Hospital Benchmarking Using Data Envelopment Analysis Report

Executive summary

Data envelopment analysis (DEA) is an approach used in the examination of multiple input and multiple output processes. DEA necessitates neither a clear formulation of the fundamental practical correlation nor pre-allotted weights for multi-outputs and multi- inputs in assessing performance concerning a process (Chan, Johansen, Mangolini, & Peacock, 2001). The key benefit of using this approach is its capability to unambiguously factor in the use of numerous inputs to designate numerous outputs. Similarly, DEA aids in limiting the intricacy of examination through the simultaneous assessment of the qualities of interest and offering a solitary and compound tally denoted as efficiency.

Problem definition

American health care spending is higher compared to the spending of other developed countries (Sherman & Zhu, 2013). In the year 2011, $2.7 trillion was spent. The above implies that approximately $8, 680 were spent per person. As compared to the spending used in the years 2009 and 2010, the amount spent in the year 2011 grew by 3.9% to $ 850 billion. The US spends over 20% of its annual budget on health care. In regard to this, is apparent that cost containment in the health care sector should be implemented. While implementing the needed changes, the sustained capability of hospitals to provide effective and standard service should be upheld.

Of particular importance to health care executives is the capability to benchmark features of their organizations’ productivity concerning their rivals. During benchmarking, several challenges are encountered. The challenges are how to develop means of operating efficacy for hospitals, how to select weights to be used in several inputs and outputs, how to undertake to benchmark, and how verdicts like the termination of some divisions should be carried out (Jacobs, 2000). The above challenges can be addressed by adopting DEA.

Solution detail

For a hospital manager to analyze the efficacy of a specific DMU carefully worked-out programming procedures are used to define weights for the comparative value of the numerous outputs and inputs that make the most of an exact DMU’s efficiency score (Sherman & Zhu, 2006). The most predominant DEA model designs in the market are attributed to Charnes, Cooper, and Rhodes. The model is illustrated below:

For each DMU_p, P = 1, 2, …,
(1) Maximize E_p = ^∑ypi^wi, i/_{∑^xpj ^vj, j}
(2) Subject to ^∑yki ^wi, i/_{∑^xkj^vj, j} ≤ 1 for k = 1, 2, …, K
E_p = Departmental, Efficiency (p = 1, 2, …, K)
w_i ³ e, for i = 1, 2, …, I; ^v j ³ e, for j = 1, 2, …, J
^xkj = input value j for DMU_k; ^yki = output value i for DMU_k
e = a – small constant

To analyze the performance measure of a hospital, the inputs and outputs should be determined (Sherman & Zhu, 2006). For instance, a hospital can have the following major departments:

1. Surgery department
2. Medicine department
3. Pediatrics department
4. Psychology department
5. Obstetrics and gynecology department
6. Orthopedic department
7. Primary care department
8. Accident and Emergency department
9. Specialty department

For such a hospital, two input variables and three output variables are chosen to quantify the efficacy for every department. The input trials are the sum of doctors’ salaries and nurses’ salaries. On the other hand, the output trials are the value of patients, bed capacity, and regular turnover interval. The trials are illustrated in the table below.

A formula for relative efficacy integrating numerous inputs and outputs is used in analyzing the above figures. Similarly, an appropriate DEA model should be used in determining relative efficiency trials. A popular measure for relative efficacy is illustrated below.

Efficiency = weighted sum of output/ weighted sum of input

(3) Efficiency of department = ^y1 j ^w1 ^+y2 j ^w2 + ^y3 j ^w3/ ^y1 j ^w1 ^+y2 j ^w2 + ^y3 j ^w3

By utilizing equations (1) and (2), the efficacy of departments can be obtained. For instance, statistics from the surgery department can be analyzed as shown below.

(4) Max E_p = ^{3120w₁+ 3.06w₂+ 2.07w₃}/_709342v1+ 750995v₂
(5) Subject to ^{3120w₁+ 3.06w₂+ 2.07w₃}/_709342v1+ 750995v₂ ≤ 1 (dep. 1)
(6) ^{6720w₁+ 5.53w₂+ 0.47w₃}/_709065v1+ 907044v₂ ≤ 1 (dep. 2)
Similar constraints are undertaken for every department: w_i³ e

Using the DEA model, the subsequent linear program is as shown:

(7) Max E_p = ∑ ^ypi ^wi, i
(8) Subject to ∑ x_ojv_j⁼¹, j
(9) ∑ y_oiw_i (i) – ∑ x_ojv_j£^{0(for all dep)} (j)
v_j³ e, w_i³ e

The efficacy of every unit is reached by using the above equations (Sherman & Zhu, 2006). The answers offer measures of the comparative efficacy of the departments and the weights indicating the efficiency.

