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Dr. Maddah
ENMG 500 Engineering Management I
10/21/07
Computational Procedure of the Simplex Method
The optimal solution of a general LP problem is obtained in the
following steps:
Step 1.
Express the problem in tableau form.
Step 2.
Select a starting basic feasible (BF) solution. This step
involves two cases:
a)
If all the constraints in the original problem are “≤” and
RHS > 0, the stack variables give the starting BF solution.
b)
Otherwise, a technique called the artificial variables
technique is used to give a starting BF solution.
Step 3.
Generate new BF solutions using both the optimality and
feasibility conditions until the optimal solution is reached.
Optimality conditions
For max problems, the entering variable is selected as the
nonbasic variable having the most negative coefficient in the
objective function row (Zrow).
For min problems, select the
most positive.
Break ties at random.
If all Zrow coefficients are nonnegative (for max problems) or
nonpositive (for min problems), the optimal solution has been
reached.
Note the optimal solution. Stop.
Feasibility conditions
The leaving variable for max and min problems is the basic
variable with the smallest ratio of the RHS to the
positive
constraint coefficient of the entering variable (denominator).
If denominator ≤ 0, ignore the corresponding variable.
Break ties at random.
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Artifi
cial variables technique (the “Big” M method)
For problems with
“ ≥” and “=”
constraints, the slack variables
cannot provide a starting feasible solution.
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 Fall '09
 DrBacelMaddah
 Optimization, optimal solution, RHS

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