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Optimal Employee Scheduling LP Model for Post Office Efficiency

Formulate a linear programming model for a post office to minimize full-time employee hiring while meeting daily needs, abiding by union rules. Understand the simplex method, vertices, and optimality concepts. Simplify scheduling complexities efficiently.

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Optimal Employee Scheduling LP Model for Post Office Efficiency

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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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