Operations research
Myth vs fact
Does Every Simplex Pivot Improve the Answer?
Your simplex tableau pivoted, but the profit did not move. Broken?
Quick check · tap an answer to continue
Lesson notes
Key points
- When a basic variable equals zero, the solution is called degenerate, and the minimum ratio test can give a step of zero.
- So the pivot swaps which variables are basic, yet you stay at the same corner with the same objective value.
Definitions
- Degenerate solution
- A basic feasible solution where at least one basic variable equals zero.
Myth: Every simplex pivot strictly improves the objective value
Fact: Degenerate pivots can leave the objective unchanged at the same corner
Takeaway: A zero-step pivot means degeneracy, not a mistake.
Quick check: Myth or fact: degenerate pivots can make simplex cycle forever without a safeguard.
- Myth
- Fact
- Depends
Cycling is possible in theory; rules like Bland's rule prevent it.
DegeneracySame corner
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