All articles by Avishek Majumder

Slacks based measure or SBM analysis in DEA

Slacks based measure (SBM) is a non-radial model to solve the problem in the “additive model” developed by Charnes, Cooper, & Rhodes in 1978. This model can discriminate between efficient and inefficient Decision-Making Units (DMU). However it does not provide an efficiency measure, so a decision maker cannot interpret the performance of the DMU. Therefore “super SBM” model was introduced to determine and rank efficient DMU. The efficiency scores are dimensionless and fall between 0 and 1, thus allowing for the comparison of different DMU in terms of efficiency.

Why SBM model?

SBM model uses “slacks” to show excess input and shortfalls in the output then it directly deals with them by maximizing these slacks. SBM analysis provides an efficiency score which is units-invariant and a monotone function of input slacks and output slacks. To rank efficiency, super SBM was introduced by Tone & Tsutsui (2001b). It is appropriate for evaluating efficiencies when inputs and outputs may change non-proportionally.

Super SBM model can be expanded by the super efficiency to the DEA models. Super efficiency rate refers to the distance between the inputs and outputs of both units. The distance is shown in variable ρ. Assuming that there exist a set of ‘n’  DMU producing the same set of outputs which consume the same set of inputs. Input and output matrix is matrix (X, Y), where (Input) X= (xij) ϵ Rmxn and (Output) Y= (yij) ϵ Rsxn.

Equations of the SBM model

λ is a nonnegative vector in Rn. The vector S ϵ Rm and S+ ϵ Rs, shows an excess input and a short falling output, respectively.  The equation for the SBM model is as follows:

Figure 1: Equation for SBM analysis model

Figure 1: Equation for SBM model

Suppose (ρ*, λ*,s-*, s+*) is the optimal condition for SBM analysis and (x0 , y0) is SBM efficient of DMU. When ρ* = 1, s-*=0 and s+*=0 (or there is no excess input and a short falling output). A super-efficiency model helps in ranking DMU. Below is the formula for super SBM analysis:

Figure 2: Equation for SBM model

Figure 2: Equation for super SBM model

Challenges of super SBM model

One of the major challenges in super SBM model is that it involves solving a complex equation. This becomes more tedious when there are large units of input and outputs. It takes a lot of effort and time to estimate the efficiency of different decision-making units manually. Therefore, it is optimal to use statistical packages like DEA solver, max DEA, and others. They are more popular than manual calculations and other measures of evaluating efficiency.

Interpretation of super SBM analysis results

This module shows the following process in determining efficiency for 10 DMU and ranks them on the basis efficiency by using Super SBM model. It uses MaxDEA software to assess efficiency. MaxDEA 7 basic is available free of cost, however, the ‘pro’ version is a paid software.

Input and output dataset for 10 DMU

OUTPUT

INPUT

DMU

Exports percentage of GDP

Export

Import

tariff

Exchange rates

1 68.12 3,069,559.00 2.27 30.73
2 19.99 3,488,123.37 1.70 1.04
3 29.67 3,696,265.19 5.02 0.64
4 100.63 4,138,413.19 1.35 3.67
5 45.40 4,736,995.93 3.79 0.75
6 75.63 4,984,467.88 1.72 3.15
7 53.88 6,682,944.91 3.96 1,094.85
8 24.50 13,177,694.49 3.04 6.20
9 15.92 13,544,244.95 3.54 97.60
10 13.64 23,869,948.68 2.65 1.00

By using maxDEA software and applying super SBM model, efficiency score for all DMU can be determined  and ranked. DEA-SBM model is non-radial and non-oriented and can deal with inputs and outputs individually. The purpose is to minimize the input and output slacks, resulting in this fractional program.

Efficiency scores and ranking from super SBM model

DMU

Score

Rank

1 0.248082 8
2 0.541691 6
3 0.651521 5
4 1 1
5 1 1
6 0.796988 4
7 0.151898 10
8 0.359254 7
9 0.227246 9
10 1 1

Determining the efficiency score of DMU

The results show that DMU4, DMU5, and DMU6 are the most efficient decision-making units achieving highest efficiency score of 1. The efficiency score of all other DMUs is less than 1 in DEA-SBM models. It reflects these DMUs have input excesses and output shortfalls. This analysis can be used in yearly data. The mean efficiency score for specific DMU over a period of time and year time efficiency can be evaluated too.

References

Role of circulating microRNA in predicting myocardial infarction

Myocardial infarction (MI) is a condition when the heart does not receive enough blood flow due to the narrowing of the blood vessels. It is also known as heart attack and caused by the plaque deposition on the arterial walls. It is a leading cause of deaths worldwide. According to several reports, micro RNA plays a critical role in myocardial infarction (Fichtlscherer et al., 2010). MicroRNA helps in controlling many biological processes and plays a role in health and heart diseases. Depletion of Dicer (a microRNA processing enzyme) leads to various defects in angiogenesis, vessel formation and cardiac development (Van Rooij and Olson, 2007). MicroRNA is detected in blood circulation and therefore can be used as potent biomarkers for cardiovascular disease (Mitchell et al., 2008). These microRNAs are also called circulating microRNA. Read more »

Importance of lipoprotein in detecting cardiovascular diseases

Cardiovascular diseases are caused by a condition known as atherosclerosis. In this, a substance called plaque builds up in the walls of arteries, making them narrow and restricting the blood flow which leads to heart attack or stroke. The plaque formation occurs due to the buildup of cholesterol in the blood vessels. This happens when the low density lipoprotein (LDL) carrying the cholesterol to the cells enters the inner lining of blood vessels and are trapped in the artery walls. Read more »

Technologies and resources used in biomarker discovery and development

Biomarker development has served as an indicator of disease progression and response to therapeutic intervention. The conventional approach involved the study of molecules (considered as biomarker) in regulatory pathways but with the advent of technologies and resources, the development and biomarker discovery gotten easier (Tong & Li, 2016). Read more »

Application of Biomarkers in personalized medicine

The concept of personalized medicine was first promoted with pharmacogenomics data on oncology trials which demonstrated subject’s unique genetic makeup (genome) influence on their response to medications (The Office of the Commissioner FDA, 2015). Treatment biomarkers comprise of genes or a DNA sequence or an RNA strand which expresses uniquely in every individual. Read more »

Classification and application of different biomarkers

Biomarkers are any substance of biological origin, which is used as an indicator for certain medical conditions. Atkinson et al., (2001) defined the biomarker as:

“A characteristic that is objectively measured and evaluated as an indicator of normal biological processes, pathogenic processes, or pharmacologic responses to a therapeutic intervention”.

The assessment stated that a factual biomarker definition includes almost any measurement imitating an interaction between a potential hazard (biological, chemical or physical) and a biological system. The response of biomarkers measure functional and cellular level physiological, biochemical or a molecular interaction. Read more »

Hamlet II is a tool for quantitative textual analysis

Quantitative analysis of textual data has been long used in the field of social sciences research. This includes data collected from open ended surveys and interview questions. Analysis of text-based data helps in assessment of trends in social sciences. Read more »

Emerging role of Bio marker in healthcare and medical sector

A bio marker or biological marker, are defined as an indicator of a biological state of a living body. It is a characteristic that is measured and evaluated as an indicator of normal biological processes. In addition, they also help in pathogenic processes or pharmacologic responses to a therapeutic intervention. Read more »

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