1 / 51

Lectures 18-19 Linear Programming

This lecture discusses the formulation of a linear programming problem to minimize the number of full-time employees that a post office needs to hire, considering various constraints such as union rules and daily requirements. The lecture also covers topics like vertex, fundamental theorem, simplex method, and optimality conditions.

tinkham
Télécharger la présentation

Lectures 18-19 Linear Programming

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Lectures 18-19Linear Programming

  2. PreparationLinear Algebra

  3. Linearly Independent

  4. Maximal Independent Subset

  5. Rank of Matrix

  6. Linear Programming

  7. LP examples • A post office requires different numbers of full-time employees on different days of the week. The number of full-time employees required on each day is given in the table. Union rules state that each full-time employee must work five consecutive days and then receive two days off. The post office wants to meet its daily requirements using only full-time employees. Formulate an LP that the post office can use to minimize the number of full-time employees that must be hired.

  8. Optimal occurs at a vertex!!! Feasible domain

  9. Slack Form

  10. What’s a vertex?

  11. Fundamental Theorem

  12. Proof.

  13. Proof (cont’s).

  14. Characterization of Vertex

  15. Proof

  16. Basic Feasible Solution

  17. Optimality Condition

  18. Degeneracy Condition

  19. Sufficiency

  20. Necessary

  21. (pivoting)

  22. Simplex Method

  23. Simplex Table

  24. Puzzle 1

  25. Puzzle 2

  26. lexicographical ordering

  27. Method

  28. Method(cont’)

  29. Method (cont’)

  30. Theorem

More Related