Operations research
POV
POV: You Are an Artificial Variable in Big M
POV: you are an artificial variable in a Big M simplex tableau
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Lesson notes
Key points
- You get added to a greater-than-or-equal or equality constraint, just so the simplex method has a starting basic feasible solution.
- In a minimisation, you carry a huge penalty cost M in the objective, so every iteration tries to push you out.
- Each pivot, a real variable with a better reduced cost enters, and soon you are the one forced to leave the basis.
- But if you are still positive in the final optimal tableau, the original problem has no feasible solution at all.
Takeaway: Artificial variables must leave; if one stays, the LP is infeasible.
Quick check: What does a positive artificial variable in the optimal tableau mean?
- Multiple optima exist
- The LP is infeasible
- The LP is unbounded
The constraints could not be met without the fake variable, so no feasible point exists.
Initial tableauBig M penaltyLeaving the basisInfeasibility signal
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