time (JIT) environment. It was observed that performances of vendors can be basically measured on the price criterion, delivery criterion and quality criterion. Jain et al. (2011) used DEA for performance measurement and target setting in two manufacturing companies of discrete production systems. Various DEA models were applied and tested; the factors contributing to lower efficiencies were identified in similar circumstances. Tripathy et al. (2012) had applied DEA to pharmaceutical firms in India for measuring the efficiency. The analysis of 90 sample firms was undertaken to measure the technical efficiency. The findings showed that performance of large number of sample firms was not optimal and the average efficiency of the R&D intensive firms is greater than that of non R&D firms. The difference in efficiencies between these two firms was statistically significant. DEA tool was first introduced by Charneset al. (1978). They described DEA as a “mathematical programming model applied to observational data that provides a new way of obtaining empirical estimates of relations such as the production functions and/or efficient production possibility surfaces-that are cornerstones of modern economics”. In very short span of time, DEA has grown rapidly as a powerful analytical tool for measuring the performance. This tool has provided new insights to the entities worldwide for example studies of benchmarking using DEA tool has provided in identifying better benchmarks in various applied studies. DEA was also used as a new managerial audit methodology (Sherman, 1982). Sherman (1982) developed DEA as a managerial audit tool for resources allocation and analytic review of efficiency when applied to given set of situations. He also interpreted strengths and limitations of DEA techniques His study was not only to evaluate the relative efficiency of non profit and public sector Decision Making Units (DMUs) but also extends to profit sector class. III. METHODOLOGY To measure the efficiency of hospitals, the technique used in this paper is Data Envelopment Analysis. Charnes et al. (1978) first introduced the DEA technique for measurement of relative efficiency of some organizations such as hospitals and schools. The linear programming technique is used in DEA to to calculate the relative efficiency for each hospital. Efficiencies vary between 0 and 1. Hospitals having a score of 1 or 100% are technically efficient and

hospitals having scores of less than 1 are technically inefficient. Constant returns to scale DEA linear programming model is depicted here under. s

u r yrj0

Max h0 = r `

Subject to: m

v j xij0 = 1 i 1 s

m

ur yrj r 1

0, j=1,….,n

vi xij i 1

u rj v j

0

Where: yrj = amount of output r from hospital j xij = amount of input i to hospital j ur = weight given to output r vi = weight given to input i n = number of hospitals s = number of outputs m = number of inputs The most prevalent DEA model formulation is the model developed by Charnes, Cooper, and Rhodes (1978), that has been modified by Banker, Charnes, and Cooper (1984) .The model is formulated as following: For each

DMU p

Maximize

EP =

p = 1,2,……….,

x pj v j

y pi wi

(1)

j

i

Subject to:

xkj v j

y ki wi i

1 for k

j

E p =Departmental Efficiency ( p = 1,2,....,K) wi

, for i = 1,2,.....,I

v

, for j = 1,2,....,J

j

x kj = input value j for DMU K y ki = output value i for DMU K

K

(2)

a small constant t Decision Variables v j Weight of input j (unitless) w i Weight of output i (unitless) DEA Analysis In this paper a comparative study of CCR and BCC models is done. Firstly, the efficiencies of DMUs are measured using CCR and BCC model. The CCR model works on the concept of constant-return-to-scale. It computes the efficiency scores, which defines Technical Efficiency (TE).“Technical efficiency measures the firms success in producing maximum output from a given set of inputs” (Debnath, 2009). The BBC model works on the concept of variable-return-to-scale. It computes the efficiency scores, which defines Pure Technical Efficiency (PTE). Thus, a relationship is established between CRR and BCC models: Technical Efficiency (TE) = Pure Technical Efficiency (PTE) X Scale Efficiency (SE). “Scale efficiency (SE) means the efficiency due to scale difference between constant-return-to-scale and variable-return-to-scale” (Jooet al., 2011). IV. ANALYSIS AND DISCUSSION The DEA model applied in this paper is all output-oriented. To compute efficiency, two DEA models namely CCRO and BCC-O have been applied. The data for study has been collected from nine private sector hospitals of Allahabad (U.P.) region. The input measures used in this study are number of doctors, number of nurses, number of paramedical staff, number of beds, number of wards whereas the output measures are average number of OPD patients per day and average number of patients admitted per day. The input-output variables are shown in Table 2.

Table 2.Hospitals input and output data. Hospitals

(I) Doctor

(I) Nurse

(I) Staff

(I) Beds

(I) Wards

(O) OPD patients

(O) Patients admitted

A

4

3

6

11

6

20

1

B

9

11

7

40

7

100

7

C

10

4

2

40

4

10

2

D

4

2

4

11

3

50

2

E

3

3

0

22

7

10

2

F

3

2

5

12

2

20

7

G

5

2

8

20

7

13

3

H

3

4

7

22

7

60

15

I

1

0

10

18

6

12

1

Table 3 depicts the efficiency score of hospitals using CCR and BCC models applying DEA solver. In this section our analysis is a three-step procedure. In first step, CCR model is used to measure technical efficiencr. In second step, BCC model is used to calculate pure technical efficiency. This helped us to identify inefficient hospitals on account of inefficient operations. Finally scale efficiency is computed by taking the ratio of CCR and BCC. SE provides information about those hospitals that are operating under disadvantageous conditions.In Table 3. DMUs A, C and G are inefficient having the CCR scores are 0.412698, 0.451613, 0.377358 respectively and BCC scores 0.5, 1, 0.383212 respectively. The scale efficiencies of these DMUs A, C, G are 0.825397, 0.451613, 0.984726 respectively. Hence these hospitals are operating under disadvantageous conditions. The hospitals, which are fully efficient in CCR score, are also efficient in BCC score where the constant-return-to-scale prevails. B, D, E, F, H and I have this status. This characteristic signifies that the hospital can scale the input or output linearly without increasing or decreasing the efficiency. Whereas, A, C and G are displaying decreasing-return-to-scale. This indicates that they have a possibility to improve their efficiency by scaling down their operations. Table 3. Efficiency under DEA-CCR and DEA-BCC model DMU (Hospitals)

CCR-O

BCC-O

Scale Efficiency (CCR-O/BCC-O)

Returns to scale

A

0.412698413

0.5

0.825396825

Decreasing

B

1

1

1

Constant

C

0.451612903

1

0.451612903

Decreasing

D

1

1

1

Constant

E

1

1

1

Constant

F

1

1

1

Constant

G

0.377358491

0.383211679

0.984725965

Decreasing

H

1

1

1

Constant

I

1

1

1

Constant

It is clear from table III that BCC model yields higher average efficiency than the CCR model. The average values of BCC and CCR are 0.87 and 0.80 respectively. An index value of 1 denotes maximum or perfect efficiency. As SD of BCC is lower as shown in Table 4., it proves to be a better model. Table 4. The comparison of efficiencies between BCC and CCR model

No. of DMUs Average SD Maximum Minimum

V.

BCC

CCR

9 0.875912409 0.233772981 1 0.383211679

9 0.804629978 0.276849137 1 0.377358491

CONCLUSION

This paper has been focused on measurement of the efficiency of hospitals located at Allahabad and ranked them according to their scale efficiency. For this, DEA models have been applied. DEA hab been proved to be a useful approach for efficiency measurement. Two models of DEA namely CCR and BCC were undertaken to obtain the efficiency scores of Allahabad hospitals. These scores have been relatively compared and scale efficiency is computed using the ratio of CCR and BCC. A comprehensive analysis of input and output variables is considered

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