# ignizio.example.3.6: Ignizio (1976) Example Data Sets In goalprog: Weighted and lexicographical goal programming and optimization

## Description

The data set that corresponds to Example 3-6 found in Ignizio (1976). These are examples of goal programming problems solved using the methods described by author.

Find {\mathbf{x}'} = [ x_1, x_2, x_3, x_4 ] , {\mathbf{n}'} = [ n_1, n_2, n_3, n_4, n_5, n_6, n_7 ] and {\mathbf{p}'} = [ p_1, p_2, p_3, p_4, p_5, p_6, p_7 ] that minimize \mathbf{a} = [ (2 p_1), (n_2), (n_3) ]
The objectives are as follows
x_1 + x_2 + n_1 - p_1 = 50000
x_1 + n_2 - p_2 = 20000
x_2 + n_3 - p_3 = 5000
x_2 + n_4 - p_4 = 15000
x_3 + n_5 - p_5 = 10000
x_4 + n_6 - p_6 = 30000
0.06 x_1 + 0.05 x_2 + 0.08 x_3 + 0.07 x_4 + n_7 - p_7 = 4000
\mathbf{x}, \mathbf{n}, \mathbf{p} ≥ \mathbf{0}
The solution is {\mathbf{x}'} = [ 20000, 5000, 0, 25000] and \mathbf{a} = [0, 0, 5000, 10800]

## Format

The data set is an R file that creates the coefficients matrix, the vector of target values and the data frame of achievement goals.

## Author(s)

Frederick Novomestky fnovomes@poly.edu

## References

Ignizio, J. P. (1976). Goal Programming and Extensions, Lexington Books.

ignizio.datasets

## Examples

 1 2  data( ignizio.example.3.6 ) soln <- llgp( coefficients, targets, achievements ) 

### Example output

Loading required package: lpSolve


goalprog documentation built on May 30, 2017, 5:07 a.m.