The Simplex Procedure

1. The Simplex Procedure Daniel B. Taylor AAEC 5024 Department of Agricultural and Applied Economics Virginia Tech

2. The Basic Model

3. Completing the Initialization Step • Add slack (Si) variables so that the constraints may be specified as equality constraints • Reformulate the objective function by moving all the terms to the left hand side of the equality sign – in part to make the interpretation of the solution more straight forward

4. The Model to Enter in the Simplex Tableau

5. The Simplex Tableau • Construct the Simplex Tableau

6. Coefficient of

7. Begin to Fill out the Tableau • The purpose of the first two columns is to give reference numbers to refer to when discussing the tableau

8. Coefficient of

9. Begin to Fill out the Tableau • The purpose of the first two columns is to give reference numbers to refer to when discussing the tableau • The iteration column records the number of the iteration you are performing • Conventionally the first tableau which really is the last phase of the initialization step is labeled zero.

10. Coefficient of

11. Continue to Fill out the Tableau • RN just stands for the row number. • We label the objective function row “0”

12. Coefficient of

13. Continue to Fill out the Tableau • RN just stands for the row number. • We label the objective function row 0 • The remaining rows contain the constraints, and in this example are labeled 1-3

14. Coefficient of

15. Coefficient of

16. Coefficient of

17. “Coefficients of” • Area of the Table

18. Coefficient of

19. “Coefficients of” • Area of the Table • Is where the decision making variables (Xj) and the slack variables (Si) are listed

20. Coefficient of

21. Coefficient of

22. Coefficient of

23. Coefficient of

24. Coefficient of

25. Basic Variables • The column labeled BV just keeps track of the basic variables following each iteration

26. Coefficient of

27. Basic Variables • The column labeled BV just keeps track of the basic variables following each iteration • Since there is not a basic variable in the objective function, we simply label the BV row “OBJ”

28. Coefficient of

29. Basic Variables • The column labeled BV just keeps track of the basic variables following each iteration • Since there is not a basic variable in the objective function, we simply label the BV row “OBJ” • In the initial tableau (0) the slack variables associated with each constraint are our basic variables

30. Coefficient of

31. Coefficient of

32. Coefficient of

33. Right Hand Side • The column labeled RHS contains the numbers on the right hand side of the equations in the linear programming problem

34. Coefficient of

35. Completing the Initialization Step • Coefficients are taken from each equation and entered into the appropriate row of the tableau • So for the first row, the objective function

36. The Model to Enter in the Simplex Tableau

37. Coefficient of

38. Coefficient of

39. Coefficient of

40. Coefficient of

41. Coefficient of

42. Coefficient of

43. Completing the Initialization Step • For the second row which is the first constraint

44. The Model to Enter in the Simplex Tableau

45. Coefficient of

46. Completing the Initialization Step • For the second constraint

47. The Model to Enter in the Simplex Tableau

48. Coefficient of

49. Completing the Initialization Step • For the third constraint

50. The Model to Enter in the Simplex Tableau