# Lecture17 - IE 505 MATHEMATICAL PROGRAMMING Bahar Yetis...

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IE 505 MATHEMATICAL PROGRAMMING Bahar Yetis Kara Lecture # 17 Date: 23th December 2008 1

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2 RECALL that
Solution Methodologies Branch and Bound Cutting Plane Algorithms 3

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Cutting Plane Algorithms Main idea is to add valid inequalities to the LP relaxation iteratively. At each iteration a valid inequality (VI) that cuts off the current fractional solution is added to the LP. If no VI is found, then the formulation improved can be input to a branch and bound algorithm. 4
Example 5 } 2 3 2 4 3 : } 1 , 0 { { 5 4 3 2 1 5 x x x x x x X Rest on Board

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Example 6 } 14 , 10 ; , : ) , {( x y x Z y R x y x X Rest on Board
In general for 7 } , ; , : ) , {( b x Cy x Z y R x y x X y C b b x Is a valid inequality 1 C b C b

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For the example: 8 ) 2 ( 4 14 10 14 4 y y b x valid inequality is: 4 1 10 14 10 14 1 C b C b } 14 , 10 ; , : ) , {( x y x Z y R x y x X y x 4 6
Problem Specific

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Lecture17 - IE 505 MATHEMATICAL PROGRAMMING Bahar Yetis...

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