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Mathematical Formulation Violation Corrections Guide

Learn how to correct violations of standard form mathematical formulations with equalities, inequalities, and negative RHS. Restore canonical form and objective functions using legal row operations.

walter-hebert
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Mathematical Formulation Violation Corrections Guide

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  1. An Over-All Example

  2. There are a number of violations of the Standard Form here! • Opt = min • An equality constraint • A >= constraint • A negative RHS

  3. Complete Reformulation

  4. Important Remark • We (all of us!) shall adopt the convention that the auxiliary variables (slack, surplus, artificial) are “named” in such a way that the initial basis appears in the last m columns of the “LHS”. • Observe that the initial basis consists of: Slack variables Artificial variables

  5. Example

  6. Phase 1

  7. We have to restore the canonical form (by legal row operations)

  8. 0 0 corrections!!!

  9. End of Phase 1: All the artificial variables are out of the basis.

  10. Phase 2 • We now have to restore the original objective function: z = 3x1 +5x2 -3 -5 0 0

  11. -3 -5 0 0 • This is not in canonical form, so we use legal row operations to restore the canonical form.

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