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Chapter 7 Integer Programming

Chapter 7 Integer Programming. POP QUIZ #8 [5 points]. POP QUIZ #8. Integer Optimization models may require: All of the decision variables to be integers Some of the decision variables to be integers Some of the decision variables to be binary (0 or 1) Any of the above. POP QUIZ #8.

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Chapter 7 Integer Programming

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  1. Chapter 7 Integer Programming

  2. POP QUIZ #8 [5 points]

  3. POP QUIZ #8 • Integer Optimization models may require: • All of the decision variables to be integers • Some of the decision variables to be integers • Some of the decision variables to be binary (0 or 1) • Any of the above

  4. POP QUIZ #8 • The graph shows the feasible region in an Integer LP. Which point is the optimal integer solution? • Point A • Point B • Point C • Point D

  5. POP QUIZ #8 • What is the “LP relaxation” of an ILP? • A solution that ignores the integrality requirement • The nearest integer solution • The nearest integer solution that is also feasible • The optimal integer solution that is also feasible

  6. POP QUIZ #8 • How do we best handle ILPs using Solver? • Solver does not handle ILPs • By adding an integrality constraint • By manually rounding the LP solution to the nearest integer • By manually rounding the LP solution to the nearest optimal integer

  7. POP QUIZ #8 • In a Max LP relaxation problem, the Optimal Value: • Always provides an upper bound on the OV of the original ILP • Always provides a lower bound on the OV of the original ILP • Always coincides with the OV of the original ILP • Is an integer approximation of the OV of the original ILP

  8. Answers! √

  9. POP QUIZ #8 • Integer Optimization models may require: • All of the decision variables to be integers • Some of the decision variables to be integers • Some of the decision variables to be binary (0 or 1) • Any of the above √

  10. POP QUIZ #8 • The graph shows the feasible region in an Integer LP. Which point is the optimal integer solution? • Point A • Point B • Point C • Point D √

  11. POP QUIZ #8 • What is the “LP relaxation” of an ILP? • A solution that ignores the integrality requirement • The nearest integer solution • The nearest integer solution that is also feasible • The optimal integer solution that is also feasible √

  12. POP QUIZ #8 • How do we best handle ILPs using Solver? • Solver does not handle ILPs • By adding an integrality constraint • By manually rounding the LP solution to the nearest integer • By manually rounding the LP solution to the nearest optimal integer √

  13. POP QUIZ #8 • In a Max LP relaxation problem, the Optimal Value: • Always provides an upper bound on the OV of the original ILP • Always provides a lower bound on the OV of the original ILP • Always coincides with the OV of the original ILP • Is an integer approximation of the OV of the original ILP √

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