dea.add {Benchmarking}R Documentation

Additive DEA model


Calculates additive efficiency as sum of input and output slacks within different DEA models


dea.add(X, Y, RTS="vrs", XREF=NULL, YREF=NULL, 



Inputs of firms to be evaluated, a K x m matrix of observations of K firms with m inputs (firm x input). In case TRANSPOSE=TRUE the input matrix is transposed to input x firm.


Outputs of firms to be evaluated, a K x n matrix of observations of K firms with n outputs (firm x input). In case TRANSPOSE=TRUE the output matrix is transposed to output x firm.


Text string or a number defining the underlying DEA technology / returns to scale assumption.

0 fdh Free disposability hull, no convexity assumption
1 vrs Variable returns to scale, convexity and free disposability
2 drs Decreasing returns to scale, convexity, down-scaling and free disposability
3 crs Constant returns to scale, convexity and free disposability
4 irs Increasing returns to scale, (up-scaling, but not down-scaling), convexity and free disposability
5 add Additivity (scaling up and down, but only with integers), and free disposability

Inputs of the firms determining the technology, defaults to X


Outputs of the firms determining the technology, defaults to Y


Index for firms determining the technology


Possible parameters. At the moment only used for RTS="fdh+" to set low and high values for restrictions on lambda; see the section details and examples for its use. Future versions might also use param for other purposes.


Input and output matrices are treated as firms times goods matrices for the default value TRANSPOSE=FALSE corresponding to the standard in R for statistical models. When TRUE data matrices are transposed to good times firms matrices as is normally used in LP formulation of the problem.


Only for debugging. If LP=TRUE then input and output for the LP program are written to standard output for each unit.


The sum of the slacks is maximized in a LP formulation of the DEA technology. The sum of the slacks can be seen as distance to the frontier when you only move parallel to the axes of inputs and outputs, i.e. not a usual Euclidean distance, but what is also known as an L1 norm.

Since it is the sum of slacks that is calculated, there is no exogenous ORIENTATION in the problem. Rather, there is generally both an input and an output direction in the slacks. The model considers the input excess and output shortfall simultaneously and finds a point on the frontier that is most distant to the point being evaluated.



Sum of all slacks for each firm, sum=sum(sx)+sum(sy).


A non-NULL vector of logical variables, TRUE if there is slack for the corresponding firm, and FALSE if the there is no slack, i.e. the sum of slacks is zero.


A matrix of input slacks for each firm


A matrix of output slack for each firm


The lambdas, i.e. the weights of the peers for each firm


This is neither a Farrell nor a Shephard like efficiency.

The value of the slacks depends on the scaling of the different inputs and outputs. Therefore the values are not independent of how the input and output are measured.


Peter Bogetoft and Lars Otto


Corresponds to Eqs. 4.34-4.38 in Cooper et al. (2007)


Bogetoft and Otto; Benchmarking with DEA, SFA, and R; Springer 2011

Cooper, Seiford, and Tone; Data Envelopment Analysis: A Comprehensive Text with Models, Applications, References and DEA-Solver Software; Second edition, Springer 2007


x <- matrix(c(2,3,2,4,6,5,6,8),ncol=1)
y <- matrix(c(1,3,2,3,5,2,3,5),ncol=1),y,txt=1:dim(x)[1])

sb <- dea.add(x,y,RTS="vrs")

[Package Benchmarking version 0.29 Index]