# ignizio.example.3.5: Ignizio (1976) Example Data Sets In goalprog: Weighted and lexicographical goal programming and optimization

## Description

The data set that corresponds to Example 3-5 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 ] , {\mathbf{n}'} = [ n_1, n_2, n_3, n_4 ] and {\mathbf{p}'} = [ p_1, p_2, p_3, p_4 ] that minimize \mathbf{a} = [ (2 p_1), (n_2), (n_3) ]
The objectives are as follows
8 x_1 + 12 x_2 + n_1 - p_1 = 10000
x_1 + 2 x_2 + n_2 - p_2 = 40
x_1 + n_3 - p_3 = 30
x_2 + n_4 - p_4 = 15
\mathbf{x}, \mathbf{n}, \mathbf{p} ≥ \mathbf{0}
The solution is {\mathbf{x}'} = [ 30, 15 ] and \mathbf{a} = [ 0, 580, 20, 0]

## 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
 1 2  data( ignizio.example.3.5 ) soln <- llgp( coefficients, targets, achievements )