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simplex_lecture_4-1

# simplex_lecture_4-1 - OTHER FORMS AND CASES OF LPs...

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OTHER FORMS AND CASES OF LPs Objective function may be a minimum. The linear Program may have multiple solutions. The linear program may be unbounded. The constraints may be equality or greater than inequality. Variables may be less that equal to 0 or unrestricted in sign. The linear program may have no feasible solution. Saigal (U of M) IOE 310 1 / 13

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PHASE 1- PHASE 2 METHOD I Step 1 Modify constraints so that the RHS is non-negative. Step 2 Convert to standard form by adding slack or excess variables. Step 3 Add an artificial variable to each constraint that has either an equality or an inequality. Step 4 Replace the original objective function with minimize w 0 = sum of all the artificial variables, and solve this LP. Saigal (U of M) IOE 310 2 / 13
SOLVING THE PHASE 1 LP I Solve by the simplex algorithm this LP. At the end, either this LP will have an optimal solution w 0 = 0 or w 0 > 0. If the optimal solution is w 0 > 0, the original LP has no feasible solution.

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simplex_lecture_4-1 - OTHER FORMS AND CASES OF LPs...

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