excess {Benchmarking} R Documentation

## 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)
```

### Arguments

 `object` A Farrell object as returned from functions like dea, dea.direct, linksdea, and mea. `X` Input matrix, only neccesary for ordinary input Farrell efficiency `Y` Ouput matrix , only neccesary for ordinary output Farrell efficiency

### 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 slackvalues. 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 then 1 and then the excess values are negative.

### Value

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

### Author(s)

Peter Bogeroft and Lars Otto larsot23@gmail.com

### 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)
```

[Package Benchmarking version 0.29 Index]