artificial variable

Example: Product Processing

We continue in the example Example with slack, surplus and artificial variables to get initial solution of the model. The initial simplex tableau in this phase will be as Table 1:

Table 1: initial tableau without artificial variable

We have 6 constrains and so should have 6 solution variables. We have only 5 solution variables and the vector with 1 on 6-th line (other coefficients 0) is missing. That’s why we have to add artificial variable with 1 on the 6-th line i.e. to the 6-th constraining. Correct initial simplex tableau in Table 2:

The artificial variables have no real interpretation. If the optimal solution contained artificial variables it would have no interpretation either. To ensure that the artificial variables will be eliminated from the optimal solution, they have prohibitive values in objective function for maximisation big negative value and big positive value for minimisation.