# lect18 - ISE 536Fall03 Linear Programming and Extensions...

This preview shows pages 1–2. Sign up to view the full content.

ISE 536–Fall03: Linear Programming and Extensions November 5, 2003 Lecture 18: Large scale LP: Column Generation Lecturer: Fernando Ord´o˜nez 1 Example Consider the problem of operating a supermarket chain. There are a large number of variables that apply only to each store: such as shelf space, shifts scheduling, inventory, cleaning. And there are a number of variables that connect all the stores in the chain: procurement of goods, budget, employee medical beneﬁt negotiation . In the case of two stores this operation can be represented by a linear programming problem such as: ( P ) z = max c t 1 x 1 + c t 2 x 2 s . t . B 1 x 1 + B 2 x 2 = b A 1 x 1 = b 1 A 2 x 2 = b 2 x 1 , x 2 0 The column generation method that we discuss performs better if m << m 1 ,m 2 . 2 Dantzig-Wolfe Decomposition Deﬁne S i := { x | A i x = b i , x 0 } , for i = 1 , 2. The problem above is equivalent to ( P ) z = max c t 1 x 1 + c t 2 x 2 s . t . B 1 x 1 + B 2 x 2 = b x 1 S 1 x 2 S 2 Since S i

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 4

lect18 - ISE 536Fall03 Linear Programming and Extensions...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online