goalprog (version 1.0-2)

ignizio.example.3.6: Ignizio (1976) Example Data Sets

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 $x_1 + x_2 + n_1 - p_1 = 50000$ $x_1 + n_2 - p_2 = 20000$ $x_2 + n_3 - p_3 = 5000$ $x_2 + n_4 - p_4 = 15000$ $x_3 + n_5 - p_5 = 10000$ $x_4 + n_6 - p_6 = 30000$ $0.06 x_1 + 0.05 x_2 + 0.08 x_3 + 0.07 x_4 + n_7 - p_7 = 4000$ $\mathbf{x}, \mathbf{n}, \mathbf{p} \ge \mathbf{0}$ 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.

References

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

See Also

ignizio.datasets

Examples

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