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simplex_method_lecture_2-1

# simplex_method_lecture_2-1 - SUMMARY OF SIMPLEX ALGORITHM...

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Unformatted text preview: SUMMARY OF SIMPLEX ALGORITHM FOR MAX PROBLEM I Step 1 Convert LP into standard form, so the tableau is canonical. Step 2 Obtain a bfs. Simple if all constraints are ≤ and RHS is ≥ 0. Step 3 If all nonbasic variables have ≥ 0 coefficients in ROW 0, optimal solution found. Otherwise choose the variable with the most negative coefficient as entering variable. [ min c j bar rule] Step 4 Perform min-ratio test to determine the leaving variable and the row in which it is basic. Step 5 Use ero’s to remove the leaving variable from the basis to obtain the new canonical form. Saigal (U of M) IOE 310 1 / 19 FLOW CHART - SIMPLEX ALGORITHM start with a bfs is it optimum ? stop yes no is there a leaving variable? stop no yes find new bfs unbounded solution optimum solution Saigal (U of M) IOE 310 2 / 19 TIES IN SIMPLEX ALGORITHM Ties can occur at two steps of the simplex algorithm: 1 While choosing entering variable. Has no effect on the ’primal’ simplex method, and ties can be broken arbitrarily. 2 While solving the min ratio test - leads to primal degeneracy. Effects the simplex method, and the method can cycle. (An example produced by Hoffman and one produced by Beale in early 50s). The Non-Degeneracy Assumption: The LP has no no basic feasible solutions that is degenerate, i.e., has strictly less than m positive variables....
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simplex_method_lecture_2-1 - SUMMARY OF SIMPLEX ALGORITHM...

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