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07 - Industrial Engineering 634 Integer Programming Fall...

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Industrial Engineering 634 Fall 2011 Integer Programming Lecturer: Nelson Uhan Scribe: Jikai Zou September 7, 2011 Lecture 7. Guidelines for Strong Formulations With linear programming, a “good” formulation is typically one that has a small number of variables and constraints. In addition, given the availability of several efficient algorithms for linear optimization, the choice of formulation is important, but not critical. However, the situation in in- teger programming is quite different. The choice of formulation critically affects whether a problem can be solved efficiently or not. Then, what makes a good integer programming formulation? Definition Given a mixed integer program [MIP] min cx + dy s.t. Ax + By = d, x,y 0 , x Z n , the linear relaxation ( sometimes called LP relaxation ) of [MIP] is defined as min cx + dy s.t. Ax + By = d, x,y 0 . Note that the binary variable constraint y ∈ { 0 , 1 } is equivalent to 0 y 1 ,y Z n . In
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07 - Industrial Engineering 634 Integer Programming Fall...

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