In the Simplex method, a tie in the Minimum Ratio Test causes a basic variable to become zero in the next table. Does degeneracy always mean the problem has a flaw, or can a real-world model be degenerate and still reach a valid optimal solution?
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No, degeneracy does not always mean the problem has a flaw. In the Simplex method, a degenerate solution can still be a valid optimal solution; it simply means at least one basic variable is zero. In real-world OR models, this can naturally happen when several constraints are active at the same solution.
No. Degeneracy does not mean the problem has a flaw. It can occur naturally when several constraints are active at the same point. The model can still have a valid and optimal solution, although it may require careful handling during the Simplex process.
No. Degeneracy does not mean the problem has a flaw. It occurs when a basic feasible solution has one or more basic variables equal to zero, often because of a tie in the Minimum Ratio Test. A degenerate solution can still be feasible and optimal and can represent a valid real-world situation where several constraints become active at the same point. However, degeneracy can sometimes cause issues such as repeated iterations or cycling in the Simplex method, so it needs to be handled carefully.
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