Articles related to DEA module

Overcome common challenges in GM (1,1) modelling using MS Excel

Grey theory deals with a system consisting of inadequate or improper information. It includes systems analysis, data processing, modelling, prediction, decision-making, and control. There are different grey models in use in many applications. Grey system theory was introduced by Julong (1989). GM (1,1) modelling is a popular grey forecasting method because of its computational efficiency. There are many challenges in GM (1,1) modelling, but they are solvable using MS Excel. This article is a detailed guide on how to overcome these challenges. Read more »

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




Exports percentage of GDP




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




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.


Malmquist index summaries interpretations from Malmquist DEA

In the previous article, we had discussed and interpreted results and terms from the results of distance summaries in Malmquist data envelopment analysis (DEA). This article, discusses and interprets the rest of the results from Malmquist DEA. Furthermore, the analysis of Malmquist index summaries for both output and input frontiers are interpreted. Read more »

Interpreting cost efficiency or cost DEA of banks using DEAP

In the previous article, execution of cost efficiency using data envelopment analysis program (DEAP). Moreover, differences between Multi-stage and Cost- data envelopment analysis (DEA) was also discussed. However, the article will only interpret the results from cost efficiency analysis from the constant returns to scale (CRS) frontier. Read more »

Executing and interpreting cost efficiency of banks through VRS cost DEA

In the previous article, discussed and interpreted the findings of cost efficiency using constant returns to scale (CRS) Cost Data Envelopment Analysis (DEA). Here, in the current article, variable returns to scale  or VRS cost DEA to check the variation of results from CRS cost DEA and will interpret the results accordingly. Read more »

Executing cost DEA of banks using Data Envelopment Analysis Program (DEAP)

The cost efficiency analysis or cost data envelopment analysis or cost DEA is evaluated when information on prices and costs are available from the source of the data collected for input and output variables (Cooper, Seiford, & Zhu, 2011). Cost efficiency test helps to improve in cost related performances of the organization and shows if the organization should lower or increase the inputs. Read more »

Malmquist productivity Index test of healthcare sector in India and interpretations

Malmquist productivity index evaluates the efficiency change over time as mentioned by Färe, Grosskopf, & Margaritis, (2011). However, Malmquist productivity index literature has been uneven with some authors assuming constant returns to scale and others allowing for variable returns to scale. This article will present the interpretations of productivity index from Malmquist Data Envelopment Analysis (DEA). Read more »

Performing Malmquist DEA in hospitality industry

The Malmquist productivity index or more commonly malmquist DEA (Data Envelopment Analysis) was first incepted by the researcher Malmquist in 1953 as a quantity to be used in the analysis of consumption of inputs (Färe, Grosskopf, & Margaritis, 2011). Read more »

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