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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 minratio 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 NonDegeneracy 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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 Spring '08
 Saigal

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