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Mathematical Formulation Violation Corrections Guide

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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.

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Mathematical Formulation Violation Corrections Guide

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Presentation Transcript

  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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