lecture6

# lecture6 - Yummy The Simplex Method HodgePodge IE426...

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Unformatted text preview: Yummy The Simplex Method HodgePodge IE426: Optimization Models and Applications: Lecture 6 Jeff Linderoth Department of Industrial and Systems Engineering Lehigh University September 14, 2006 Jeff Linderoth IE426:Lecture 6 Yummy The Simplex Method HodgePodge Don’t Hate Me Please turn in the homework! Do you hate me? You can’t hate a puppy! Next homework coming soon! Feedback/Survey TV Viewers — Please email me how I will receive your homework Jeff Linderoth IE426:Lecture 6 Yummy The Simplex Method HodgePodge Background Model Components Making it Linear The Simplex Method 0. Start from an extreme point. 1. Find an improving direction d . If none exists, STOP. The extreme point is an optimal solution. 2. Move along d until you hit a new extreme point. Go to 1. Jeff Linderoth IE426:Lecture 6 Yummy The Simplex Method HodgePodge Background Model Components Making it Linear Simplex Method – What can go wrong? Simplex Method: Step 0 Start from an extreme point What if there are no extreme points? This (usually) means that the feasible region is empty. The instance is infeasible. P = { x ∈ R 2 : x 1 + x 2 ≤ 1 , x 1 + x 2 ≥ 2 } How will we know if an instance is infeasible? “Big-M”, “Two-Phase”? The solver will tell us! Jeff Linderoth IE426:Lecture 6 Yummy The Simplex Method HodgePodge Background Model Components Making it Linear Simplex Method – What else can go wrong? Simplex Method: Step 2 Move along d until you hit a new extreme point. What if we don’t hit an extreme point? max x 1 + x 2 s.t. x 1 + 2 x 2 ≥ 1 x 1 , x 2 ≥ Usually this means you forgot some constraints. Maybe your variable bounds? Just because the region is unbounded doesn’t mean that the LP is unbounded. Jeff Linderoth IE426:Lecture 6 Yummy The Simplex Method HodgePodge Background Model Components Making it Linear Simplex Method – What else can go wrong? Simplex Method: Step 2 Move along d until you hit a new extreme point. What if moving in our “improving direction” doesn’t take us anywhere! max x 1 + x 2 s.t. x 1 + 2 x 2 ≤ 1 x 1 ≤ 1 x 1 + 3 x 2 ≤ 1 2 x 1- 4 x 2 ≤ 2 x 1 , x 2 ≥ Jeff Linderoth IE426:Lecture 6 Yummy The Simplex Method HodgePodge Background Model Components Making it Linear I’m a Degenerate! The previous case is known as the LP being degenerate Degeneracy is what happens when more than n inequalities intersect at a point. This doesn’t seem likely to happen, but BELIEVE ME it does happen in nearly all practical problems....
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lecture6 - Yummy The Simplex Method HodgePodge IE426...

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