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Post Office Employee Scheduling Optimization with LP

Learn how to optimize post office employee scheduling using Linear Programming, ensuring daily requirements are met and minimizing full-time hires. Explore the Simplex Method to find optimal solutions at vertices. Understand the Fundamental Theorem, Vertex Characterization, and Optimality Conditions. Dive into LP complexities and methodologies.

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Post Office Employee Scheduling Optimization with LP

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  1. Chapter 7Linear Programming Ding-Zhu Du I. Simplex Method

  2. 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.

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

  4. Slack Form

  5. What’s a vertex?

  6. Fundamental Theorem

  7. Proof.

  8. Proof (cont’s).

  9. Characterization of Vertex

  10. Proof

  11. Basic Feasible Solution

  12. Optimality Condition

  13. Sufficiency

  14. Nondegeneracy Assumption Remark

  15. Necessary

  16. (pivoting)

  17. Simplex Method

  18. Simplex Table

  19. Puzzle 1

  20. Artificial Feasible Basis

  21. Puzzle 2

  22. lexicographical ordering

  23. Method

  24. Method(cont’)

  25. Method (cont’)

  26. Theorem

  27. Puzzle 3

  28. Complexity of LP

  29. Thanks, End

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