slack {Benchmarking}

Calculate slack in an efficiency analysis

Description

Slacks are calculated after taking the efficiency into consideration.

Usage

slack(X, Y, e, XREF = NULL, YREF = NULL, FRONT.IDX = NULL, LP = FALSE, CONTROL=NULL)

Arguments

X

Inputs of firms to be evaluated, a K x m matrix of observations of K firms with m inputs (firm x input).

Y

Outputs of firms to be evaluated, a K x n matrix of observations of K firms with n outputs (firm x input).

e

A Farrell object as returned from dea et al.

XREF

Inputs of the firms determining the technology, defaults to X

YREF

Outputs of the firms determining the technology, defaults to Y

FRONT.IDX

Index for firms determining the technology

LP

Set TRUE for debugging.

CONTROL

Possible controls to lpSolveAPI, see the documentation for that package. For examples of use see the function dea.

Details

Slacks are calculated in a LP problem where the sum of all slacks are maximised after correction for efficiency. The for calculating slacks for orientation graph is low because of the low precision in the calculated graph efficiency.

Value

The result is returned as the Farrell object used as the argument in the call of the function with the following added components:

slack

A logical vector where the component for a firm is TRUE if the sums of slacks for the corresponding firm is positive. Only calculated in dea when option SLACK=TRUE

sum

A vector with sums of the slacks for each firm. Only calculated in dea when option SLACK=TRUE

sx

A matrix for input slacks for each firm, only calculated if the option SLACK is TRUE or returned from the method slack

sy

A matrix for output slack, see sx

Note

If a numerical problem occurs, status=5, or if no solution can be found, the best solution is often to scale the input X and output Y yourself or use the option CONTROL to change scaling in the program itself, as described in the notes for dea.

Author(s)

Peter Bogetoft and Lars Otto [e-mail]

References

Peter Bogetoft and Lars Otto; Benchmarking with DEA, SFA, and R; Springer 2011. Sect. 5.6 page 127.

WW Cooper, LM Seiford, and K Tone; Data Envelopment Analysis: A Comprehensive Text with Models, Applications, References and DEA-Solver Software, 2nd edn. Springer 2007 .

Examples

x <- matrix(c(100,200,300,500,100,200,600),ncol=1)
y <- matrix(c(75,100,300,400,25,50,400),ncol=1)
dea.plot.frontier(x,y,txt=1:dim(x)[1])

e <- dea(x,y)
eff(e)

# calculate slacks
sl <- slack(x,y,e)
data.frame(e$eff,sl$slack,sl$sx,sl$sy)