Business benefit

DEA has numerous benefits, which makes it the ideal tool for calculating relative efficiency between regions and in so doing defining rankings (Sherman & Zhu, 2006). For instance, numerous inputs and outputs of opposing units can be utilized if the inputs and outputs are alike for every unit being likened. Thus, inputs like the number of beds, number of doctors, number of nurses, and outputs like a sum of immunization and working days can be utilized.

Efficacy scores obtained by the use of DEA are highly sensitive to inputs and outputs. Therefore, it is a valuable instrument to be used in addressing strategic and policy-related, and operational issues in hospitals. Similarly, DEA aids in limiting the intricacy of examination through the simultaneous assessment of the qualities of interest and offering a solitary and compound tally denoted as efficiency.

As illustrated above, DEA is a very efficient way of hospital benchmarking. Therefore, it is apparent that the approach would enable the health care system to assess the efficiency of its departments with ease. Hospital managers would be able to manage their organizations with ease with the use of information system tools such as DEA. The tool would allow them to collect and process accurate and timely data. With the advancements of technology, many opportunities will emerge from the use of the program more health care centers will adopt it. In the future, the development of user-friendly software would progress the advancement and the adoption of the program.

If effectively implemented, DEA programs will reduce healthcare expenditure and reduce the deficit. For the health care management to overcome its current challenges such as increased employee turnover, reduced personnel, reduced funding, and increased competition, its leaders should adopt DEA programs in their management systems. Therefore, hospital managers should adopt DEA for their organizations to gain a competitive advantage in an age of fast transformations in the country’s health care delivery system.

Summary

DEA does not need a clear formulation of the fundamental practical correlation nor pre-allotted weights for multi-outputs and multi- inputs in assessing performance concerning a process. The significant benefit of using this approach is its capability to unmistakably factor in the use of numerous inputs to designate numerous outputs. For a hospital manager to analyze the efficacy of a specific DMU, carefully worked-out programming procedures are used to define weights for the comparative value of the numerous outputs and inputs, which make the most of an exact DMU’s efficacy score (Sah, 2009).

Based on this, the weights are considered the original variables in the arithmetic program. A specific DMU may use any arrangement of inputs and outputs to make the most of its efficacy tally subjects given that all other DMU’s efficacy tallies are less than or equivalent to unity. A distinct linear programming design is utilized to evaluate the efficacy tally for each DMU. It is significant to note that DEA simulations yield only relative efficacy tallies in contrast to all other DMUs. Not like regression techniques, which approximate a normal performance function, DEA procedures recognize two subsections of DMUs.

Call of action

Evaluation of health care activities is very significant for running and refining all features of a hospital. As indicated above, several tools have been developed for the effective monitoring of health care activities. The DEA approach is considered one of the most efficient tools. The tool has been used by both business and health care organizations. The tool does not only factor in all the inputs and outputs but also has the benefit of automatically regulating the inputs and outputs’ weights. Through this, it offers an equal playing ground to every process guaranteeing the wider suitability within a hospital.

In this regard, all hospitals should adopt the use of the tool. By doing so, the hospitals will be able to reduce the healthcare expenditure and reduce the deficit. Similarly, managers will be able to tackle increased employee turnover, reduced personnel, reduced funding, and increased competition with the adoption of the tool.

Equally, more research needs to be done on how to increase the efficiency of the tool. The tool can be very effective if its efficiency is enhanced. Similarly, researchers will lead to the development of a more user-friendly tool. A more user-friendly tool would progress the advancement and the adoption of the program. Based on the above illustrations, it is apparent that all the stakeholders should work together towards the realization of having a more effective and advanced DEA in the health care sector.

References

Chan, C., Johansen, D., Mangolini, M., & Peacock, S. (2001). Techniques for Measuring Efficiency in Health Services. Web.

Jacobs, R. (2000). Alternative Methods to Examine Hospital Efficiency: Data Envelopment Analysis and Stochastic Frontier Analysis Rowena Jacobs DISCUSSION. Web.

Sah, P. a. (2009) 1 P Cube – A Data Envelopment Analysis Based Solution for Business Process Intelligence. Web.

Sherman, D., & Zhu, J. (2006). Service productivity management improving service performance using data envelopment analysis. New York: Springer.

Sherman, D., & Zhu, J. (2013). Analyzing Performance in Service Organizations. MIT Sloan Management Review, 54(4), 36-43.