Simplex Algorithm: examples and several types of solution

Simplex Algorithm: un example:

See the example 



Simplex Algorithm: several types of solution:

Summary of solution types

• Proper optimal and unique solution (global strict):

An optimum solution has been found, and for all non-basic variable is true that: 𝑧𝑗 𝑐𝑗≠ (non-null values).

• Proper, optimal, but multiple bounded solution:

An optimum solution has been found. However, there is at least one non-basic variable with 𝑧𝑗 𝑐𝑗= (null value).

• Proper, optimal, but multiple unbounded solution:

The optimality condition has not been found, but it is observed that, for the entering variable, the column Ratio cannot be calculated because all values in the entering column (pivot) are non-positive.

• Unfeasible solution:

A global optimum solution has been found. However, in the base there is still at least an artificial variable with non-zero value.

• Degenerate solution:

A solution has been found for which at least one of the basic variables is null. In this case, to avoid the risk of infinite cycle, it is recommended to follow the Bland's rule.

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