Benchmarking (version 0.33)

excess: Excess input compared over frontier input

Description

Excess input compared over frontier input and/or less output than frontier/transformation/optimal output.

Usage

excess(object, X = NULL, Y = NULL)

Value

Return a matrix with exces input and/or less output.

Arguments

object

A Farrell object as returned from functions like dea, dea.direct, sdea, and mea.

X

Input matrix, only necessary for ordinary input Farrell efficiency

Y

Ouput matrix , only necessary for ordinary output Farrell efficiency

Author

Peter Bogeroft and Lars Otto

Details

For Farrell input efficiency E the exess input is \((1-E) X\) and for Farrell ouput efficiency F the missing output is \((F-1) Y\).

Notice that the excess calculated does not include any slack values. In case slacks are present and calculated it might be more appropriate to add slack, i.e. to use excess(object, X, Y) + slack(X, Y, object).

For directional efficiency e in the direction D the excess input is \(e D\).

If a firm is outside the technology set, as could be the case when calculating super-efficiencies, the Farrell input efficiency is larger than 1, and then the excess values are negative.

References

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

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)

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

e <- dea(x,y, ORIENTATION="graph")
excess(e, x, y)
x - eff(e) * x
1/eff(e) * y -y

me <- mea(x,y)
excess(me)