Chap 3 The simplex method q Linear Programming

Chap 3. The simplex method q Linear Programming 2012 1

3. 1 Optimality conditions q Linear Programming 2012 2

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E F G q Linear Programming 2012 7

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3. 2 Development of the simplex method q Linear Programming 2012 11

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Remarks q Linear Programming 2012 16

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Simplex method for degenerate problems q Linear Programming 2012 19

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q Cycling : a sequence of basis changes that leads back to the initial basis. ( only basis changes, no solution change) q Cycling may occur if there exists degeneracy. Finite termination of the simplex method is not guaranteed. Need special rules for entering and/or leaving variable selection to avoid cycling (later). q Although cycling hardly occurs in practice, prolonged degenerate iterations might happen frequently, especially in well-structured problems. Hence how to get out of degenerate iterations as early as possible is of practical concern. Linear Programming 2012 21

Pivot Selection q Linear Programming 2012 22

Review of calculus q Linear Programming 2012 23

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