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LP by the revised simplex method Solves
an LP problem in standard form by the revised simplex method. |
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| Optimization |
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Maximization or minimization. • |
| CT |
Coefficients in the objective function,
z = CT x . (Here,
use 0 for artificial variables.)
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In this plate:
Use no tab characters; decimal mark is point; b
≥ 0 • |
A | b
(m×n,
m×1) |
Constraints, A x = b
(m equality constraints): row(1), b(1)
[: row(i), b(i), i = 2..m]
(':' = 'new line'.)
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| Artificial variables |
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Which artificial variables (0 if none). • |
| Big M |
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Big M (∞), ignored if unnecessary. • |
| Initial basis |
| Variables (m)
in initial basis. • |
| First graph basis |
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First basis for graph (avoid artificials). • |
| Show values ? |
Test: (0, 1, 2) |
Shows the coordinates of the graph; & test level. • |
Solves a Linear Programming problem
supplied by the user in standard form, by Dantzig's
simplex method in the revised simplex (i.e., matrix) form.
In the standard form: all the constraints must be given
as equations, typically after insertion of slack
(or surplus) or artificial variables;
and with non-negative right-hand side constants,
i.e., b ≥ 0.
If any artificial variable is present, its coefficient (given as 0)
will be made ±M, according to the direction
of optimization ('+' for min, '−' for max).
Base problem is: Case 0 — Bronson 4.2; z*min = 71 2/3, X = (7/12, 5/12) =
(0.58(3), 0.41(6))
 Other data.pdf...
Bland's anti-cycling rule is included (under observation).
A plot of the objective function, z, is presented
as a function of the successive bases.
The initial basis is № 0. |
| References: |
Plate: LP_revised_Bland |
• Bland,
Robert G., 1977, "New finite pivoting rules for the simplex method".pdf,
Mathematics of Operations Research, 2(2), pp 103–107.
• Wikipedia: Revised simplex method.
Decimal mark
• Google: "revised simplex method"
• 1869-03-10: Kagan, Benjamin Fedorovich
(1953-05-08). |
